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Complete non-self-adjacent paths:Results 01
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- 1 a = 2, b = 2
- 2 a = 3, b = 2
- 3 a = 4, b = 2
- 4 a = 5, b = 2
- 5 a = 6, b = 2
- 6 a = 7, b = 2
- 7 a = 8, b = 2
- 8 a = 9, b = 2
- 9 a = 10, b = 2
- 10 a = 11, b = 2
- 11 a = 12, b = 2
- 12 a = 13, b = 2
- 13 a = 14, b = 2
- 14 a = 15, b = 2
- 15 a = 16, b = 2
- 16 a = 17, b = 2
- 17 a = 18, b = 2
- 18 a = 19, b = 2
- 19 a = 20, b = 2
- 20 a = 21, b = 2
- 21 a = 22, b = 2
- 22 a = 23, b = 2
- 23 a = 24, b = 2
- 24 a = 25, b = 2
a = 2, b = 2
L C S
3 8 2
Total 8 2
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1
2 3
L
3 2 2
2 2
Total 2 2
2 2
Grand total = 4*2
= 8
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1
2 3
L
3 2 2
2 2
Total 2 2
2 2
Grand total = 4*2
= 8
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1
2 3
L
3 6 6
6 6
Total 6 6
6 6
Grand total = 4*6
= 24
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3
EN
0 0 0 0 2
1 0 0 2 0
2 0 2 0 0
3 2 0 0 0
Sum of all rows = 4(3*0 + 1*2)
= 8
Value repetition frequencies = 4(1*1 + 1*3)
= 16
Number of distinct row element sets = 1
Number of rows = 1*4
= 4
Number of distinct values = 2
Distinct values 0 2
Frequency 12 4
Sum of distinct value frequencies = 1*4 + 1*12
= 16
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*1
= 4
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 8
Number of possible SN-EN pairs with SN != EN = 3*4
= 12
a = 3, b = 2
L C S
3 8 2
4 8 4
5 4 2
Total 20 8
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2
3 4 5
L
3 0 4 0
0 4 0
4 2 0 2
2 0 2
5 1 0 1
1 0 1
Total 3 4 3
3 4 3
Grand total = 4*3 + 2*4
= 20
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2
3 4 5
L
3 2 0 2
2 0 2
4 2 0 2
2 0 2
5 1 0 1
1 0 1
Total 5 0 5
5 0 5
Grand total = 4*5
= 20
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2
3 4 5
L
3 3 6 3
3 6 3
4 5 6 5
5 6 5
5 4 2 4
4 2 4
Total 12 14 12
12 14 12
Grand total = 4*12 + 2*14
= 76
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5
EN
0 0 0 1 0 2 2
1 0 0 0 0 0 0
2 1 0 0 2 2 0
3 0 2 2 0 0 1
4 0 0 0 0 0 0
5 2 2 0 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 2*2) +
2(6*0)
= 20
Value repetition frequencies = 4(1*1 + 1*2 + 1*3) +
2(1*6)
= 36
Number of distinct row element sets = 2
Number of rows = 1*2 + 1*4
= 6
Number of distinct values = 3
Distinct values 0 1 2
Frequency 24 4 8
Sum of distinct value frequencies = 1*4 + 1*8 + 1*24
= 36
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*3
= 12
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 18
Number of possible SN-EN pairs with SN != EN = 5*6
= 30
a = 4, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 12 6
Total 40 18
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3
4 5 6 7
L
3 0 2 2 0
0 2 2 0
4 0 2 2 0
0 2 2 0
5 2 1 1 2
2 1 1 2
6 3 0 0 3
3 0 0 3
Total 5 5 5 5
5 5 5 5
Grand total = 8*5
= 40
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3
4 5 6 7
L
3 2 0 0 2
2 0 0 2
4 2 0 0 2
2 0 0 2
5 3 0 0 3
3 0 0 3
6 3 0 0 3
3 0 0 3
Total 10 0 0 10
10 0 0 10
Grand total = 4*10
= 40
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3
4 5 6 7
L
3 3 3 3 3
3 3 3 3
4 3 5 5 3
3 5 5 3
5 7 8 8 7
7 8 8 7
6 10 8 8 10
10 8 8 10
Total 23 24 24 23
23 24 24 23
Grand total = 4*23 + 4*24
= 188
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7
EN
0 0 0 1 3 0 2 2 2
1 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0
3 3 1 0 0 2 2 2 0
4 0 2 2 2 0 0 1 3
5 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0
7 2 2 2 0 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 1*3) +
4(8*0)
= 40
Value repetition frequencies = 4(2*1 + 2*3) +
4(1*8)
= 64
Number of distinct row element sets = 2
Number of rows = 2*4
= 8
Number of distinct values = 4
Distinct values 0 1 2 3
Frequency 44 4 12 4
Sum of distinct value frequencies = 2*4 + 1*12 + 1*44
= 64
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*5
= 20
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 36
Number of possible SN-EN pairs with SN != EN = 7*8
= 56
a = 5, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 20 10
8 4 2
Total 72 34
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4
5 6 7 8 9
L
3 0 2 0 2 0
0 2 0 2 0
4 0 0 4 0 0
0 0 4 0 0
5 0 2 2 2 0
0 2 2 2 0
6 2 3 0 3 2
2 3 0 3 2
7 5 0 0 0 5
5 0 0 0 5
8 1 0 0 0 1
1 0 0 0 1
Total 8 7 6 7 8
8 7 6 7 8
Grand total = 2*6 + 4*7 + 4*8
= 72
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4
5 6 7 8 9
L
3 2 0 0 0 2
2 0 0 0 2
4 2 0 0 0 2
2 0 0 0 2
5 3 0 0 0 3
3 0 0 0 3
6 5 0 0 0 5
5 0 0 0 5
7 5 0 0 0 5
5 0 0 0 5
8 1 0 0 0 1
1 0 0 0 1
Total 18 0 0 0 18
18 0 0 0 18
Grand total = 4*18
= 72
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4
5 6 7 8 9
L
3 3 3 0 3 3
3 3 0 3 3
4 3 3 4 3 3
3 3 4 3 3
5 5 6 8 6 5
5 6 8 6 5
6 10 14 12 14 10
10 14 12 14 10
7 15 14 12 14 15
15 14 12 14 15
8 4 2 4 2 4
4 2 4 2 4
Total 40 42 40 42 40
40 42 40 42 40
Grand total = 6*40 + 4*42
= 408
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9
EN
0 0 0 1 3 5 0 2 2 2 3
1 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0
4 5 3 1 0 0 3 2 2 2 0
5 0 2 2 2 3 0 0 1 3 5
6 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0
9 3 2 2 2 0 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5) +
6(10*0)
= 72
Value repetition frequencies = 4(2*1 + 1*2 + 2*3) +
6(1*10)
= 100
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*6
= 10
Number of distinct values = 5
Distinct values 0 1 2 3 5
Frequency 72 4 12 8 4
Sum of distinct value frequencies = 2*4 + 1*8 + 1*12 + 1*72
= 100
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*7
= 28
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 62
Number of possible SN-EN pairs with SN != EN = 9*10
= 90
a = 6, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 32 16
9 16 8
Total 124 60
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5
6 7 8 9 10 11
L
3 0 2 0 0 2 0
0 2 0 0 2 0
4 0 0 2 2 0 0
0 0 2 2 0 0
5 0 0 3 3 0 0
0 0 3 3 0 0
6 0 2 3 3 2 0
0 2 3 3 2 0
7 2 5 0 0 5 2
2 5 0 0 5 2
8 7 1 0 0 1 7
7 1 0 0 1 7
9 4 0 0 0 0 4
4 0 0 0 0 4
Total 13 10 8 8 10 13
13 10 8 8 10 13
Grand total = 4*8 + 4*10 + 4*13
= 124
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5
6 7 8 9 10 11
L
3 2 0 0 0 0 2
2 0 0 0 0 2
4 2 0 0 0 0 2
2 0 0 0 0 2
5 3 0 0 0 0 3
3 0 0 0 0 3
6 5 0 0 0 0 5
5 0 0 0 0 5
7 7 0 0 0 0 7
7 0 0 0 0 7
8 8 0 0 0 0 8
8 0 0 0 0 8
9 4 0 0 0 0 4
4 0 0 0 0 4
Total 31 0 0 0 0 31
31 0 0 0 0 31
Grand total = 4*31
= 124
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5
6 7 8 9 10 11
L
3 3 3 0 0 3 3
3 3 0 0 3 3
4 3 3 2 2 3 3
3 3 2 2 3 3
5 5 4 6 6 4 5
5 4 6 6 4 5
6 8 9 13 13 9 8
8 9 13 13 9 8
7 13 19 17 17 19 13
13 19 17 17 19 13
8 22 22 20 20 22 22
22 22 20 20 22 22
9 14 10 12 12 10 14
14 10 12 12 10 14
Total 68 70 70 70 70 68
68 70 70 70 70 68
Grand total = 4*68 + 8*70
= 832
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11
EN
0 0 0 1 3 5 7 0 2 2 2 3 6
1 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0
5 7 5 3 1 0 0 6 3 2 2 2 0
6 0 2 2 2 3 6 0 0 1 3 5 7
7 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0
11 6 3 2 2 2 0 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7) +
8(12*0)
= 124
Value repetition frequencies = 4(4*1 + 1*2 + 2*3) +
8(1*12)
= 144
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*8
= 12
Number of distinct values = 7
Distinct values 0 1 2 3 5 6 7
Frequency 108 4 12 8 4 4 4
Sum of distinct value frequencies = 4*4 + 1*8 + 1*12 + 1*108
= 144
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*9
= 36
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 96
Number of possible SN-EN pairs with SN != EN = 11*12
= 132
a = 7, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 52 26
10 36 18
11 4 2
Total 208 102
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6
7 8 9 10 11 12 13
L
3 0 2 0 0 0 2 0
0 2 0 0 0 2 0
4 0 0 2 0 2 0 0
0 0 2 0 2 0 0
5 0 0 1 4 1 0 0
0 0 1 4 1 0 0
6 0 0 2 6 2 0 0
0 0 2 6 2 0 0
7 0 2 5 0 5 2 0
0 2 5 0 5 2 0
8 2 7 1 0 1 7 2
2 7 1 0 1 7 2
9 9 4 0 0 0 4 9
9 4 0 0 0 4 9
10 9 0 0 0 0 0 9
9 0 0 0 0 0 9
11 1 0 0 0 0 0 1
1 0 0 0 0 0 1
Total 21 15 11 10 11 15 21
21 15 11 10 11 15 21
Grand total = 4*21 + 4*15 + 4*11 + 2*10
= 208
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6
7 8 9 10 11 12 13
L
3 2 0 0 0 0 0 2
2 0 0 0 0 0 2
4 2 0 0 0 0 0 2
2 0 0 0 0 0 2
5 3 0 0 0 0 0 3
3 0 0 0 0 0 3
6 5 0 0 0 0 0 5
5 0 0 0 0 0 5
7 7 0 0 0 0 0 7
7 0 0 0 0 0 7
8 10 0 0 0 0 0 10
10 0 0 0 0 0 10
9 13 0 0 0 0 0 13
13 0 0 0 0 0 13
10 9 0 0 0 0 0 9
9 0 0 0 0 0 9
11 1 0 0 0 0 0 1
1 0 0 0 0 0 1
Total 52 0 0 0 0 0 52
52 0 0 0 0 0 52
Grand total = 4*52
= 208
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6
7 8 9 10 11 12 13
L
3 3 3 0 0 0 3 3
3 3 0 0 0 3 3
4 3 3 2 0 2 3 3
3 3 2 0 2 3 3
5 5 4 4 4 4 4 5
5 4 4 4 4 4 5
6 8 7 8 14 8 7 8
8 7 8 14 8 7 8
7 11 12 17 18 17 12 11
11 12 17 18 17 12 11
8 18 25 25 24 25 25 18
18 25 25 24 25 25 18
9 32 36 32 34 32 36 32
32 36 32 34 32 36 32
10 29 24 24 26 24 24 29
29 24 24 26 24 24 29
11 4 2 4 2 4 2 4
4 2 4 2 4 2 4
Total 113 116 116 122 116 116 113
113 116 116 122 116 116 113
Grand total = 4*113 + 8*116 + 2*122
= 1624
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13
EN
0 0 0 1 3 5 7 10 0 2 2 2 3 6 11
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 10 7 5 3 1 0 0 11 6 3 2 2 2 0
7 0 2 2 2 3 6 11 0 0 1 3 5 7 10
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 11 6 3 2 2 2 0 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11) +
10(14*0)
= 208
Value repetition frequencies = 4(6*1 + 1*2 + 2*3) +
10(1*14)
= 196
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*10
= 14
Number of distinct values = 9
Distinct values 0 1 2 3 5 6 7 10 11
Frequency 152 4 12 8 4 4 4 4 4
Sum of distinct value frequencies = 6*4 + 1*8 + 1*12 + 1*152
= 196
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*11
= 44
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 138
Number of possible SN-EN pairs with SN != EN = 13*14
= 182
a = 8, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 80 40
11 68 34
12 20 10
Total 344 170
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15
L
3 0 2 0 0 0 0 2 0
0 2 0 0 0 0 2 0
4 0 0 2 0 0 2 0 0
0 0 2 0 0 2 0 0
5 0 0 1 2 2 1 0 0
0 0 1 2 2 1 0 0
6 0 0 0 5 5 0 0 0
0 0 0 5 5 0 0 0
7 0 0 2 5 5 2 0 0
0 0 2 5 5 2 0 0
8 0 2 7 1 1 7 2 0
0 2 7 1 1 7 2 0
9 2 9 4 0 0 4 9 2
2 9 4 0 0 4 9 2
10 11 9 0 0 0 0 9 11
11 9 0 0 0 0 9 11
11 16 1 0 0 0 0 1 16
16 1 0 0 0 0 1 16
12 5 0 0 0 0 0 0 5
5 0 0 0 0 0 0 5
Total 34 23 16 13 13 16 23 34
34 23 16 13 13 16 23 34
Grand total = 4*13 + 4*16 + 4*23 + 4*34
= 344
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15
L
3 2 0 0 0 0 0 0 2
2 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 2
2 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 3
3 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 5
5 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 7
7 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 10
10 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 15
15 0 0 0 0 0 0 15
10 20 0 0 0 0 0 0 20
20 0 0 0 0 0 0 20
11 17 0 0 0 0 0 0 17
17 0 0 0 0 0 0 17
12 5 0 0 0 0 0 0 5
5 0 0 0 0 0 0 5
Total 86 0 0 0 0 0 0 86
86 0 0 0 0 0 0 86
Grand total = 4*86
= 344
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15
L
3 3 3 0 0 0 0 3 3
3 3 0 0 0 0 3 3
4 3 3 2 0 0 2 3 3
3 3 2 0 0 2 3 3
5 5 4 4 2 2 4 4 5
5 4 4 2 2 4 4 5
6 8 7 6 9 9 6 7 8
8 7 6 9 9 6 7 8
7 11 10 10 18 18 10 10 11
11 10 10 18 18 10 10 11
8 16 16 23 25 25 23 16 16
16 16 23 25 25 23 16 16
9 26 34 38 37 37 38 34 26
26 34 38 37 37 38 34 26
10 45 55 49 51 51 49 55 45
45 55 49 51 51 49 55 45
11 51 46 44 46 46 44 46 51
51 46 44 46 46 44 46 51
12 18 12 16 14 14 16 12 18
18 12 16 14 14 16 12 18
Total 186 190 192 202 202 192 190 186
186 190 192 202 202 192 190 186
Grand total = 4*186 + 4*190 + 4*192 + 4*202
= 3080
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
EN
0 0 0 1 3 5 7 10 16 0 2 2 2 3 6 11 18
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 16 10 7 5 3 1 0 0 18 11 6 3 2 2 2 0
8 0 2 2 2 3 6 11 18 0 0 1 3 5 7 10 16
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 18 11 6 3 2 2 2 0 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18) +
12(16*0)
= 344
Value repetition frequencies = 4(8*1 + 1*2 + 2*3) +
12(1*16)
= 256
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*12
= 16
Number of distinct values = 11
Distinct values 0 1 2 3 5 6 7 10 11 16 18
Frequency 204 4 12 8 4 4 4 4 4 4 4
Sum of distinct value frequencies = 8*4 + 1*8 + 1*12 + 1*204
= 256
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*13
= 52
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 188
Number of possible SN-EN pairs with SN != EN = 15*16
= 240
a = 9, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 120 60
12 120 60
13 56 28
14 4 2
Total 564 280
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
L
3 0 2 0 0 0 0 0 2 0
0 2 0 0 0 0 0 2 0
4 0 0 2 0 0 0 2 0 0
0 0 2 0 0 0 2 0 0
5 0 0 1 2 0 2 1 0 0
0 0 1 2 0 2 1 0 0
6 0 0 0 3 4 3 0 0 0
0 0 0 3 4 3 0 0 0
7 0 0 0 2 10 2 0 0 0
0 0 0 2 10 2 0 0 0
8 0 0 2 7 2 7 2 0 0
0 0 2 7 2 7 2 0 0
9 0 2 9 4 0 4 9 2 0
0 2 9 4 0 4 9 2 0
10 2 11 9 0 0 0 9 11 2
2 11 9 0 0 0 9 11 2
11 13 16 1 0 0 0 1 16 13
13 16 1 0 0 0 1 16 13
12 25 5 0 0 0 0 0 5 25
25 5 0 0 0 0 0 5 25
13 14 0 0 0 0 0 0 0 14
14 0 0 0 0 0 0 0 14
14 1 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 1
Total 55 36 24 18 16 18 24 36 55
55 36 24 18 16 18 24 36 55
Grand total = 2*16 + 4*18 + 4*24 + 4*36 + 4*55
= 564
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
L
3 2 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 22
11 30 0 0 0 0 0 0 0 30
30 0 0 0 0 0 0 0 30
12 30 0 0 0 0 0 0 0 30
30 0 0 0 0 0 0 0 30
13 14 0 0 0 0 0 0 0 14
14 0 0 0 0 0 0 0 14
14 1 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 1
Total 141 0 0 0 0 0 0 0 141
141 0 0 0 0 0 0 0 141
Grand total = 4*141
= 564
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
L
3 3 3 0 0 0 0 0 3 3
3 3 0 0 0 0 0 3 3
4 3 3 2 0 0 0 2 3 3
3 3 2 0 0 0 2 3 3
5 5 4 4 2 0 2 4 4 5
5 4 4 2 0 2 4 4 5
6 8 7 6 7 4 7 6 7 8
8 7 6 7 4 7 6 7 8
7 11 10 8 11 18 11 8 10 11
11 10 8 11 18 11 8 10 11
8 16 14 14 23 26 23 14 14 16
16 14 14 23 26 23 14 14 16
9 24 23 31 39 36 39 31 23 24
24 23 31 39 36 39 31 23 24
10 37 46 55 55 54 55 55 46 37
37 46 55 55 54 55 55 46 37
11 63 80 74 75 76 75 74 80 63
63 80 74 75 76 75 74 80 63
12 83 82 76 80 78 80 76 82 83
83 82 76 80 78 80 76 82 83
13 47 36 40 40 38 40 40 36 47
47 36 40 40 38 40 40 36 47
14 4 2 4 2 4 2 4 2 4
4 2 4 2 4 2 4 2 4
Total 304 310 314 334 334 334 314 310 304
304 310 314 334 334 334 314 310 304
Grand total = 4*304 + 4*310 + 4*314 + 6*334
= 5716
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
EN
0 0 0 1 3 5 7 10 16 27 0 2 2 2 3 6 11 18 28
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 27 16 10 7 5 3 1 0 0 28 18 11 6 3 2 2 2 0
9 0 2 2 2 3 6 11 18 28 0 0 1 3 5 7 10 16 27
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 28 18 11 6 3 2 2 2 0 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28) +
14(18*0)
= 564
Value repetition frequencies = 4(10*1 + 1*2 + 2*3) +
14(1*18)
= 324
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*14
= 18
Number of distinct values = 13
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28
Frequency 264 4 12 8 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 10*4 + 1*8 + 1*12 + 1*264
= 324
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*15
= 60
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 246
Number of possible SN-EN pairs with SN != EN = 17*18
= 306
a = 10, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 180 90
13 200 100
14 124 62
15 24 12
Total 920 458
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
L
3 0 2 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 2 0 0
0 0 2 0 0 0 0 2 0 0
5 0 0 1 2 0 0 2 1 0 0
0 0 1 2 0 0 2 1 0 0
6 0 0 0 3 2 2 3 0 0 0
0 0 0 3 2 2 3 0 0 0
7 0 0 0 0 7 7 0 0 0 0
0 0 0 0 7 7 0 0 0 0
8 0 0 0 2 8 8 2 0 0 0
0 0 0 2 8 8 2 0 0 0
9 0 0 2 9 4 4 9 2 0 0
0 0 2 9 4 4 9 2 0 0
10 0 2 11 9 0 0 9 11 2 0
0 2 11 9 0 0 9 11 2 0
11 2 13 16 1 0 0 1 16 13 2
2 13 16 1 0 0 1 16 13 2
12 15 25 5 0 0 0 0 5 25 15
15 25 5 0 0 0 0 5 25 15
13 36 14 0 0 0 0 0 0 14 36
36 14 0 0 0 0 0 0 14 36
14 30 1 0 0 0 0 0 0 1 30
30 1 0 0 0 0 0 0 1 30
15 6 0 0 0 0 0 0 0 0 6
6 0 0 0 0 0 0 0 0 6
Total 89 57 37 26 21 21 26 37 57 89
89 57 37 26 21 21 26 37 57 89
Grand total = 4*21 + 4*26 + 4*37 + 4*57 + 4*89
= 920
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
L
3 2 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 32
12 45 0 0 0 0 0 0 0 0 45
45 0 0 0 0 0 0 0 0 45
13 50 0 0 0 0 0 0 0 0 50
50 0 0 0 0 0 0 0 0 50
14 31 0 0 0 0 0 0 0 0 31
31 0 0 0 0 0 0 0 0 31
15 6 0 0 0 0 0 0 0 0 6
6 0 0 0 0 0 0 0 0 6
Total 230 0 0 0 0 0 0 0 0 230
230 0 0 0 0 0 0 0 0 230
Grand total = 4*230
= 920
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
L
3 3 3 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 2 3 3
3 3 2 0 0 0 0 2 3 3
5 5 4 4 2 0 0 2 4 4 5
5 4 4 2 0 0 2 4 4 5
6 8 7 6 7 2 2 7 6 7 8
8 7 6 7 2 2 7 6 7 8
7 11 10 8 9 11 11 9 8 10 11
11 10 8 9 11 11 9 8 10 11
8 16 14 12 14 24 24 14 12 14 16
16 14 12 14 24 24 14 12 14 16
9 24 21 20 32 38 38 32 20 21 24
24 21 20 32 38 38 32 20 21 24
10 35 33 41 57 54 54 57 41 33 35
35 33 41 57 54 54 57 41 33 35
11 53 62 78 80 79 79 80 78 62 53
53 62 78 80 79 79 80 78 62 53
12 89 114 112 112 113 113 112 112 114 89
89 114 112 112 113 113 112 112 114 89
13 128 137 125 131 129 129 131 125 137 128
128 137 125 131 129 129 131 125 137 128
14 98 82 84 86 84 84 86 84 82 98
98 82 84 86 84 84 86 84 82 98
15 22 14 20 16 18 18 16 20 14 22
22 14 20 16 18 18 16 20 14 22
Total 495 504 512 546 552 552 546 512 504 495
495 504 512 546 552 552 546 512 504 495
Grand total = 4*495 + 4*504 + 4*512 + 4*546 + 4*552
= 10436
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
EN
0 0 0 1 3 5 7 10 16 27 45 0 2 2 2 3 6 11 18 28 44
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 45 27 16 10 7 5 3 1 0 0 44 28 18 11 6 3 2 2 2 0
10 0 2 2 2 3 6 11 18 28 44 0 0 1 3 5 7 10 16 27 45
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 44 28 18 11 6 3 2 2 2 0 45 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45) +
16(20*0)
= 920
Value repetition frequencies = 4(12*1 + 1*2 + 2*3) +
16(1*20)
= 400
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*16
= 20
Number of distinct values = 15
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45
Frequency 332 4 12 8 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 12*4 + 1*8 + 1*12 + 1*332
= 400
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*17
= 68
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 312
Number of possible SN-EN pairs with SN != EN = 19*20
= 380
a = 11, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 268 134
14 320 160
15 244 122
16 80 40
17 4 2
Total 1496 746
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21
L
3 0 2 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 2 1 0 0
0 0 1 2 0 0 0 2 1 0 0
6 0 0 0 3 2 0 2 3 0 0 0
0 0 0 3 2 0 2 3 0 0 0
7 0 0 0 0 5 4 5 0 0 0 0
0 0 0 0 5 4 5 0 0 0 0
8 0 0 0 0 3 14 3 0 0 0 0
0 0 0 0 3 14 3 0 0 0 0
9 0 0 0 2 9 8 9 2 0 0 0
0 0 0 2 9 8 9 2 0 0 0
10 0 0 2 11 9 0 9 11 2 0 0
0 0 2 11 9 0 9 11 2 0 0
11 0 2 13 16 1 0 1 16 13 2 0
0 2 13 16 1 0 1 16 13 2 0
12 2 15 25 5 0 0 0 5 25 15 2
2 15 25 5 0 0 0 5 25 15 2
13 17 36 14 0 0 0 0 0 14 36 17
17 36 14 0 0 0 0 0 14 36 17
14 49 30 1 0 0 0 0 0 1 30 49
49 30 1 0 0 0 0 0 1 30 49
15 55 6 0 0 0 0 0 0 0 6 55
55 6 0 0 0 0 0 0 0 6 55
16 20 0 0 0 0 0 0 0 0 0 20
20 0 0 0 0 0 0 0 0 0 20
17 1 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 1
Total 144 91 58 39 29 26 29 39 58 91 144
144 91 58 39 29 26 29 39 58 91 144
Grand total = 2*26 + 4*29 + 4*39 + 4*58 + 4*91 + 4*144
= 1496
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21
L
3 2 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 47
13 67 0 0 0 0 0 0 0 0 0 67
67 0 0 0 0 0 0 0 0 0 67
14 80 0 0 0 0 0 0 0 0 0 80
80 0 0 0 0 0 0 0 0 0 80
15 61 0 0 0 0 0 0 0 0 0 61
61 0 0 0 0 0 0 0 0 0 61
16 20 0 0 0 0 0 0 0 0 0 20
20 0 0 0 0 0 0 0 0 0 20
17 1 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 1
Total 374 0 0 0 0 0 0 0 0 0 374
374 0 0 0 0 0 0 0 0 0 374
Grand total = 4*374
= 1496
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21
L
3 3 3 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 2 4 4 5
5 4 4 2 0 0 0 2 4 4 5
6 8 7 6 7 2 0 2 7 6 7 8
8 7 6 7 2 0 2 7 6 7 8
7 11 10 8 9 9 4 9 9 8 10 11
11 10 8 9 9 4 9 9 8 10 11
8 16 14 12 12 15 22 15 12 12 14 16
16 14 12 12 15 22 15 12 12 14 16
9 24 21 18 21 31 40 31 21 18 21 24
24 21 18 21 31 40 31 21 18 21 24
10 35 31 28 43 56 54 56 43 28 31 35
35 31 28 43 56 54 56 43 28 31 35
11 51 47 55 80 80 78 80 80 55 47 51
51 47 55 80 80 78 80 80 55 47 51
12 77 85 109 119 115 118 115 119 109 85 77
77 85 109 119 115 118 115 119 109 85 77
13 126 160 167 167 167 168 167 167 167 160 126
126 160 167 167 167 168 167 167 167 160 126
14 191 217 199 206 205 204 205 206 199 217 191
191 217 199 206 205 204 205 206 199 217 191
15 181 164 160 166 162 164 162 166 160 164 181
181 164 160 166 162 164 162 166 160 164 181
16 69 50 60 56 56 58 56 56 60 50 69
69 50 60 56 56 58 56 56 60 50 69
17 4 2 4 2 4 2 4 2 4 2 4
4 2 4 2 4 2 4 2 4 2 4
Total 804 818 832 890 902 912 902 890 832 818 804
804 818 832 890 902 912 902 890 832 818 804
Grand total = 4*804 + 4*818 + 4*832 + 4*890 + 4*902 + 2*912
= 18808
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
EN
0 0 0 1 3 5 7 10 16 27 45 73 0 2 2 2 3 6 11 18 28 44 71
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 73 45 27 16 10 7 5 3 1 0 0 71 44 28 18 11 6 3 2 2 2 0
11 0 2 2 2 3 6 11 18 28 44 71 0 0 1 3 5 7 10 16 27 45 73
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 71 44 28 18 11 6 3 2 2 2 0 73 45 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73) +
18(22*0)
= 1496
Value repetition frequencies = 4(14*1 + 1*2 + 2*3) +
18(1*22)
= 484
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*18
= 22
Number of distinct values = 17
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73
Frequency 408 4 8 12 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 14*4 + 1*8 + 1*12 + 1*408
= 484
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*19
= 76
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 386
Number of possible SN-EN pairs with SN != EN = 21*22
= 462
a = 12, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 276 138
14 396 198
15 500 250
16 444 222
17 204 102
18 28 14
Total 2428 1212
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21 22 23
L
3 0 2 0 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 0 2 1 0 0
0 0 1 2 0 0 0 0 2 1 0 0
6 0 0 0 3 2 0 0 2 3 0 0 0
0 0 0 3 2 0 0 2 3 0 0 0
7 0 0 0 0 5 2 2 5 0 0 0 0
0 0 0 0 5 2 2 5 0 0 0 0
8 0 0 0 0 1 9 9 1 0 0 0 0
0 0 0 0 1 9 9 1 0 0 0 0
9 0 0 0 0 2 13 13 2 0 0 0 0
0 0 0 0 2 13 13 2 0 0 0 0
10 0 0 0 2 11 9 9 11 2 0 0 0
0 0 0 2 11 9 9 11 2 0 0 0
11 0 0 2 13 16 1 1 16 13 2 0 0
0 0 2 13 16 1 1 16 13 2 0 0
12 0 2 15 25 5 0 0 5 25 15 2 0
0 2 15 25 5 0 0 5 25 15 2 0
13 2 17 36 14 0 0 0 0 14 36 17 2
2 17 36 14 0 0 0 0 14 36 17 2
14 19 49 30 1 0 0 0 0 1 30 49 19
19 49 30 1 0 0 0 0 1 30 49 19
15 64 55 6 0 0 0 0 0 0 6 55 64
64 55 6 0 0 0 0 0 0 6 55 64
16 91 20 0 0 0 0 0 0 0 0 20 91
91 20 0 0 0 0 0 0 0 0 20 91
17 50 1 0 0 0 0 0 0 0 0 1 50
50 1 0 0 0 0 0 0 0 0 1 50
18 7 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 7
Total 233 146 92 60 42 34 34 42 60 92 146 233
233 146 92 60 42 34 34 42 60 92 146 233
Grand total = 4*34 + 4*42 + 4*60 + 4*92 + 4*146 + 4*233
= 2428
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21 22 23
L
3 2 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 0 47
13 69 0 0 0 0 0 0 0 0 0 0 69
69 0 0 0 0 0 0 0 0 0 0 69
14 99 0 0 0 0 0 0 0 0 0 0 99
99 0 0 0 0 0 0 0 0 0 0 99
15 125 0 0 0 0 0 0 0 0 0 0 125
125 0 0 0 0 0 0 0 0 0 0 125
16 111 0 0 0 0 0 0 0 0 0 0 111
111 0 0 0 0 0 0 0 0 0 0 111
17 51 0 0 0 0 0 0 0 0 0 0 51
51 0 0 0 0 0 0 0 0 0 0 51
18 7 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 7
Total 607 0 0 0 0 0 0 0 0 0 0 607
607 0 0 0 0 0 0 0 0 0 0 607
Grand total = 4*607
= 2428
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21 22 23
L
3 3 3 0 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 0 2 4 4 5
5 4 4 2 0 0 0 0 2 4 4 5
6 8 7 6 7 2 0 0 2 7 6 7 8
8 7 6 7 2 0 0 2 7 6 7 8
7 11 10 8 9 9 2 2 9 9 8 10 11
11 10 8 9 9 2 2 9 9 8 10 11
8 16 14 12 12 13 13 13 13 12 12 14 16
16 14 12 12 13 13 13 13 12 12 14 16
9 24 21 18 19 20 33 33 20 19 18 21 24
24 21 18 19 20 33 33 20 19 18 21 24
10 35 31 26 30 42 56 56 42 30 26 31 35
35 31 26 30 42 56 56 42 30 26 31 35
11 51 45 40 57 80 79 79 80 57 40 45 51
51 45 40 57 80 79 79 80 57 40 45 51
12 75 68 75 112 118 116 116 118 112 75 68 75
75 68 75 112 118 116 116 118 112 75 68 75
13 112 118 150 176 169 172 172 169 176 150 118 112
112 118 150 176 169 172 172 169 176 150 118 112
14 179 222 245 247 246 247 247 246 247 245 222 179
179 222 245 247 246 247 247 246 247 245 222 179
15 280 331 311 318 318 317 317 318 318 311 331 280
280 331 311 318 318 317 317 318 318 311 331 280
16 309 301 285 297 291 293 293 291 297 285 301 309
309 301 285 297 291 293 293 291 297 285 301 309
17 167 132 144 142 140 142 142 140 142 144 132 167
167 132 144 142 140 142 142 140 142 144 132 167
18 26 16 24 18 22 20 20 22 18 24 16 26
26 16 24 18 22 20 20 22 18 24 16 26
Total 1304 1326 1350 1446 1470 1490 1490 1470 1446 1350 1326 1304
1304 1326 1350 1446 1470 1490 1490 1470 1446 1350 1326 1304
Grand total = 4*1304 + 4*1326 + 4*1350 + 4*1446 + 4*1470 + 4*1490
= 33544
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
EN
0 0 0 1 3 5 7 10 16 27 45 73 117 0 2 2 2 3 6 11 18 28 44 71 116
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 117 73 45 27 16 10 7 5 3 1 0 0 116 71 44 28 18 11 6 3 2 2 2 0
12 0 2 2 2 3 6 11 18 28 44 71 116 0 0 1 3 5 7 10 16 27 45 73 117
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 116 71 44 28 18 11 6 3 2 2 2 0 117 73 45 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73 + 1*116 + 1*117) +
20(24*0)
= 2428
Value repetition frequencies = 4(16*1 + 1*2 + 2*3) +
20(1*24)
= 576
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*20
= 24
Number of distinct values = 19
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73 116 117
Frequency 492 4 12 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 16*4 + 1*8 + 1*12 + 1*492
= 576
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*21
= 84
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 468
Number of possible SN-EN pairs with SN != EN = 23*24
= 552
a = 13, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 276 138
14 404 202
15 584 292
16 768 384
17 764 382
18 448 224
19 108 54
20 4 2
Total 3936 1966
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24 25
L
3 0 2 0 0 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 0 0 2 1 0 0
0 0 1 2 0 0 0 0 0 2 1 0 0
6 0 0 0 3 2 0 0 0 2 3 0 0 0
0 0 0 3 2 0 0 0 2 3 0 0 0
7 0 0 0 0 5 2 0 2 5 0 0 0 0
0 0 0 0 5 2 0 2 5 0 0 0 0
8 0 0 0 0 1 7 4 7 1 0 0 0 0
0 0 0 0 1 7 4 7 1 0 0 0 0
9 0 0 0 0 0 6 18 6 0 0 0 0 0
0 0 0 0 0 6 18 6 0 0 0 0 0
10 0 0 0 0 2 11 18 11 2 0 0 0 0
0 0 0 0 2 11 18 11 2 0 0 0 0
11 0 0 0 2 13 16 2 16 13 2 0 0 0
0 0 0 2 13 16 2 16 13 2 0 0 0
12 0 0 2 15 25 5 0 5 25 15 2 0 0
0 0 2 15 25 5 0 5 25 15 2 0 0
13 0 2 17 36 14 0 0 0 14 36 17 2 0
0 2 17 36 14 0 0 0 14 36 17 2 0
14 2 19 49 30 1 0 0 0 1 30 49 19 2
2 19 49 30 1 0 0 0 1 30 49 19 2
15 21 64 55 6 0 0 0 0 0 6 55 64 21
21 64 55 6 0 0 0 0 0 6 55 64 21
16 81 91 20 0 0 0 0 0 0 0 20 91 81
81 91 20 0 0 0 0 0 0 0 20 91 81
17 140 50 1 0 0 0 0 0 0 0 1 50 140
140 50 1 0 0 0 0 0 0 0 1 50 140
18 105 7 0 0 0 0 0 0 0 0 0 7 105
105 7 0 0 0 0 0 0 0 0 0 7 105
19 27 0 0 0 0 0 0 0 0 0 0 0 27
27 0 0 0 0 0 0 0 0 0 0 0 27
20 1 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 1
Total 377 235 147 94 63 47 42 47 63 94 147 235 377
377 235 147 94 63 47 42 47 63 94 147 235 377
Grand total = 2*42 + 4*47 + 4*63 + 4*94 + 4*147 + 4*235 + 4*377
= 3936
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24 25
L
3 2 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 0 0 47
13 69 0 0 0 0 0 0 0 0 0 0 0 69
69 0 0 0 0 0 0 0 0 0 0 0 69
14 101 0 0 0 0 0 0 0 0 0 0 0 101
101 0 0 0 0 0 0 0 0 0 0 0 101
15 146 0 0 0 0 0 0 0 0 0 0 0 146
146 0 0 0 0 0 0 0 0 0 0 0 146
16 192 0 0 0 0 0 0 0 0 0 0 0 192
192 0 0 0 0 0 0 0 0 0 0 0 192
17 191 0 0 0 0 0 0 0 0 0 0 0 191
191 0 0 0 0 0 0 0 0 0 0 0 191
18 112 0 0 0 0 0 0 0 0 0 0 0 112
112 0 0 0 0 0 0 0 0 0 0 0 112
19 27 0 0 0 0 0 0 0 0 0 0 0 27
27 0 0 0 0 0 0 0 0 0 0 0 27
20 1 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 1
Total 984 0 0 0 0 0 0 0 0 0 0 0 984
984 0 0 0 0 0 0 0 0 0 0 0 984
Grand total = 4*984
= 3936
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24 25
L
3 3 3 0 0 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 0 0 2 4 4 5
5 4 4 2 0 0 0 0 0 2 4 4 5
6 8 7 6 7 2 0 0 0 2 7 6 7 8
8 7 6 7 2 0 0 0 2 7 6 7 8
7 11 10 8 9 9 2 0 2 9 9 8 10 11
11 10 8 9 9 2 0 2 9 9 8 10 11
8 16 14 12 12 13 11 4 11 13 12 12 14 16
16 14 12 12 13 11 4 11 13 12 12 14 16
9 24 21 18 19 18 22 26 22 18 19 18 21 24
24 21 18 19 18 22 26 22 18 19 18 21 24
10 35 31 26 28 29 42 58 42 29 28 26 31 35
35 31 26 28 29 42 58 42 29 28 26 31 35
11 51 45 38 42 57 79 80 79 57 42 38 45 51
51 45 38 42 57 79 80 79 57 42 38 45 51
12 75 66 58 78 111 119 114 119 111 78 58 66 75
75 66 58 78 111 119 114 119 111 78 58 66 75
13 110 99 103 155 174 170 172 170 174 155 103 99 110
110 99 103 155 174 170 172 170 174 155 103 99 110
14 163 165 205 256 249 250 252 250 249 256 205 165 163
163 165 205 256 249 250 252 250 249 256 205 165 163
15 256 307 354 366 361 365 362 365 361 366 354 307 256
256 307 354 366 361 365 362 365 361 366 354 307 256
16 406 491 478 485 485 485 484 485 485 485 478 491 406
406 491 478 485 485 485 484 485 485 485 478 491 406
17 500 518 484 503 496 497 498 497 496 503 484 518 500
500 518 484 503 496 497 498 497 496 503 484 518 500
18 348 296 304 308 302 306 304 306 302 308 304 296 348
348 296 304 308 302 306 304 306 302 308 304 296 348
19 95 66 84 74 78 78 76 78 78 74 84 66 95
95 66 84 74 78 78 76 78 78 74 84 66 95
20 4 2 4 2 4 2 4 2 4 2 4 2 4
4 2 4 2 4 2 4 2 4 2 4 2 4
Total 2113 2148 2188 2346 2388 2428 2434 2428 2388 2346 2188 2148 2113
2113 2148 2188 2346 2388 2428 2434 2428 2388 2346 2188 2148 2113
Grand total = 4*2113 + 4*2148 + 4*2188 + 4*2346 + 4*2388 + 4*2428 + 2*2434
= 59312
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
EN
0 0 0 1 3 5 7 10 16 27 45 73 117 188 0 2 2 2 3 6 11 18 28 44 71 116 189
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 188 117 73 45 27 16 10 7 5 3 1 0 0 189 116 71 44 28 18 11 6 3 2 2 2 0
13 0 2 2 2 3 6 11 18 28 44 71 116 189 0 0 1 3 5 7 10 16 27 45 73 117 188
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 189 116 71 44 28 18 11 6 3 2 2 2 0 188 117 73 45 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73 + 1*116 + 1*117 + 1*188 + 1*189) +
22(26*0)
= 3936
Value repetition frequencies = 4(18*1 + 1*2 + 2*3) +
22(1*26)
= 676
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*22
= 26
Number of distinct values = 21
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73 116 117 188 189
Frequency 584 4 12 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 18*4 + 1*8 + 1*12 + 1*584
= 676
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*23
= 92
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 558
Number of possible SN-EN pairs with SN != EN = 25*26
= 650
a = 14, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 276 138
14 404 202
15 592 296
16 860 430
17 1164 582
18 1264 632
19 892 446
20 312 156
21 32 16
Total 6376 3186
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13
14 15 16 17 18 19 20 21 22 23 24 25 26 27
L
3 0 2 0 0 0 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 0 0 0 2 1 0 0
0 0 1 2 0 0 0 0 0 0 2 1 0 0
6 0 0 0 3 2 0 0 0 0 2 3 0 0 0
0 0 0 3 2 0 0 0 0 2 3 0 0 0
7 0 0 0 0 5 2 0 0 2 5 0 0 0 0
0 0 0 0 5 2 0 0 2 5 0 0 0 0
8 0 0 0 0 1 7 2 2 7 1 0 0 0 0
0 0 0 0 1 7 2 2 7 1 0 0 0 0
9 0 0 0 0 0 4 11 11 4 0 0 0 0 0
0 0 0 0 0 4 11 11 4 0 0 0 0 0
10 0 0 0 0 0 2 20 20 2 0 0 0 0 0
0 0 0 0 0 2 20 20 2 0 0 0 0 0
11 0 0 0 0 2 13 17 17 13 2 0 0 0 0
0 0 0 0 2 13 17 17 13 2 0 0 0 0
12 0 0 0 2 15 25 5 5 25 15 2 0 0 0
0 0 0 2 15 25 5 5 25 15 2 0 0 0
13 0 0 2 17 36 14 0 0 14 36 17 2 0 0
0 0 2 17 36 14 0 0 14 36 17 2 0 0
14 0 2 19 49 30 1 0 0 1 30 49 19 2 0
0 2 19 49 30 1 0 0 1 30 49 19 2 0
15 2 21 64 55 6 0 0 0 0 6 55 64 21 2
2 21 64 55 6 0 0 0 0 6 55 64 21 2
16 23 81 91 20 0 0 0 0 0 0 20 91 81 23
23 81 91 20 0 0 0 0 0 0 20 91 81 23
17 100 140 50 1 0 0 0 0 0 0 1 50 140 100
100 140 50 1 0 0 0 0 0 0 1 50 140 100
18 204 105 7 0 0 0 0 0 0 0 0 7 105 204
204 105 7 0 0 0 0 0 0 0 0 7 105 204
19 196 27 0 0 0 0 0 0 0 0 0 0 27 196
196 27 0 0 0 0 0 0 0 0 0 0 27 196
20 77 1 0 0 0 0 0 0 0 0 0 0 1 77
77 1 0 0 0 0 0 0 0 0 0 0 1 77
21 8 0 0 0 0 0 0 0 0 0 0 0 0 8
8 0 0 0 0 0 0 0 0 0 0 0 0 8
Total 610 379 236 149 97 68 55 55 68 97 149 236 379 610
610 379 236 149 97 68 55 55 68 97 149 236 379 610
Grand total = 4*55 + 4*68 + 4*97 + 4*149 + 4*236 + 4*379 + 4*610
= 6376
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13
14 15 16 17 18 19 20 21 22 23 24 25 26 27
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 0 0 0 47
13 69 0 0 0 0 0 0 0 0 0 0 0 0 69
69 0 0 0 0 0 0 0 0 0 0 0 0 69
14 101 0 0 0 0 0 0 0 0 0 0 0 0 101
101 0 0 0 0 0 0 0 0 0 0 0 0 101
15 148 0 0 0 0 0 0 0 0 0 0 0 0 148
148 0 0 0 0 0 0 0 0 0 0 0 0 148
16 215 0 0 0 0 0 0 0 0 0 0 0 0 215
215 0 0 0 0 0 0 0 0 0 0 0 0 215
17 291 0 0 0 0 0 0 0 0 0 0 0 0 291
291 0 0 0 0 0 0 0 0 0 0 0 0 291
18 316 0 0 0 0 0 0 0 0 0 0 0 0 316
316 0 0 0 0 0 0 0 0 0 0 0 0 316
19 223 0 0 0 0 0 0 0 0 0 0 0 0 223
223 0 0 0 0 0 0 0 0 0 0 0 0 223
20 78 0 0 0 0 0 0 0 0 0 0 0 0 78
78 0 0 0 0 0 0 0 0 0 0 0 0 78
21 8 0 0 0 0 0 0 0 0 0 0 0 0 8
8 0 0 0 0 0 0 0 0 0 0 0 0 8
Total 1594 0 0 0 0 0 0 0 0 0 0 0 0 1594
1594 0 0 0 0 0 0 0 0 0 0 0 0 1594
Grand total = 4*1594
= 6376
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13
14 15 16 17 18 19 20 21 22 23 24 25 26 27
L
3 3 3 0 0 0 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 0 0 0 2 4 4 5
5 4 4 2 0 0 0 0 0 0 2 4 4 5
6 8 7 6 7 2 0 0 0 0 2 7 6 7 8
8 7 6 7 2 0 0 0 0 2 7 6 7 8
7 11 10 8 9 9 2 0 0 2 9 9 8 10 11
11 10 8 9 9 2 0 0 2 9 9 8 10 11
8 16 14 12 12 13 11 2 2 11 13 12 12 14 16
16 14 12 12 13 11 2 2 11 13 12 12 14 16
9 24 21 18 19 18 20 15 15 20 18 19 18 21 24
24 21 18 19 18 20 15 15 20 18 19 18 21 24
10 35 31 26 28 27 29 44 44 29 27 28 26 31 35
35 31 26 28 27 29 44 44 29 27 28 26 31 35
11 51 45 38 40 42 56 80 80 56 42 40 38 45 51
51 45 38 40 42 56 80 80 56 42 40 38 45 51
12 75 66 56 61 77 112 117 117 112 77 61 56 66 75
75 66 56 61 77 112 117 117 112 77 61 56 66 75
13 110 97 84 108 153 175 170 170 175 153 108 84 97 110
110 97 84 108 153 175 170 170 175 153 108 84 97 110
14 161 144 143 212 254 249 251 251 249 254 212 143 144 161
161 144 143 212 254 249 251 251 249 254 212 143 144 161
15 238 233 280 368 367 366 368 368 366 367 368 280 233 238
238 233 280 368 367 366 368 368 366 367 368 280 233 238
16 368 425 504 542 530 537 534 534 537 530 542 504 425 368
368 425 504 542 530 537 534 534 537 530 542 504 425 368
17 585 713 723 732 731 732 731 731 732 731 732 723 713 585
585 713 723 732 731 732 731 731 732 731 732 723 713 585
18 780 849 795 821 814 814 815 815 814 814 821 795 849 780
780 849 795 821 814 814 815 815 814 814 821 795 849 780
19 657 597 589 605 593 599 597 597 599 593 605 589 597 657
657 597 589 605 593 599 597 597 599 593 605 589 597 657
20 262 198 228 216 218 220 218 218 220 218 216 228 198 262
262 198 228 216 218 220 218 218 220 218 216 228 198 262
21 30 18 28 20 26 22 24 24 22 26 20 28 18 30
30 18 28 20 26 22 24 24 22 26 20 28 18 30
Total 3422 3478 3544 3802 3874 3944 3966 3966 3944 3874 3802 3544 3478 3422
3422 3478 3544 3802 3874 3944 3966 3966 3944 3874 3802 3544 3478 3422
Grand total = 4*3422 + 4*3478 + 4*3544 + 4*3802 + 4*3874 + 4*3944 + 4*3966
= 104120
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
EN
0 0 0 1 3 5 7 10 16 27 45 73 117 188 304 0 2 2 2 3 6 11 18 28 44 71 116 189 306
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 304 188 117 73 45 27 16 10 7 5 3 1 0 0 306 189 116 71 44 28 18 11 6 3 2 2 2 0
14 0 2 2 2 3 6 11 18 28 44 71 116 189 306 0 0 1 3 5 7 10 16 27 45 73 117 188 304
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 306 189 116 71 44 28 18 11 6 3 2 2 2 0 304 188 117 73 45 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73 + 1*116 + 1*117 + 1*188 + 1*189 + 1*304 + 1*306) +
24(28*0)
= 6376
Value repetition frequencies = 4(20*1 + 1*2 + 2*3) +
24(1*28)
= 784
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*24
= 28
Number of distinct values = 23
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73 116 117 188 189 304 306
Frequency 684 4 12 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 20*4 + 1*8 + 1*12 + 1*684
= 784
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*25
= 100
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 656
Number of possible SN-EN pairs with SN != EN = 27*28
= 756
a = 15, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 276 138
14 404 202
15 592 296
16 868 434
17 1264 632
18 1748 874
19 2032 1016
20 1656 828
21 760 380
22 140 70
23 4 2
Total 10324 5160
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
L
3 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 0 0 0 0 2 1 0 0
0 0 1 2 0 0 0 0 0 0 0 2 1 0 0
6 0 0 0 3 2 0 0 0 0 0 2 3 0 0 0
0 0 0 3 2 0 0 0 0 0 2 3 0 0 0
7 0 0 0 0 5 2 0 0 0 2 5 0 0 0 0
0 0 0 0 5 2 0 0 0 2 5 0 0 0 0
8 0 0 0 0 1 7 2 0 2 7 1 0 0 0 0
0 0 0 0 1 7 2 0 2 7 1 0 0 0 0
9 0 0 0 0 0 4 9 4 9 4 0 0 0 0 0
0 0 0 0 0 4 9 4 9 4 0 0 0 0 0
10 0 0 0 0 0 0 11 22 11 0 0 0 0 0 0
0 0 0 0 0 0 11 22 11 0 0 0 0 0 0
11 0 0 0 0 0 2 14 32 14 2 0 0 0 0 0
0 0 0 0 0 2 14 32 14 2 0 0 0 0 0
12 0 0 0 0 2 15 25 10 25 15 2 0 0 0 0
0 0 0 0 2 15 25 10 25 15 2 0 0 0 0
13 0 0 0 2 17 36 14 0 14 36 17 2 0 0 0
0 0 0 2 17 36 14 0 14 36 17 2 0 0 0
14 0 0 2 19 49 30 1 0 1 30 49 19 2 0 0
0 0 2 19 49 30 1 0 1 30 49 19 2 0 0
15 0 2 21 64 55 6 0 0 0 6 55 64 21 2 0
0 2 21 64 55 6 0 0 0 6 55 64 21 2 0
16 2 23 81 91 20 0 0 0 0 0 20 91 81 23 2
2 23 81 91 20 0 0 0 0 0 20 91 81 23 2
17 25 100 140 50 1 0 0 0 0 0 1 50 140 100 25
25 100 140 50 1 0 0 0 0 0 1 50 140 100 25
18 121 204 105 7 0 0 0 0 0 0 0 7 105 204 121
121 204 105 7 0 0 0 0 0 0 0 7 105 204 121
19 285 196 27 0 0 0 0 0 0 0 0 0 27 196 285
285 196 27 0 0 0 0 0 0 0 0 0 27 196 285
20 336 77 1 0 0 0 0 0 0 0 0 0 1 77 336
336 77 1 0 0 0 0 0 0 0 0 0 1 77 336
21 182 8 0 0 0 0 0 0 0 0 0 0 0 8 182
182 8 0 0 0 0 0 0 0 0 0 0 0 8 182
22 35 0 0 0 0 0 0 0 0 0 0 0 0 0 35
35 0 0 0 0 0 0 0 0 0 0 0 0 0 35
23 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Total 987 612 380 238 152 102 76 68 76 102 152 238 380 612 987
987 612 380 238 152 102 76 68 76 102 152 238 380 612 987
Grand total = 2*68 + 4*76 + 4*102 + 4*152 + 4*238 + 4*380 + 4*612 + 4*987
= 10324
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 0 0 0 0 47
13 69 0 0 0 0 0 0 0 0 0 0 0 0 0 69
69 0 0 0 0 0 0 0 0 0 0 0 0 0 69
14 101 0 0 0 0 0 0 0 0 0 0 0 0 0 101
101 0 0 0 0 0 0 0 0 0 0 0 0 0 101
15 148 0 0 0 0 0 0 0 0 0 0 0 0 0 148
148 0 0 0 0 0 0 0 0 0 0 0 0 0 148
16 217 0 0 0 0 0 0 0 0 0 0 0 0 0 217
217 0 0 0 0 0 0 0 0 0 0 0 0 0 217
17 316 0 0 0 0 0 0 0 0 0 0 0 0 0 316
316 0 0 0 0 0 0 0 0 0 0 0 0 0 316
18 437 0 0 0 0 0 0 0 0 0 0 0 0 0 437
437 0 0 0 0 0 0 0 0 0 0 0 0 0 437
19 508 0 0 0 0 0 0 0 0 0 0 0 0 0 508
508 0 0 0 0 0 0 0 0 0 0 0 0 0 508
20 414 0 0 0 0 0 0 0 0 0 0 0 0 0 414
414 0 0 0 0 0 0 0 0 0 0 0 0 0 414
21 190 0 0 0 0 0 0 0 0 0 0 0 0 0 190
190 0 0 0 0 0 0 0 0 0 0 0 0 0 190
22 35 0 0 0 0 0 0 0 0 0 0 0 0 0 35
35 0 0 0 0 0 0 0 0 0 0 0 0 0 35
23 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Total 2581 0 0 0 0 0 0 0 0 0 0 0 0 0 2581
2581 0 0 0 0 0 0 0 0 0 0 0 0 0 2581
Grand total = 4*2581
= 10324
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
L
3 3 3 0 0 0 0 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 0 0 0 0 2 4 4 5
5 4 4 2 0 0 0 0 0 0 0 2 4 4 5
6 8 7 6 7 2 0 0 0 0 0 2 7 6 7 8
8 7 6 7 2 0 0 0 0 0 2 7 6 7 8
7 11 10 8 9 9 2 0 0 0 2 9 9 8 10 11
11 10 8 9 9 2 0 0 0 2 9 9 8 10 11
8 16 14 12 12 13 11 2 0 2 11 13 12 12 14 16
16 14 12 12 13 11 2 0 2 11 13 12 12 14 16
9 24 21 18 19 18 20 13 4 13 20 18 19 18 21 24
24 21 18 19 18 20 13 4 13 20 18 19 18 21 24
10 35 31 26 28 27 27 31 30 31 27 27 28 26 31 35
35 31 26 28 27 27 31 30 31 27 27 28 26 31 35
11 51 45 38 40 40 41 57 80 57 41 40 40 38 45 51
51 45 38 40 40 41 57 80 57 41 40 40 38 45 51
12 75 66 56 59 60 78 110 120 110 78 60 59 56 66 75
75 66 56 59 60 78 110 120 110 78 60 59 56 66 75
13 110 97 82 89 106 154 175 168 175 154 106 89 82 97 110
110 97 82 89 106 154 175 168 175 154 106 89 82 97 110
14 161 142 122 150 210 254 250 250 250 254 210 150 122 142 161
161 142 122 150 210 254 250 250 250 254 210 150 122 142 161
15 236 210 201 290 365 368 365 370 365 368 365 290 201 210 236
236 210 201 290 365 368 365 370 365 368 365 290 201 210 236
16 348 332 383 523 541 536 540 538 540 536 541 523 383 332 348
348 332 383 523 541 536 540 538 540 536 541 523 383 332 348
17 531 590 709 798 779 787 786 784 786 787 779 798 709 590 531
531 590 709 798 779 787 786 784 786 787 779 798 709 590 531
18 841 1020 1077 1098 1092 1097 1093 1096 1093 1097 1092 1098 1077 1020 841
841 1020 1077 1098 1092 1097 1093 1096 1093 1097 1092 1098 1077 1020 841
19 1186 1340 1273 1306 1299 1299 1299 1300 1299 1299 1299 1306 1273 1340 1186
1186 1340 1273 1306 1299 1299 1299 1300 1299 1299 1299 1306 1273 1340 1186
20 1157 1115 1073 1108 1089 1096 1095 1094 1095 1096 1089 1108 1073 1115 1157
1157 1115 1073 1108 1089 1096 1095 1094 1095 1096 1089 1108 1073 1115 1157
21 610 494 532 524 520 526 522 524 522 526 520 524 532 494 610
610 494 532 524 520 526 522 524 522 526 520 524 532 494 610
22 125 84 112 94 104 100 100 102 100 100 104 94 112 84 125
125 84 112 94 104 100 100 102 100 100 104 94 112 84 125
23 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4
4 2 4 2 4 2 4 2 4 2 4 2 4 2 4
Total 5540 5630 5738 6158 6278 6398 6442 6462 6442 6398 6278 6158 5738 5630 5540
5540 5630 5738 6158 6278 6398 6442 6462 6442 6398 6278 6158 5738 5630 5540
Grand total = 4*5540 + 4*5630 + 4*5738 + 4*6158 + 4*6278 + 4*6398 + 4*6442 + 2*6462
= 181660
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
EN
0 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 0 2 2 2 3 6 11 18 28 44 71 116 18 30 494
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0
15 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73 + 1*116 + 1*117 + 1*188 + 1*189 + 1*304 + 1*306 + 1*493 + 1*494) +
26(30*0)
= 10324
Value repetition frequencies = 4(22*1 + 1*2 + 2*3) +
26(1*30)
= 900
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*26
= 30
Number of distinct values = 25
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73 116 117 188 189 304 306 493 494
Frequency 792 4 12 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 22*4 + 1*8 + 1*12 + 1*792
= 900
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*27
= 108
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 762
Number of possible SN-EN pairs with SN != EN = 29*30
= 870
a = 16, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 276 138
14 404 202
15 592 296
16 868 434
17 1272 636
18 1856 928
19 2608 1304
20 3196 1598
21 2920 1460
22 1652 826
23 452 226
24 36 18
Total 16712 8354
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
L
3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 0 0 0 0 0 2 1 0 0
0 0 1 2 0 0 0 0 0 0 0 0 2 1 0 0
6 0 0 0 3 2 0 0 0 0 0 0 2 3 0 0 0
0 0 0 3 2 0 0 0 0 0 0 2 3 0 0 0
7 0 0 0 0 5 2 0 0 0 0 2 5 0 0 0 0
0 0 0 0 5 2 0 0 0 0 2 5 0 0 0 0
8 0 0 0 0 1 7 2 0 0 2 7 1 0 0 0 0
0 0 0 0 1 7 2 0 0 2 7 1 0 0 0 0
9 0 0 0 0 0 4 9 2 2 9 4 0 0 0 0 0
0 0 0 0 0 4 9 2 2 9 4 0 0 0 0 0
10 0 0 0 0 0 0 9 13 13 9 0 0 0 0 0 0
0 0 0 0 0 0 9 13 13 9 0 0 0 0 0 0
11 0 0 0 0 0 0 3 29 29 3 0 0 0 0 0 0
0 0 0 0 0 0 3 29 29 3 0 0 0 0 0 0
12 0 0 0 0 0 2 15 30 30 15 2 0 0 0 0 0
0 0 0 0 0 2 15 30 30 15 2 0 0 0 0 0
13 0 0 0 0 2 17 36 14 14 36 17 2 0 0 0 0
0 0 0 0 2 17 36 14 14 36 17 2 0 0 0 0
14 0 0 0 2 19 49 30 1 1 30 49 19 2 0 0 0
0 0 0 2 19 49 30 1 1 30 49 19 2 0 0 0
15 0 0 2 21 64 55 6 0 0 6 55 64 21 2 0 0
0 0 2 21 64 55 6 0 0 6 55 64 21 2 0 0
16 0 2 23 81 91 20 0 0 0 0 20 91 81 23 2 0
0 2 23 81 91 20 0 0 0 0 20 91 81 23 2 0
17 2 25 100 140 50 1 0 0 0 0 1 50 140 100 25 2
2 25 100 140 50 1 0 0 0 0 1 50 140 100 25 2
18 27 121 204 105 7 0 0 0 0 0 0 7 105 204 121 27
27 121 204 105 7 0 0 0 0 0 0 7 105 204 121 27
19 144 285 196 27 0 0 0 0 0 0 0 0 27 196 285 144
144 285 196 27 0 0 0 0 0 0 0 0 27 196 285 144
20 385 336 77 1 0 0 0 0 0 0 0 0 1 77 336 385
385 336 77 1 0 0 0 0 0 0 0 0 1 77 336 385
21 540 182 8 0 0 0 0 0 0 0 0 0 0 8 182 540
540 182 8 0 0 0 0 0 0 0 0 0 0 8 182 540
22 378 35 0 0 0 0 0 0 0 0 0 0 0 0 35 378
378 35 0 0 0 0 0 0 0 0 0 0 0 0 35 378
23 112 1 0 0 0 0 0 0 0 0 0 0 0 0 1 112
112 1 0 0 0 0 0 0 0 0 0 0 0 0 1 112
24 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
Total 1597 989 613 382 241 157 110 89 89 110 157 241 382 613 989 1597
1597 989 613 382 241 157 110 89 89 110 157 241 382 613 989 1597
Grand total = 4*89 + 4*110 + 4*157 + 4*241 + 4*382 + 4*613 + 4*989 + 4*1597
= 16712
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
13 69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
14 101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
15 148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
16 217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
17 318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
18 464 0 0 0 0 0 0 0 0 0 0 0 0 0 0 464
464 0 0 0 0 0 0 0 0 0 0 0 0 0 0 464
19 652 0 0 0 0 0 0 0 0 0 0 0 0 0 0 652
652 0 0 0 0 0 0 0 0 0 0 0 0 0 0 652
20 799 0 0 0 0 0 0 0 0 0 0 0 0 0 0 799
799 0 0 0 0 0 0 0 0 0 0 0 0 0 0 799
21 730 0 0 0 0 0 0 0 0 0 0 0 0 0 0 730
730 0 0 0 0 0 0 0 0 0 0 0 0 0 0 730
22 413 0 0 0 0 0 0 0 0 0 0 0 0 0 0 413
413 0 0 0 0 0 0 0 0 0 0 0 0 0 0 413
23 113 0 0 0 0 0 0 0 0 0 0 0 0 0 0 113
113 0 0 0 0 0 0 0 0 0 0 0 0 0 0 113
24 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
Total 4178 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4178
4178 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4178
Grand total = 4*4178
= 16712
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
L
3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 0 0 0 0 0 2 4 4 5
5 4 4 2 0 0 0 0 0 0 0 0 2 4 4 5
6 8 7 6 7 2 0 0 0 0 0 0 2 7 6 7 8
8 7 6 7 2 0 0 0 0 0 0 2 7 6 7 8
7 11 10 8 9 9 2 0 0 0 0 2 9 9 8 10 11
11 10 8 9 9 2 0 0 0 0 2 9 9 8 10 11
8 16 14 12 12 13 11 2 0 0 2 11 13 12 12 14 16
16 14 12 12 13 11 2 0 0 2 11 13 12 12 14 16
9 24 21 18 19 18 20 13 2 2 13 20 18 19 18 21 24
24 21 18 19 18 20 13 2 2 13 20 18 19 18 21 24
10 35 31 26 28 27 27 29 17 17 29 27 27 28 26 31 35
35 31 26 28 27 27 29 17 17 29 27 27 28 26 31 35
11 51 45 38 40 40 39 42 57 57 42 39 40 40 38 45 51
51 45 38 40 40 39 42 57 57 42 39 40 40 38 45 51
12 75 66 56 59 58 61 76 113 113 76 61 58 59 56 66 75
75 66 56 59 58 61 76 113 113 76 61 58 59 56 66 75
13 110 97 82 87 87 107 154 173 173 154 107 87 87 82 97 110
110 97 82 87 87 107 154 173 173 154 107 87 87 82 97 110
14 161 142 120 129 148 210 255 249 249 255 210 148 129 120 142 161
161 142 120 129 148 210 255 249 249 255 210 148 129 120 142 161
15 236 208 178 211 287 366 367 367 367 367 366 287 211 178 208 236
236 208 178 211 287 366 367 367 367 367 366 287 211 178 208 236
16 346 307 285 398 518 543 535 540 540 535 543 518 398 285 307 346
346 307 285 398 518 543 535 540 540 535 543 518 398 285 307 346
17 509 476 526 735 795 785 791 789 789 791 785 795 735 526 476 509
509 476 526 735 795 785 791 789 789 791 785 795 735 526 476 509
18 769 823 989 1166 1146 1153 1154 1152 1152 1154 1153 1146 1166 989 823 769
769 823 989 1166 1146 1153 1154 1152 1152 1154 1153 1146 1166 989 823 769
19 1209 1445 1581 1640 1622 1634 1627 1630 1630 1627 1634 1622 1640 1581 1445 1209
1209 1445 1581 1640 1622 1634 1627 1630 1630 1627 1634 1622 1640 1581 1445 1209
20 1771 2053 1996 2038 2030 2031 2030 2031 2031 2030 2031 2030 2038 1996 2053 1771
1771 2053 1996 2038 2030 2031 2030 2031 2031 2030 2031 2030 2038 1996 2053 1771
21 1937 1964 1868 1929 1903 1910 1910 1909 1909 1910 1910 1903 1929 1868 1964 1937
1937 1964 1868 1929 1903 1910 1910 1909 1909 1910 1910 1903 1929 1868 1964 1937
22 1267 1091 1121 1129 1113 1125 1119 1121 1121 1119 1125 1113 1129 1121 1091 1267
1267 1091 1121 1129 1113 1125 1119 1121 1121 1119 1125 1113 1129 1121 1091 1267
23 387 282 340 310 322 320 318 320 320 318 320 322 310 340 282 387
387 282 340 310 322 320 318 320 320 318 320 322 310 340 282 387
24 34 20 32 22 30 24 28 26 26 28 24 30 22 32 20 34
34 20 32 22 30 24 28 26 26 28 24 30 22 32 20 34
Total 8967 9112 9288 9970 10168 10368 10450 10496 10496 10450 10368 10168 9970 9288 9112 8967
8967 9112 9288 9970 10168 10368 10450 10496 10496 10450 10368 10168 9970 9288 9112 8967
Grand total = 4*8967 + 4*9112 + 4*9288 + 4*9970 + 4*10168 + 4*10368 + 4*10450 + 4*10496
= 315276
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
EN
0 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0
16 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
31 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73 + 1*116 + 1*117 + 1*188 + 1*189 + 1*304 + 1*306 + 1*493 + 1*494 + 1*798 + 1*799) +
28(32*0)
= 16712
Value repetition frequencies = 4(24*1 + 1*2 + 2*3) +
28(1*32)
= 1024
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*28
= 32
Number of distinct values = 27
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73 116 117 188 189 304 306 493 494 798 799
Frequency 908 4 12 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 24*4 + 1*8 + 1*12 + 1*908
= 1024
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*29
= 116
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 876
Number of possible SN-EN pairs with SN != EN = 31*32
= 992
a = 17, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 276 138
14 404 202
15 592 296
16 868 434
17 1272 636
18 1864 932
19 2724 1362
20 3872 1936
21 4944 2472
22 4952 2476
23 3308 1654
24 1212 606
25 176 88
26 4 2
Total 27048 13522
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
L
3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 0 0 0 0 0 0 2 1 0 0
0 0 1 2 0 0 0 0 0 0 0 0 0 2 1 0 0
6 0 0 0 3 2 0 0 0 0 0 0 0 2 3 0 0 0
0 0 0 3 2 0 0 0 0 0 0 0 2 3 0 0 0
7 0 0 0 0 5 2 0 0 0 0 0 2 5 0 0 0 0
0 0 0 0 5 2 0 0 0 0 0 2 5 0 0 0 0
8 0 0 0 0 1 7 2 0 0 0 2 7 1 0 0 0 0
0 0 0 0 1 7 2 0 0 0 2 7 1 0 0 0 0
9 0 0 0 0 0 4 9 2 0 2 9 4 0 0 0 0 0
0 0 0 0 0 4 9 2 0 2 9 4 0 0 0 0 0
10 0 0 0 0 0 0 9 11 4 11 9 0 0 0 0 0 0
0 0 0 0 0 0 9 11 4 11 9 0 0 0 0 0 0
11 0 0 0 0 0 0 1 18 26 18 1 0 0 0 0 0 0
0 0 0 0 0 0 1 18 26 18 1 0 0 0 0 0 0
12 0 0 0 0 0 0 2 20 50 20 2 0 0 0 0 0 0
0 0 0 0 0 0 2 20 50 20 2 0 0 0 0 0 0
13 0 0 0 0 0 2 17 36 28 36 17 2 0 0 0 0 0
0 0 0 0 0 2 17 36 28 36 17 2 0 0 0 0 0
14 0 0 0 0 2 19 49 30 2 30 49 19 2 0 0 0 0
0 0 0 0 2 19 49 30 2 30 49 19 2 0 0 0 0
15 0 0 0 2 21 64 55 6 0 6 55 64 21 2 0 0 0
0 0 0 2 21 64 55 6 0 6 55 64 21 2 0 0 0
16 0 0 2 23 81 91 20 0 0 0 20 91 81 23 2 0 0
0 0 2 23 81 91 20 0 0 0 20 91 81 23 2 0 0
17 0 2 25 100 140 50 1 0 0 0 1 50 140 100 25 2 0
0 2 25 100 140 50 1 0 0 0 1 50 140 100 25 2 0
18 2 27 121 204 105 7 0 0 0 0 0 7 105 204 121 27 2
2 27 121 204 105 7 0 0 0 0 0 7 105 204 121 27 2
19 29 144 285 196 27 0 0 0 0 0 0 0 27 196 285 144 29
29 144 285 196 27 0 0 0 0 0 0 0 27 196 285 144 29
20 169 385 336 77 1 0 0 0 0 0 0 0 1 77 336 385 169
169 385 336 77 1 0 0 0 0 0 0 0 1 77 336 385 169
21 506 540 182 8 0 0 0 0 0 0 0 0 0 8 182 540 506
506 540 182 8 0 0 0 0 0 0 0 0 0 8 182 540 506
22 825 378 35 0 0 0 0 0 0 0 0 0 0 0 35 378 825
825 378 35 0 0 0 0 0 0 0 0 0 0 0 35 378 825
23 714 112 1 0 0 0 0 0 0 0 0 0 0 0 1 112 714
714 112 1 0 0 0 0 0 0 0 0 0 0 0 1 112 714
24 294 9 0 0 0 0 0 0 0 0 0 0 0 0 0 9 294
294 9 0 0 0 0 0 0 0 0 0 0 0 0 0 9 294
25 44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 44
44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 44
26 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Total 2584 1599 990 615 385 246 165 123 110 123 165 246 385 615 990 1599 2584
2584 1599 990 615 385 246 165 123 110 123 165 246 385 615 990 1599 2584
Grand total = 2*110 + 4*123 + 4*165 + 4*246 + 4*385 + 4*615 + 4*990 + 4*1599 + 4*2584
= 27048
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
13 69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
14 101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
15 148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
16 217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
17 318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
18 466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
19 681 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 681
681 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 681
20 968 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 968
968 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 968
21 1236 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1236
1236 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1236
22 1238 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1238
1238 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1238
23 827 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 827
827 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 827
24 303 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 303
303 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 303
25 44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 44
44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 44
26 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Total 6762 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6762
6762 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6762
Grand total = 4*6762
= 27048
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
L
3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 0 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 0 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 0 0 0 0 0 0 2 4 4 5
5 4 4 2 0 0 0 0 0 0 0 0 0 2 4 4 5
6 8 7 6 7 2 0 0 0 0 0 0 0 2 7 6 7 8
8 7 6 7 2 0 0 0 0 0 0 0 2 7 6 7 8
7 11 10 8 9 9 2 0 0 0 0 0 2 9 9 8 10 11
11 10 8 9 9 2 0 0 0 0 0 2 9 9 8 10 11
8 16 14 12 12 13 11 2 0 0 0 2 11 13 12 12 14 16
16 14 12 12 13 11 2 0 0 0 2 11 13 12 12 14 16
9 24 21 18 19 18 20 13 2 0 2 13 20 18 19 18 21 24
24 21 18 19 18 20 13 2 0 2 13 20 18 19 18 21 24
10 35 31 26 28 27 27 29 15 4 15 29 27 27 28 26 31 35
35 31 26 28 27 27 29 15 4 15 29 27 27 28 26 31 35
11 51 45 38 40 40 39 40 42 34 42 40 39 40 40 38 45 51
51 45 38 40 40 39 40 42 34 42 40 39 40 40 38 45 51
12 75 66 56 59 58 59 59 79 106 79 59 59 58 59 56 66 75
75 66 56 59 58 59 59 79 106 79 59 59 58 59 56 66 75
13 110 97 82 87 85 88 107 152 178 152 107 88 85 87 82 97 110
110 97 82 87 85 88 107 152 178 152 107 88 85 87 82 97 110
14 161 142 120 127 127 148 211 254 248 254 211 148 127 127 120 142 161
161 142 120 127 127 148 211 254 248 254 211 148 127 127 120 142 161
15 236 208 176 188 208 288 365 369 364 369 365 288 208 188 176 208 236
236 208 176 188 208 288 365 369 364 369 365 288 208 188 176 208 236
16 346 305 260 300 393 520 542 535 542 535 542 520 393 300 260 305 346
346 305 260 300 393 520 542 535 542 535 542 520 393 300 260 305 346
17 507 449 407 548 728 797 785 790 790 790 785 797 728 548 407 449 507
507 449 407 548 728 797 785 790 790 790 785 797 728 548 407 449 507
18 745 686 727 1025 1160 1153 1156 1159 1154 1159 1156 1153 1160 1025 727 686 745
745 686 727 1025 1160 1153 1156 1159 1154 1159 1156 1153 1160 1025 727 686 745
19 1117 1155 1372 1689 1687 1689 1694 1690 1692 1690 1694 1689 1687 1689 1372 1155 1117
1117 1155 1372 1689 1687 1689 1694 1690 1692 1690 1694 1689 1687 1689 1372 1155 1117
20 1740 2035 2290 2438 2401 2421 2413 2414 2416 2414 2413 2421 2401 2438 2290 2035 1740
1740 2035 2290 2438 2401 2421 2413 2414 2416 2414 2413 2421 2401 2438 2290 2035 1740
21 2612 3073 3073 3136 3122 3128 3123 3127 3124 3127 3123 3128 3122 3136 3073 3073 2612
2612 3073 3073 3136 3122 3128 3123 3127 3124 3127 3123 3128 3122 3136 3073 3073 2612
22 3123 3304 3141 3235 3202 3209 3209 3209 3208 3209 3209 3209 3202 3235 3141 3304 3123
3123 3304 3141 3235 3202 3209 3209 3209 3208 3209 3209 3209 3202 3235 3141 3304 3123
23 2424 2206 2194 2237 2202 2221 2214 2215 2216 2215 2214 2221 2202 2237 2194 2206 2424
2424 2206 2194 2237 2202 2221 2214 2215 2216 2215 2214 2221 2202 2237 2194 2206 2424
24 997 776 872 834 842 846 840 844 842 844 840 846 842 834 872 776 997
997 776 872 834 842 846 840 844 842 844 840 846 842 834 872 776 997
25 159 104 144 116 134 124 128 128 126 128 128 124 134 116 144 104 159
159 104 144 116 134 124 128 128 126 128 128 124 134 116 144 104 159
26 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4
4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4
Total 14512 14746 15032 16138 16462 16792 16934 17026 17048 17026 16934 16792 16462 16138 15032 14746 14512
14512 14746 15032 16138 16462 16792 16934 17026 17048 17026 16934 16792 16462 16138 15032 14746 14512
Grand total = 4*14512 + 4*14746 + 4*15032 + 4*16138 + 4*16462 + 4*16792 + 4*16934 + 4*17026 + 2*17048
= 544664
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
EN
0 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 1293 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 1291
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 1293 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0 1291 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0
17 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 1291 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 1293
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
33 1291 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0 1293 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73 + 1*116 + 1*117 + 1*188 + 1*189 + 1*304 + 1*306 + 1*493 + 1*494 + 1*798 + 1*799 +
1*1291 + 1*1293) +
30(34*0)
= 27048
Value repetition frequencies = 4(26*1 + 1*2 + 2*3) +
30(1*34)
= 1156
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*30
= 34
Number of distinct values = 29
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73 116 117 188
Frequency 1032 4 12 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 189 304 306 493 494 798 799 1291 1293
Frequency 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 26*4 + 1*8 + 1*12 + 1*1032
= 1156
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*31
= 124
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 998
Number of possible SN-EN pairs with SN != EN = 33*34
= 1122
a = 18, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 276 138
14 404 202
15 592 296
16 868 434
17 1272 636
18 1864 932
19 2732 1366
20 3996 1998
21 5728 2864
22 7552 3776
23 8148 4074
24 6228 3114
25 2864 1432
26 628 314
27 40 20
Total 43772 21884
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
L
3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 0 0 0 0 0 0 0 2 1 0 0
0 0 1 2 0 0 0 0 0 0 0 0 0 0 2 1 0 0
6 0 0 0 3 2 0 0 0 0 0 0 0 0 2 3 0 0 0
0 0 0 3 2 0 0 0 0 0 0 0 0 2 3 0 0 0
7 0 0 0 0 5 2 0 0 0 0 0 0 2 5 0 0 0 0
0 0 0 0 5 2 0 0 0 0 0 0 2 5 0 0 0 0
8 0 0 0 0 1 7 2 0 0 0 0 2 7 1 0 0 0 0
0 0 0 0 1 7 2 0 0 0 0 2 7 1 0 0 0 0
9 0 0 0 0 0 4 9 2 0 0 2 9 4 0 0 0 0 0
0 0 0 0 0 4 9 2 0 0 2 9 4 0 0 0 0 0
10 0 0 0 0 0 0 9 11 2 2 11 9 0 0 0 0 0 0
0 0 0 0 0 0 9 11 2 2 11 9 0 0 0 0 0 0
11 0 0 0 0 0 0 1 16 15 15 16 1 0 0 0 0 0 0
0 0 0 0 0 0 1 16 15 15 16 1 0 0 0 0 0 0
12 0 0 0 0 0 0 0 7 40 40 7 0 0 0 0 0 0 0
0 0 0 0 0 0 0 7 40 40 7 0 0 0 0 0 0 0
13 0 0 0 0 0 0 2 17 50 50 17 2 0 0 0 0 0 0
0 0 0 0 0 0 2 17 50 50 17 2 0 0 0 0 0 0
14 0 0 0 0 0 2 19 49 31 31 49 19 2 0 0 0 0 0
0 0 0 0 0 2 19 49 31 31 49 19 2 0 0 0 0 0
15 0 0 0 0 2 21 64 55 6 6 55 64 21 2 0 0 0 0
0 0 0 0 2 21 64 55 6 6 55 64 21 2 0 0 0 0
16 0 0 0 2 23 81 91 20 0 0 20 91 81 23 2 0 0 0
0 0 0 2 23 81 91 20 0 0 20 91 81 23 2 0 0 0
17 0 0 2 25 100 140 50 1 0 0 1 50 140 100 25 2 0 0
0 0 2 25 100 140 50 1 0 0 1 50 140 100 25 2 0 0
18 0 2 27 121 204 105 7 0 0 0 0 7 105 204 121 27 2 0
0 2 27 121 204 105 7 0 0 0 0 7 105 204 121 27 2 0
19 2 29 144 285 196 27 0 0 0 0 0 0 27 196 285 144 29 2
2 29 144 285 196 27 0 0 0 0 0 0 27 196 285 144 29 2
20 31 169 385 336 77 1 0 0 0 0 0 0 1 77 336 385 169 31
31 169 385 336 77 1 0 0 0 0 0 0 1 77 336 385 169 31
21 196 506 540 182 8 0 0 0 0 0 0 0 0 8 182 540 506 196
196 506 540 182 8 0 0 0 0 0 0 0 0 8 182 540 506 196
22 650 825 378 35 0 0 0 0 0 0 0 0 0 0 35 378 825 650
650 825 378 35 0 0 0 0 0 0 0 0 0 0 35 378 825 650
23 1210 714 112 1 0 0 0 0 0 0 0 0 0 0 1 112 714 1210
1210 714 112 1 0 0 0 0 0 0 0 0 0 0 1 112 714 1210
24 1254 294 9 0 0 0 0 0 0 0 0 0 0 0 0 9 294 1254
1254 294 9 0 0 0 0 0 0 0 0 0 0 0 0 9 294 1254
25 672 44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 44 672
672 44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 44 672
26 156 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 156
156 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 156
27 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
Total 4181 2586 1600 992 618 390 254 178 144 144 178 254 390 618 992 1600 2586 4181
4181 2586 1600 992 618 390 254 178 144 144 178 254 390 618 992 1600 2586 4181
Grand total = 4*144 + 4*178 + 4*254 + 4*390 + 4*618 + 4*992 + 4*1600 + 4*2586 + 4*4181
= 43772
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
13 69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
14 101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
15 148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
16 217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
17 318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
18 466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
19 683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
20 999 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 999
999 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 999
21 1432 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1432
1432 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1432
22 1888 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1888
1888 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1888
23 2037 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2037
2037 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2037
24 1557 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1557
1557 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1557
25 716 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 716
716 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 716
26 157 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 157
157 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 157
27 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
Total 10943 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10943
10943 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10943
Grand total = 4*10943
= 43772
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
L
3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 0 0 0 0 0 0 0 2 4 4 5
5 4 4 2 0 0 0 0 0 0 0 0 0 0 2 4 4 5
6 8 7 6 7 2 0 0 0 0 0 0 0 0 2 7 6 7 8
8 7 6 7 2 0 0 0 0 0 0 0 0 2 7 6 7 8
7 11 10 8 9 9 2 0 0 0 0 0 0 2 9 9 8 10 11
11 10 8 9 9 2 0 0 0 0 0 0 2 9 9 8 10 11
8 16 14 12 12 13 11 2 0 0 0 0 2 11 13 12 12 14 16
16 14 12 12 13 11 2 0 0 0 0 2 11 13 12 12 14 16
9 24 21 18 19 18 20 13 2 0 0 2 13 20 18 19 18 21 24
24 21 18 19 18 20 13 2 0 0 2 13 20 18 19 18 21 24
10 35 31 26 28 27 27 29 15 2 2 15 29 27 27 28 26 31 35
35 31 26 28 27 27 29 15 2 2 15 29 27 27 28 26 31 35
11 51 45 38 40 40 39 40 40 19 19 40 40 39 40 40 38 45 51
51 45 38 40 40 39 40 40 19 19 40 40 39 40 40 38 45 51
12 75 66 56 59 58 59 57 62 72 72 62 57 59 58 59 56 66 75
75 66 56 59 58 59 57 62 72 72 62 57 59 58 59 56 66 75
13 110 97 82 87 85 86 88 105 157 157 105 88 86 85 87 82 97 110
110 97 82 87 85 86 88 105 157 157 105 88 86 85 87 82 97 110
14 161 142 120 127 125 127 149 210 253 253 210 149 127 125 127 120 142 161
161 142 120 127 125 127 149 210 253 253 210 149 127 125 127 120 142 161
15 236 208 176 186 185 209 287 367 366 366 367 287 209 185 186 176 208 236
236 208 176 186 185 209 287 367 366 366 367 287 209 185 186 176 208 236
16 346 305 258 275 295 395 519 542 537 537 542 519 395 295 275 258 305 346
346 305 258 275 295 395 519 542 537 537 542 519 395 295 275 258 305 346
17 507 447 380 429 541 730 797 784 791 791 784 797 730 541 429 380 447 507
507 447 380 429 541 730 797 784 791 791 784 797 730 541 429 380 447 507
18 743 657 585 759 1015 1163 1152 1157 1157 1157 1157 1152 1163 1015 759 585 657 743
743 657 585 759 1015 1163 1152 1157 1157 1157 1157 1152 1163 1015 759 585 657 743
19 1091 993 1012 1423 1678 1696 1691 1699 1694 1694 1699 1691 1696 1678 1423 1012 993 1091
1091 993 1012 1423 1678 1696 1691 1699 1694 1694 1699 1691 1696 1678 1423 1012 993 1091
20 1626 1631 1898 2424 2482 2474 2485 2479 2481 2481 2479 2485 2474 2482 2424 1898 1631 1626
1626 1631 1898 2424 2482 2474 2485 2479 2481 2481 2479 2485 2474 2482 2424 1898 1631 1626
21 2509 2858 3279 3604 3547 3574 3567 3566 3568 3568 3566 3567 3574 3547 3604 3279 2858 2509
2509 2858 3279 3604 3547 3574 3567 3566 3568 3568 3566 3567 3574 3547 3604 3279 2858 2509
22 3821 4518 4654 4776 4744 4762 4750 4757 4754 4754 4757 4750 4762 4744 4776 4654 4518 3821
3821 4518 4654 4776 4744 4762 4750 4757 4754 4754 4757 4750 4762 4744 4776 4654 4518 3821
23 4894 5357 5137 5273 5232 5240 5239 5240 5239 5239 5240 5239 5240 5232 5273 5137 5357 4894
4894 5357 5137 5273 5232 5240 5239 5240 5239 5239 5240 5239 5240 5232 5273 5137 5357 4894
24 4361 4170 4062 4166 4105 4131 4124 4124 4125 4125 4124 4124 4131 4105 4166 4062 4170 4361
4361 4170 4062 4166 4105 4131 4124 4124 4125 4125 4124 4124 4131 4105 4166 4062 4170 4361
25 2264 1867 1993 1963 1955 1971 1959 1965 1963 1963 1965 1959 1971 1955 1963 1993 1867 2264
2264 1867 1993 1963 1955 1971 1959 1965 1963 1963 1965 1959 1971 1955 1963 1993 1867 2264
26 546 386 484 426 456 444 446 448 446 446 448 446 444 456 426 484 386 546
546 386 484 426 456 444 446 448 446 446 448 446 444 456 426 484 386 546
27 38 22 36 24 34 26 32 28 30 30 28 32 26 34 24 36 22 38
38 22 36 24 34 26 32 28 30 30 28 32 26 34 24 36 22 38
Total 23484 23862 24326 26118 26646 27186 27426 27590 27654 27654 27590 27426 27186 26646 26118 24326 23862 23484
23484 23862 24326 26118 26646 27186 27426 27590 27654 27654 27590 27426 27186 26646 26118 24326 23862 23484
Grand total = 4*23484 + 4*23862 + 4*24326 + 4*26118 + 4*26646 + 4*27186 + 4*27426 + 4*27590 + 4*27654
= 937168
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
EN
0 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 1293 2091 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 1291 2090
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 2091 1293 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0 2090 1291 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0
18 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 1291 2090 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 1293 2091
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
35 2090 1291 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0 2091 1293 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73 + 1*116 + 1*117 + 1*188 + 1*189 + 1*304 + 1*306 + 1*493 + 1*494 + 1*798 + 1*799 +
1*1291 + 1*1293 + 1*2090 + 1*2091) +
32(36*0)
= 43772
Value repetition frequencies = 4(28*1 + 1*2 + 2*3) +
32(1*36)
= 1296
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*32
= 36
Number of distinct values = 31
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73 116 117 188
Frequency 1164 4 12 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 189 304 306 493 494 798 799 1291 1293 2090 2091
Frequency 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 28*4 + 1*8 + 1*12 + 1*1164
= 1296
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*33
= 132
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 1128
Number of possible SN-EN pairs with SN != EN = 35*36
= 1260
a = 19, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 276 138
14 404 202
15 592 296
16 868 434
17 1272 636
18 1864 932
19 2732 1366
20 4004 2002
21 5860 2930
22 8452 4226
23 11424 5712
24 13092 6546
25 11180 5590
26 6172 3086
27 1840 920
28 216 108
29 4 2
Total 70832 35414
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
L
3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0
0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0
6 0 0 0 3 2 0 0 0 0 0 0 0 0 0 2 3 0 0 0
0 0 0 3 2 0 0 0 0 0 0 0 0 0 2 3 0 0 0
7 0 0 0 0 5 2 0 0 0 0 0 0 0 2 5 0 0 0 0
0 0 0 0 5 2 0 0 0 0 0 0 0 2 5 0 0 0 0
8 0 0 0 0 1 7 2 0 0 0 0 0 2 7 1 0 0 0 0
0 0 0 0 1 7 2 0 0 0 0 0 2 7 1 0 0 0 0
9 0 0 0 0 0 4 9 2 0 0 0 2 9 4 0 0 0 0 0
0 0 0 0 0 4 9 2 0 0 0 2 9 4 0 0 0 0 0
10 0 0 0 0 0 0 9 11 2 0 2 11 9 0 0 0 0 0 0
0 0 0 0 0 0 9 11 2 0 2 11 9 0 0 0 0 0 0
11 0 0 0 0 0 0 1 16 13 4 13 16 1 0 0 0 0 0 0
0 0 0 0 0 0 1 16 13 4 13 16 1 0 0 0 0 0 0
12 0 0 0 0 0 0 0 5 27 30 27 5 0 0 0 0 0 0 0
0 0 0 0 0 0 0 5 27 30 27 5 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 2 31 72 31 2 0 0 0 0 0 0 0
0 0 0 0 0 0 0 2 31 72 31 2 0 0 0 0 0 0 0
14 0 0 0 0 0 0 2 19 50 60 50 19 2 0 0 0 0 0 0
0 0 0 0 0 0 2 19 50 60 50 19 2 0 0 0 0 0 0
15 0 0 0 0 0 2 21 64 55 12 55 64 21 2 0 0 0 0 0
0 0 0 0 0 2 21 64 55 12 55 64 21 2 0 0 0 0 0
16 0 0 0 0 2 23 81 91 20 0 20 91 81 23 2 0 0 0 0
0 0 0 0 2 23 81 91 20 0 20 91 81 23 2 0 0 0 0
17 0 0 0 2 25 100 140 50 1 0 1 50 140 100 25 2 0 0 0
0 0 0 2 25 100 140 50 1 0 1 50 140 100 25 2 0 0 0
18 0 0 2 27 121 204 105 7 0 0 0 7 105 204 121 27 2 0 0
0 0 2 27 121 204 105 7 0 0 0 7 105 204 121 27 2 0 0
19 0 2 29 144 285 196 27 0 0 0 0 0 27 196 285 144 29 2 0
0 2 29 144 285 196 27 0 0 0 0 0 27 196 285 144 29 2 0
20 2 31 169 385 336 77 1 0 0 0 0 0 1 77 336 385 169 31 2
2 31 169 385 336 77 1 0 0 0 0 0 1 77 336 385 169 31 2
21 33 196 506 540 182 8 0 0 0 0 0 0 0 8 182 540 506 196 33
33 196 506 540 182 8 0 0 0 0 0 0 0 8 182 540 506 196 33
22 225 650 825 378 35 0 0 0 0 0 0 0 0 0 35 378 825 650 225
225 650 825 378 35 0 0 0 0 0 0 0 0 0 35 378 825 650 225
23 819 1210 714 112 1 0 0 0 0 0 0 0 0 0 1 112 714 1210 819
819 1210 714 112 1 0 0 0 0 0 0 0 0 0 1 112 714 1210 819
24 1716 1254 294 9 0 0 0 0 0 0 0 0 0 0 0 9 294 1254 1716
1716 1254 294 9 0 0 0 0 0 0 0 0 0 0 0 9 294 1254 1716
25 2079 672 44 0 0 0 0 0 0 0 0 0 0 0 0 0 44 672 2079
2079 672 44 0 0 0 0 0 0 0 0 0 0 0 0 0 44 672 2079
26 1386 156 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 156 1386
1386 156 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 156 1386
27 450 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 450
450 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 450
28 54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 54
54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 54
29 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Total 6765 4183 2587 1602 995 623 398 267 199 178 199 267 398 623 995 1602 2587 4183 6765
6765 4183 2587 1602 995 623 398 267 199 178 199 267 398 623 995 1602 2587 4183 6765
Grand total = 2*178 + 4*199 + 4*267 + 4*398 + 4*623 + 4*995 + 4*1602 + 4*2587 + 4*4183 + 4*6765
= 70832
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
13 69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
14 101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
15 148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
16 217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
17 318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
18 466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
19 683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
20 1001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1001
1001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1001
21 1465 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1465
1465 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1465
22 2113 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2113
2113 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2113
23 2856 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2856
2856 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2856
24 3273 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3273
3273 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3273
25 2795 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2795
2795 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2795
26 1543 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1543
1543 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1543
27 460 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 460
460 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 460
28 54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 54
54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 54
29 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Total 17708 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17708
17708 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17708
Grand total = 4*17708
= 70832
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
L
3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5
5 4 4 2 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5
6 8 7 6 7 2 0 0 0 0 0 0 0 0 0 2 7 6 7 8
8 7 6 7 2 0 0 0 0 0 0 0 0 0 2 7 6 7 8
7 11 10 8 9 9 2 0 0 0 0 0 0 0 2 9 9 8 10 11
11 10 8 9 9 2 0 0 0 0 0 0 0 2 9 9 8 10 11
8 16 14 12 12 13 11 2 0 0 0 0 0 2 11 13 12 12 14 16
16 14 12 12 13 11 2 0 0 0 0 0 2 11 13 12 12 14 16
9 24 21 18 19 18 20 13 2 0 0 0 2 13 20 18 19 18 21 24
24 21 18 19 18 20 13 2 0 0 0 2 13 20 18 19 18 21 24
10 35 31 26 28 27 27 29 15 2 0 2 15 29 27 27 28 26 31 35
35 31 26 28 27 27 29 15 2 0 2 15 29 27 27 28 26 31 35
11 51 45 38 40 40 39 40 40 17 4 17 40 40 39 40 40 38 45 51
51 45 38 40 40 39 40 40 17 4 17 40 40 39 40 40 38 45 51
12 75 66 56 59 58 59 57 60 55 38 55 60 57 59 58 59 56 66 75
75 66 56 59 58 59 57 60 55 38 55 60 57 59 58 59 56 66 75
13 110 97 82 87 85 86 86 86 110 136 110 86 86 86 85 87 82 97 110
110 97 82 87 85 86 86 86 110 136 110 86 86 86 85 87 82 97 110
14 161 142 120 127 125 125 128 148 209 258 209 148 128 125 125 127 120 142 161
161 142 120 127 125 125 128 148 209 258 209 148 128 125 125 127 120 142 161
15 236 208 176 186 183 186 208 289 364 368 364 289 208 186 183 186 176 208 236
236 208 176 186 183 186 208 289 364 368 364 289 208 186 183 186 176 208 236
16 346 305 258 273 270 297 394 519 544 532 544 519 394 297 270 273 258 305 346
346 305 258 273 270 297 394 519 544 532 544 519 394 297 270 273 258 305 346
17 507 447 378 402 422 543 730 796 785 792 785 796 730 543 422 402 378 447 507
507 447 378 402 422 543 730 796 785 792 785 796 730 543 422 402 378 447 507
18 743 655 556 617 749 1018 1162 1153 1155 1160 1155 1153 1162 1018 749 617 556 655 743
743 655 556 617 749 1018 1162 1153 1155 1160 1155 1153 1162 1018 749 617 556 655 743
19 1089 962 845 1059 1408 1683 1694 1692 1699 1692 1699 1692 1694 1683 1408 1059 845 962 1089
1089 962 845 1059 1408 1683 1694 1692 1699 1692 1699 1692 1694 1683 1408 1059 845 962 1089
20 1598 1442 1419 1971 2406 2493 2476 2489 2484 2484 2484 2489 2476 2493 2406 1971 1419 1442 1598
1598 1442 1419 1971 2406 2493 2476 2489 2484 2484 2484 2489 2476 2493 2406 1971 1419 1442 1598
21 2371 2317 2625 3449 3642 3627 3641 3638 3635 3640 3635 3638 3641 3627 3642 3449 2625 2317 2371
2371 2317 2625 3449 3642 3627 3641 3638 3635 3640 3635 3638 3641 3627 3642 3449 2625 2317 2371
22 3626 4013 4651 5293 5234 5263 5261 5256 5260 5258 5260 5256 5261 5263 5234 5293 4651 4013 3626
3626 4013 4651 5293 5234 5263 5261 5256 5260 5258 5260 5256 5261 5263 5234 5293 4651 4013 3626
23 5561 6553 6944 7214 7145 7183 7163 7171 7170 7168 7170 7171 7163 7183 7145 7214 6944 6553 5561
5561 6553 6944 7214 7145 7183 7163 7171 7170 7168 7170 7171 7163 7183 7145 7214 6944 6553 5561
24 7506 8430 8210 8409 8354 8368 8362 8367 8363 8366 8363 8367 8362 8368 8354 8409 8210 8430 7506
7506 8430 8210 8409 8354 8368 8362 8367 8363 8366 8363 8367 8362 8368 8354 8409 8210 8430 7506
25 7484 7474 7203 7401 7307 7340 7333 7333 7333 7334 7333 7333 7333 7340 7307 7401 7203 7474 7484
7484 7474 7203 7401 7307 7340 7333 7333 7333 7334 7333 7333 7333 7340 7307 7401 7203 7474 7484
26 4688 4073 4187 4200 4157 4192 4173 4180 4179 4178 4179 4180 4173 4192 4157 4200 4187 4073 4688
4688 4073 4187 4200 4157 4192 4173 4180 4179 4178 4179 4180 4173 4192 4157 4200 4187 4073 4688
27 1543 1162 1356 1260 1298 1290 1286 1292 1288 1290 1288 1292 1286 1290 1298 1260 1356 1162 1543
1543 1162 1356 1260 1298 1290 1286 1292 1288 1290 1288 1292 1286 1290 1298 1260 1356 1162 1543
28 197 126 180 140 168 150 160 156 156 158 156 156 160 150 168 140 180 126 197
197 126 180 140 168 150 160 156 156 158 156 156 160 150 168 140 180 126 197
29 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4
4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4
Total 38001 38612 39364 42266 43124 44004 44402 44684 44812 44858 44812 44684 44402 44004 43124 42266 39364 38612 38001
38001 38612 39364 42266 43124 44004 44402 44684 44812 44858 44812 44684 44402 44004 43124 42266 39364 38612 38001
Grand total = 4*38001 + 4*38612 + 4*39364 + 4*42266 + 4*43124 + 4*44004 + 4*44402 + 4*44684 + 4*44812 + 2*44858
= 1606792
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
EN
0 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 1293 2091 3382 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 1291 2090 3383
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 3382 2091 1293 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0 3383 2090 1291 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0
19 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 1291 2090 3383 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 1293 2091 3382
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
37 3383 2090 1291 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0 3382 2091 1293 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73 + 1*116 + 1*117 + 1*188 + 1*189 + 1*304 + 1*306 + 1*493 + 1*494 + 1*798 + 1*799 +
1*1291 + 1*1293 + 1*2090 + 1*2091 + 1*3382 + 1*3383) +
34(38*0)
= 70832
Value repetition frequencies = 4(30*1 + 1*2 + 2*3) +
34(1*38)
= 1444
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*34
= 38
Number of distinct values = 33
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73 116 117 188
Frequency 1304 4 12 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 189 304 306 493 494 798 799 1291 1293 2090 2091 3382 3383
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 30*4 + 1*8 + 1*12 + 1*1304
= 1444
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*35
= 140
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 1266
Number of possible SN-EN pairs with SN != EN = 37*38
= 1406
a = 20, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 276 138
14 404 202
15 592 296
16 868 434
17 1272 636
18 1864 932
19 2732 1366
20 4004 2002
21 5868 2934
22 8592 4296
23 12448 6224
24 17152 8576
25 20644 10322
26 19328 9664
27 12400 6200
28 4704 2352
29 844 422
30 44 22
Total 114616 57306
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
L
3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0
0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0
6 0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0
0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0
7 0 0 0 0 5 2 0 0 0 0 0 0 0 0 2 5 0 0 0 0
0 0 0 0 5 2 0 0 0 0 0 0 0 0 2 5 0 0 0 0
8 0 0 0 0 1 7 2 0 0 0 0 0 0 2 7 1 0 0 0 0
0 0 0 0 1 7 2 0 0 0 0 0 0 2 7 1 0 0 0 0
9 0 0 0 0 0 4 9 2 0 0 0 0 2 9 4 0 0 0 0 0
0 0 0 0 0 4 9 2 0 0 0 0 2 9 4 0 0 0 0 0
10 0 0 0 0 0 0 9 11 2 0 0 2 11 9 0 0 0 0 0 0
0 0 0 0 0 0 9 11 2 0 0 2 11 9 0 0 0 0 0 0
11 0 0 0 0 0 0 1 16 13 2 2 13 16 1 0 0 0 0 0 0
0 0 0 0 0 0 1 16 13 2 2 13 16 1 0 0 0 0 0 0
12 0 0 0 0 0 0 0 5 25 17 17 25 5 0 0 0 0 0 0 0
0 0 0 0 0 0 0 5 25 17 17 25 5 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 16 53 53 16 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 16 53 53 16 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 2 20 79 79 20 2 0 0 0 0 0 0 0
0 0 0 0 0 0 0 2 20 79 79 20 2 0 0 0 0 0 0 0
15 0 0 0 0 0 0 2 21 64 61 61 64 21 2 0 0 0 0 0 0
0 0 0 0 0 0 2 21 64 61 61 64 21 2 0 0 0 0 0 0
16 0 0 0 0 0 2 23 81 91 20 20 91 81 23 2 0 0 0 0 0
0 0 0 0 0 2 23 81 91 20 20 91 81 23 2 0 0 0 0 0
17 0 0 0 0 2 25 100 140 50 1 1 50 140 100 25 2 0 0 0 0
0 0 0 0 2 25 100 140 50 1 1 50 140 100 25 2 0 0 0 0
18 0 0 0 2 27 121 204 105 7 0 0 7 105 204 121 27 2 0 0 0
0 0 0 2 27 121 204 105 7 0 0 7 105 204 121 27 2 0 0 0
19 0 0 2 29 144 285 196 27 0 0 0 0 27 196 285 144 29 2 0 0
0 0 2 29 144 285 196 27 0 0 0 0 27 196 285 144 29 2 0 0
20 0 2 31 169 385 336 77 1 0 0 0 0 1 77 336 385 169 31 2 0
0 2 31 169 385 336 77 1 0 0 0 0 1 77 336 385 169 31 2 0
21 2 33 196 506 540 182 8 0 0 0 0 0 0 8 182 540 506 196 33 2
2 33 196 506 540 182 8 0 0 0 0 0 0 8 182 540 506 196 33 2
22 35 225 650 825 378 35 0 0 0 0 0 0 0 0 35 378 825 650 225 35
35 225 650 825 378 35 0 0 0 0 0 0 0 0 35 378 825 650 225 35
23 256 819 1210 714 112 1 0 0 0 0 0 0 0 0 1 112 714 1210 819 256
256 819 1210 714 112 1 0 0 0 0 0 0 0 0 1 112 714 1210 819 256
24 1015 1716 1254 294 9 0 0 0 0 0 0 0 0 0 0 9 294 1254 1716 1015
1015 1716 1254 294 9 0 0 0 0 0 0 0 0 0 0 9 294 1254 1716 1015
25 2366 2079 672 44 0 0 0 0 0 0 0 0 0 0 0 0 44 672 2079 2366
2366 2079 672 44 0 0 0 0 0 0 0 0 0 0 0 0 44 672 2079 2366
26 3289 1386 156 1 0 0 0 0 0 0 0 0 0 0 0 0 1 156 1386 3289
3289 1386 156 1 0 0 0 0 0 0 0 0 0 0 0 0 1 156 1386 3289
27 2640 450 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 450 2640
2640 450 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 450 2640
28 1122 54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 54 1122
1122 54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 54 1122
29 210 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 210
210 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 210
30 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
Total 10946 6767 4184 2589 1605 1000 631 411 288 233 233 288 411 631 1000 1605 2589 4184 6767 10946
10946 6767 4184 2589 1605 1000 631 411 288 233 233 288 411 631 1000 1605 2589 4184 6767 10946
Grand total = 4*233 + 4*288 + 4*411 + 4*631 + 4*1000 + 4*1605 + 4*2589 + 4*4184 + 4*6767 + 4*10946
= 114616
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
13 69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
14 101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
15 148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
16 217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
17 318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
18 466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
19 683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
20 1001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1001
1001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1001
21 1467 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1467
1467 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1467
22 2148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2148
2148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2148
23 3112 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3112
3112 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3112
24 4288 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4288
4288 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4288
25 5161 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5161
5161 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5161
26 4832 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4832
4832 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4832
27 3100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3100
3100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3100
28 1176 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1176
1176 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1176
29 211 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 211
211 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 211
30 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
Total 28654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28654
28654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28654
Grand total = 4*28654
= 114616
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
L
3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5
5 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5
6 8 7 6 7 2 0 0 0 0 0 0 0 0 0 0 2 7 6 7 8
8 7 6 7 2 0 0 0 0 0 0 0 0 0 0 2 7 6 7 8
7 11 10 8 9 9 2 0 0 0 0 0 0 0 0 2 9 9 8 10 11
11 10 8 9 9 2 0 0 0 0 0 0 0 0 2 9 9 8 10 11
8 16 14 12 12 13 11 2 0 0 0 0 0 0 2 11 13 12 12 14 16
16 14 12 12 13 11 2 0 0 0 0 0 0 2 11 13 12 12 14 16
9 24 21 18 19 18 20 13 2 0 0 0 0 2 13 20 18 19 18 21 24
24 21 18 19 18 20 13 2 0 0 0 0 2 13 20 18 19 18 21 24
10 35 31 26 28 27 27 29 15 2 0 0 2 15 29 27 27 28 26 31 35
35 31 26 28 27 27 29 15 2 0 0 2 15 29 27 27 28 26 31 35
11 51 45 38 40 40 39 40 40 17 2 2 17 40 40 39 40 40 38 45 51
51 45 38 40 40 39 40 40 17 2 2 17 40 40 39 40 40 38 45 51
12 75 66 56 59 58 59 57 60 53 21 21 53 60 57 59 58 59 56 66 75
75 66 56 59 58 59 57 60 53 21 21 53 60 57 59 58 59 56 66 75
13 110 97 82 87 85 86 86 84 91 89 89 91 84 86 86 85 87 82 97 110
110 97 82 87 85 86 86 84 91 89 89 91 84 86 86 85 87 82 97 110
14 161 142 120 127 125 125 126 127 147 214 214 147 127 126 125 125 127 120 142 161
161 142 120 127 125 125 126 127 147 214 214 147 127 126 125 125 127 120 142 161
15 236 208 176 186 183 184 185 210 286 366 366 286 210 185 184 183 186 176 208 236
236 208 176 186 183 184 185 210 286 366 366 286 210 185 184 183 186 176 208 236
16 346 305 258 273 268 272 296 394 521 539 539 521 394 296 272 268 273 258 305 346
346 305 258 273 268 272 296 394 521 539 539 521 394 296 272 268 273 258 305 346
17 507 447 378 400 395 424 543 729 797 786 786 797 729 543 424 395 400 378 447 507
507 447 378 400 395 424 543 729 797 786 786 797 729 543 424 395 400 378 447 507
18 743 655 554 588 607 752 1017 1163 1151 1158 1158 1151 1163 1017 752 607 588 554 655 743
743 655 554 588 607 752 1017 1163 1151 1158 1158 1151 1163 1017 752 607 588 554 655 743
19 1089 960 814 892 1044 1413 1681 1695 1692 1697 1697 1692 1695 1681 1413 1044 892 814 960 1089
1089 960 814 892 1044 1413 1681 1695 1692 1697 1697 1692 1695 1681 1413 1044 892 814 960 1089
20 1596 1409 1225 1488 1949 2413 2491 2476 2490 2483 2483 2490 2476 2491 2413 1949 1488 1225 1409 1596
1596 1409 1225 1488 1949 2413 2491 2476 2490 2483 2483 2490 2476 2491 2413 1949 1488 1225 1409 1596
21 2341 2099 2004 2730 3421 3656 3628 3646 3641 3641 3641 3641 3646 3628 3656 3421 2730 2004 2099 2341
2341 2099 2004 2730 3421 3656 3628 3646 3641 3641 3641 3641 3646 3628 3656 3421 2730 2004 2099 2341
22 3462 3310 3637 4872 5320 5323 5332 5337 5329 5334 5334 5329 5337 5332 5323 5320 4872 3637 3310 3462
3462 3310 3637 4872 5320 5323 5332 5337 5329 5334 5334 5329 5337 5332 5323 5320 4872 3637 3310 3462
23 5252 5644 6549 7717 7716 7737 7746 7735 7741 7739 7739 7741 7735 7746 7737 7716 7717 6549 5644 5252
5252 5644 6549 7717 7716 7737 7746 7735 7741 7739 7739 7741 7735 7746 7737 7716 7717 6549 5644 5252
24 8070 9411 10223 10818 10692 10757 10730 10737 10738 10736 10736 10738 10737 10730 10757 10692 10818 10223 9411 8070
8070 9411 10223 10818 10692 10757 10730 10737 10738 10736 10736 10738 10737 10730 10757 10692 10818 10223 9411 8070
25 11327 12948 12864 13185 13098 13130 13112 13124 13117 13120 13120 13117 13124 13112 13130 13098 13185 12864 12948 11327
11327 12948 12864 13185 13098 13130 13112 13124 13117 13120 13120 13117 13124 13112 13130 13098 13185 12864 12948 11327
26 12378 12831 12340 12674 12539 12580 12572 12573 12572 12573 12573 12572 12573 12572 12580 12539 12674 12340 12831 12378
12378 12831 12340 12674 12539 12580 12572 12573 12572 12573 12573 12572 12573 12572 12580 12539 12674 12340 12831 12378
27 9049 8243 8249 8366 8262 8323 8297 8304 8304 8303 8303 8304 8304 8297 8323 8262 8366 8249 8243 9049
9049 8243 8249 8366 8262 8323 8297 8304 8304 8303 8303 8304 8304 8297 8323 8262 8366 8249 8243 9049
28 3807 3029 3349 3223 3253 3261 3245 3257 3251 3253 3253 3251 3257 3245 3261 3253 3223 3349 3029 3807
3807 3029 3349 3223 3253 3261 3245 3257 3251 3253 3253 3251 3257 3245 3261 3253 3223 3349 3029 3807
29 743 512 664 566 624 594 606 604 602 604 604 602 604 606 594 624 566 664 512 743
743 512 664 566 624 594 606 604 602 604 604 602 604 606 594 624 566 664 512 743
30 42 24 40 26 38 28 36 30 34 32 32 34 30 36 28 38 26 40 24 42
42 24 40 26 38 28 36 30 34 32 32 34 30 36 28 38 26 40 24 42
Total 61490 62478 63696 68394 69786 71216 71870 72342 72576 72690 72690 72576 72342 71870 71216 69786 68394 63696 62478 61490
61490 62478 63696 68394 69786 71216 71870 72342 72576 72690 72690 72576 72342 71870 71216 69786 68394 63696 62478 61490
Grand total = 4*61490 + 4*62478 + 4*63696 + 4*68394 + 4*69786 + 4*71216 + 4*71870 + 4*72342 + 4*72576 + 4*72690
= 2746152
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
EN
0 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 1293 2091 3382 5472 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 1291 2090 3383 5474
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 5472 3382 2091 1293 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0 5474 3383 2090 1291 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0
20 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 1291 2090 3383 5474 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 1293 2091 3382 5472
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
39 5474 3383 2090 1291 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0 5472 3382 2091 1293 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73 + 1*116 + 1*117 + 1*188 + 1*189 + 1*304 + 1*306 + 1*493 + 1*494 + 1*798 + 1*799 +
1*1291 + 1*1293 + 1*2090 + 1*2091 + 1*3382 + 1*3383 + 1*5472 + 1*5474) +
36(40*0)
= 114616
Value repetition frequencies = 4(32*1 + 1*2 + 2*3) +
36(1*40)
= 1600
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*36
= 40
Number of distinct values = 35
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73 116 117 188
Frequency 1452 4 12 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 189 304 306 493 494 798 799 1291 1293 2090 2091 3382 3383 5472 5474
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 32*4 + 1*8 + 1*12 + 1*1452
= 1600
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*37
= 148
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 1412
Number of possible SN-EN pairs with SN != EN = 39*40
= 1560
a = 21, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 276 138
14 404 202
15 592 296
16 868 434
17 1272 636
18 1864 932
19 2732 1366
20 4004 2002
21 5868 2934
22 8600 4300
23 12596 6298
24 18308 9154
25 25604 12802
26 32068 16034
27 32420 16210
28 23580 11790
29 10876 5438
30 2684 1342
31 260 130
32 4 2
Total 185460 92728
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
L
3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0
0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0
6 0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0
0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0
7 0 0 0 0 5 2 0 0 0 0 0 0 0 0 0 2 5 0 0 0 0
0 0 0 0 5 2 0 0 0 0 0 0 0 0 0 2 5 0 0 0 0
8 0 0 0 0 1 7 2 0 0 0 0 0 0 0 2 7 1 0 0 0 0
0 0 0 0 1 7 2 0 0 0 0 0 0 0 2 7 1 0 0 0 0
9 0 0 0 0 0 4 9 2 0 0 0 0 0 2 9 4 0 0 0 0 0
0 0 0 0 0 4 9 2 0 0 0 0 0 2 9 4 0 0 0 0 0
10 0 0 0 0 0 0 9 11 2 0 0 0 2 11 9 0 0 0 0 0 0
0 0 0 0 0 0 9 11 2 0 0 0 2 11 9 0 0 0 0 0 0
11 0 0 0 0 0 0 1 16 13 2 0 2 13 16 1 0 0 0 0 0 0
0 0 0 0 0 0 1 16 13 2 0 2 13 16 1 0 0 0 0 0 0
12 0 0 0 0 0 0 0 5 25 15 4 15 25 5 0 0 0 0 0 0 0
0 0 0 0 0 0 0 5 25 15 4 15 25 5 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 14 38 34 38 14 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 14 38 34 38 14 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 3 49 98 49 3 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 3 49 98 49 3 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 2 21 70 110 70 21 2 0 0 0 0 0 0 0
0 0 0 0 0 0 0 2 21 70 110 70 21 2 0 0 0 0 0 0 0
16 0 0 0 0 0 0 2 23 81 91 40 91 81 23 2 0 0 0 0 0 0
0 0 0 0 0 0 2 23 81 91 40 91 81 23 2 0 0 0 0 0 0
17 0 0 0 0 0 2 25 100 140 50 2 50 140 100 25 2 0 0 0 0 0
0 0 0 0 0 2 25 100 140 50 2 50 140 100 25 2 0 0 0 0 0
18 0 0 0 0 2 27 121 204 105 7 0 7 105 204 121 27 2 0 0 0 0
0 0 0 0 2 27 121 204 105 7 0 7 105 204 121 27 2 0 0 0 0
19 0 0 0 2 29 144 285 196 27 0 0 0 27 196 285 144 29 2 0 0 0
0 0 0 2 29 144 285 196 27 0 0 0 27 196 285 144 29 2 0 0 0
20 0 0 2 31 169 385 336 77 1 0 0 0 1 77 336 385 169 31 2 0 0
0 0 2 31 169 385 336 77 1 0 0 0 1 77 336 385 169 31 2 0 0
21 0 2 33 196 506 540 182 8 0 0 0 0 0 8 182 540 506 196 33 2 0
0 2 33 196 506 540 182 8 0 0 0 0 0 8 182 540 506 196 33 2 0
22 2 35 225 650 825 378 35 0 0 0 0 0 0 0 35 378 825 650 225 35 2
2 35 225 650 825 378 35 0 0 0 0 0 0 0 35 378 825 650 225 35 2
23 37 256 819 1210 714 112 1 0 0 0 0 0 0 0 1 112 714 1210 819 256 37
37 256 819 1210 714 112 1 0 0 0 0 0 0 0 1 112 714 1210 819 256 37
24 289 1015 1716 1254 294 9 0 0 0 0 0 0 0 0 0 9 294 1254 1716 1015 289
289 1015 1716 1254 294 9 0 0 0 0 0 0 0 0 0 9 294 1254 1716 1015 289
25 1240 2366 2079 672 44 0 0 0 0 0 0 0 0 0 0 0 44 672 2079 2366 1240
1240 2366 2079 672 44 0 0 0 0 0 0 0 0 0 0 0 44 672 2079 2366 1240
26 3185 3289 1386 156 1 0 0 0 0 0 0 0 0 0 0 0 1 156 1386 3289 3185
3185 3289 1386 156 1 0 0 0 0 0 0 0 0 0 0 0 1 156 1386 3289 3185
27 5005 2640 450 10 0 0 0 0 0 0 0 0 0 0 0 0 0 10 450 2640 5005
5005 2640 450 10 0 0 0 0 0 0 0 0 0 0 0 0 0 10 450 2640 5005
28 4719 1122 54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 54 1122 4719
4719 1122 54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 54 1122 4719
29 2508 210 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 210 2508
2508 210 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 210 2508
30 660 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 660
660 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 660
31 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 65
65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 65
32 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Total 17711 10948 6768 4186 2592 1610 1008 644 432 322 288 322 432 644 1008 1610 2592 4186 6768 10948 17711
17711 10948 6768 4186 2592 1610 1008 644 432 322 288 322 432 644 1008 1610 2592 4186 6768 10948 17711
Grand total = 2*288 + 4*322 + 4*432 + 4*644 + 4*1008 + 4*1610 + 4*2592 + 4*4186 + 4*6768 + 4*10948 + 4*17711
= 185460
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
13 69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
14 101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
15 148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
16 217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
17 318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
18 466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
19 683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
20 1001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1001
1001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1001
21 1467 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1467
1467 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1467
22 2150 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2150
2150 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2150
23 3149 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3149
3149 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3149
24 4577 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4577
4577 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4577
25 6401 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6401
6401 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6401
26 8017 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8017
8017 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8017
27 8105 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8105
8105 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8105
28 5895 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5895
5895 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5895
29 2719 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2719
2719 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2719
30 671 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 671
671 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 671
31 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 65
65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 65
32 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Total 46365 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 46365
46365 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 46365
Grand total = 4*46365
= 185460
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
L
3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5
5 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5
6 8 7 6 7 2 0 0 0 0 0 0 0 0 0 0 0 2 7 6 7 8
8 7 6 7 2 0 0 0 0 0 0 0 0 0 0 0 2 7 6 7 8
7 11 10 8 9 9 2 0 0 0 0 0 0 0 0 0 2 9 9 8 10 11
11 10 8 9 9 2 0 0 0 0 0 0 0 0 0 2 9 9 8 10 11
8 16 14 12 12 13 11 2 0 0 0 0 0 0 0 2 11 13 12 12 14 16
16 14 12 12 13 11 2 0 0 0 0 0 0 0 2 11 13 12 12 14 16
9 24 21 18 19 18 20 13 2 0 0 0 0 0 2 13 20 18 19 18 21 24
24 21 18 19 18 20 13 2 0 0 0 0 0 2 13 20 18 19 18 21 24
10 35 31 26 28 27 27 29 15 2 0 0 0 2 15 29 27 27 28 26 31 35
35 31 26 28 27 27 29 15 2 0 0 0 2 15 29 27 27 28 26 31 35
11 51 45 38 40 40 39 40 40 17 2 0 2 17 40 40 39 40 40 38 45 51
51 45 38 40 40 39 40 40 17 2 0 2 17 40 40 39 40 40 38 45 51
12 75 66 56 59 58 59 57 60 53 19 4 19 53 60 57 59 58 59 56 66 75
75 66 56 59 58 59 57 60 53 19 4 19 53 60 57 59 58 59 56 66 75
13 110 97 82 87 85 86 86 84 89 70 42 70 89 84 86 86 85 87 82 97 110
110 97 82 87 85 86 86 84 89 70 42 70 89 84 86 86 85 87 82 97 110
14 161 142 120 127 125 125 126 125 126 152 170 152 126 125 126 125 125 127 120 142 161
161 142 120 127 125 125 126 125 126 152 170 152 126 125 126 125 125 127 120 142 161
15 236 208 176 186 183 184 183 187 207 288 364 288 207 187 183 184 183 186 176 208 236
236 208 176 186 183 184 183 187 207 288 364 288 207 187 183 184 183 186 176 208 236
16 346 305 258 273 268 270 271 296 396 516 546 516 396 296 271 270 268 273 258 305 346
346 305 258 273 268 270 271 296 396 516 546 516 396 296 271 270 268 273 258 305 346
17 507 447 378 400 393 397 424 542 730 798 780 798 730 542 424 397 393 400 378 447 507
507 447 378 400 393 397 424 542 730 798 780 798 730 542 424 397 393 400 378 447 507
18 743 655 554 586 578 610 751 1018 1161 1154 1156 1154 1161 1018 751 610 578 586 554 655 743
743 655 554 586 578 610 751 1018 1161 1154 1156 1154 1161 1018 751 610 578 586 554 655 743
19 1089 960 812 861 877 1049 1411 1682 1695 1690 1702 1690 1695 1682 1411 1049 877 861 812 960 1089
1089 960 812 861 877 1049 1411 1682 1695 1690 1702 1690 1695 1682 1411 1049 877 861 812 960 1089
20 1596 1407 1192 1294 1466 1956 2411 2491 2477 2489 2482 2489 2477 2491 2411 1956 1466 1294 1192 1407 1596
1596 1407 1192 1294 1466 1956 2411 2491 2477 2489 2482 2489 2477 2491 2411 1956 1466 1294 1192 1407 1596
21 2339 2064 1781 2105 2698 3431 3653 3629 3645 3643 3638 3643 3645 3629 3653 3431 2698 2105 1781 2064 2339
2339 2064 1781 2105 2698 3431 3653 3629 3645 3643 3638 3643 3645 3629 3653 3431 2698 2105 1781 2064 2339
22 3430 3061 2849 3789 4829 5339 5322 5338 5340 5333 5340 5333 5340 5338 5322 5339 4829 3789 2849 3061 3430
3430 3061 2849 3789 4829 5339 5322 5338 5340 5333 5340 5333 5340 5338 5322 5339 4829 3789 2849 3061 3430
23 5060 4752 5056 6843 7726 7816 7808 7826 7813 7818 7818 7818 7813 7826 7808 7816 7726 6843 5056 4752 5060
5060 4752 5056 6843 7726 7816 7808 7826 7813 7818 7818 7818 7813 7826 7808 7816 7726 6843 5056 4752 5060
24 7623 7961 9174 11166 11358 11364 11387 11373 11376 11379 11374 11379 11376 11373 11387 11364 11358 11166 9174 7961 7623
7623 7961 9174 11166 11358 11364 11387 11373 11376 11379 11374 11379 11376 11373 11387 11364 11358 11166 9174 7961 7623
25 11696 13424 14874 16111 15926 16020 15991 15993 15998 15994 15996 15994 15998 15993 15991 16020 15926 16111 14874 13424 11696
11696 13424 14874 16111 15926 16020 15991 15993 15998 15994 15996 15994 15998 15993 15991 16020 15926 16111 14874 13424 11696
26 16888 19501 19808 20399 20243 20313 20275 20295 20287 20288 20290 20288 20287 20295 20275 20313 20243 20399 19808 19501 16888
16888 19501 19808 20399 20243 20313 20275 20295 20287 20288 20290 20288 20287 20295 20275 20313 20243 20399 19808 19501 16888
27 19884 21261 20550 21083 20893 20948 20934 20940 20935 20939 20936 20939 20935 20940 20934 20948 20893 21083 20550 21261 19884
19884 21261 20550 21083 20893 20948 20934 20940 20935 20939 20936 20939 20935 20940 20934 20948 20893 21083 20550 21261 19884
28 16533 15717 15452 15767 15569 15663 15630 15637 15637 15637 15636 15637 15637 15637 15630 15663 15569 15767 15452 15717 16533
16533 15717 15452 15767 15569 15663 15630 15637 15637 15637 15636 15637 15637 15637 15630 15663 15569 15767 15452 15717 16533
29 8495 7102 7536 7423 7410 7453 7418 7437 7430 7431 7432 7431 7430 7437 7418 7453 7410 7423 7536 7102 8495
8495 7102 7536 7423 7410 7453 7418 7437 7430 7431 7432 7431 7430 7437 7418 7453 7410 7423 7536 7102 8495
30 2286 1674 2020 1826 1922 1884 1892 1896 1890 1894 1892 1894 1890 1896 1892 1884 1922 1826 2020 1674 2286
2286 1674 2020 1826 1922 1884 1892 1896 1890 1894 1892 1894 1890 1896 1892 1884 1922 1826 2020 1674 2286
31 239 150 220 166 206 178 196 186 190 190 188 190 190 186 196 178 206 166 220 150 239
239 150 220 166 206 178 196 186 190 190 188 190 190 186 196 178 206 166 220 150 239
32 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4
4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4
Total 99496 101094 103066 110670 112926 115246 116314 117094 117498 117726 117790 117726 117498 117094 116314 115246 112926 110670 103066 101094 99496
99496 101094 103066 110670 112926 115246 116314 117094 117498 117726 117790 117726 117498 117094 116314 115246 112926 110670 103066 101094 99496
Grand total = 4*99496 + 4*101094 + 4*103066 + 4*110670 + 4*112926 + 4*115246 + 4*116314 + 4*117094 + 4*117498 + 4*117726 + 2*117790
= 4680100
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
EN
0 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 1293 2091 3382 5472 8855 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 1291 2090 3383 5474 8856
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 8855 5472 3382 2091 1293 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0 8856 5474 3383 2090 1291 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0
21 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 1291 2090 3383 5474 8856 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 1293 2091 3382 5472 8855
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
41 8856 5474 3383 2090 1291 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0 8855 5472 3382 2091 1293 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73 + 1*116 + 1*117 + 1*188 + 1*189 + 1*304 + 1*306 + 1*493 + 1*494 + 1*798 + 1*799 +
1*1291 + 1*1293 + 1*2090 + 1*2091 + 1*3382 + 1*3383 + 1*5472 + 1*5474 + 1*8855 + 1*8856) +
38(42*0)
= 185460
Value repetition frequencies = 4(34*1 + 1*2 + 2*3) +
38(1*42)
= 1764
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*38
= 42
Number of distinct values = 37
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73 116 117 188
Frequency 1608 4 12 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 189 304 306 493 494 798 799 1291 1293 2090 2091 3382 3383 5472 5474 8855 8856
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 34*4 + 1*8 + 1*12 + 1*1608
= 1764
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*39
= 156
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 1566
Number of possible SN-EN pairs with SN != EN = 41*42
= 1722
a = 22, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 276 138
14 404 202
15 592 296
16 868 434
17 1272 636
18 1864 932
19 2732 1366
20 4004 2002
21 5868 2934
22 8600 4300
23 12604 6302
24 18464 9232
25 26900 13450
26 38052 19026
27 49220 24610
28 53064 26532
29 42908 21454
30 23276 11638
31 7388 3694
32 1104 552
33 48 24
Total 300088 150042
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
L
3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0
0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0
6 0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0
0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0
7 0 0 0 0 5 2 0 0 0 0 0 0 0 0 0 0 2 5 0 0 0 0
0 0 0 0 5 2 0 0 0 0 0 0 0 0 0 0 2 5 0 0 0 0
8 0 0 0 0 1 7 2 0 0 0 0 0 0 0 0 2 7 1 0 0 0 0
0 0 0 0 1 7 2 0 0 0 0 0 0 0 0 2 7 1 0 0 0 0
9 0 0 0 0 0 4 9 2 0 0 0 0 0 0 2 9 4 0 0 0 0 0
0 0 0 0 0 4 9 2 0 0 0 0 0 0 2 9 4 0 0 0 0 0
10 0 0 0 0 0 0 9 11 2 0 0 0 0 2 11 9 0 0 0 0 0 0
0 0 0 0 0 0 9 11 2 0 0 0 0 2 11 9 0 0 0 0 0 0
11 0 0 0 0 0 0 1 16 13 2 0 0 2 13 16 1 0 0 0 0 0 0
0 0 0 0 0 0 1 16 13 2 0 0 2 13 16 1 0 0 0 0 0 0
12 0 0 0 0 0 0 0 5 25 15 2 2 15 25 5 0 0 0 0 0 0 0
0 0 0 0 0 0 0 5 25 15 2 2 15 25 5 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 14 36 19 19 36 14 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 14 36 19 19 36 14 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 1 32 68 68 32 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 32 68 68 32 1 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 2 27 119 119 27 2 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 2 27 119 119 27 2 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 2 23 81 111 111 81 23 2 0 0 0 0 0 0 0
0 0 0 0 0 0 0 2 23 81 111 111 81 23 2 0 0 0 0 0 0 0
17 0 0 0 0 0 0 2 25 100 140 51 51 140 100 25 2 0 0 0 0 0 0
0 0 0 0 0 0 2 25 100 140 51 51 140 100 25 2 0 0 0 0 0 0
18 0 0 0 0 0 2 27 121 204 105 7 7 105 204 121 27 2 0 0 0 0 0
0 0 0 0 0 2 27 121 204 105 7 7 105 204 121 27 2 0 0 0 0 0
19 0 0 0 0 2 29 144 285 196 27 0 0 27 196 285 144 29 2 0 0 0 0
0 0 0 0 2 29 144 285 196 27 0 0 27 196 285 144 29 2 0 0 0 0
20 0 0 0 2 31 169 385 336 77 1 0 0 1 77 336 385 169 31 2 0 0 0
0 0 0 2 31 169 385 336 77 1 0 0 1 77 336 385 169 31 2 0 0 0
21 0 0 2 33 196 506 540 182 8 0 0 0 0 8 182 540 506 196 33 2 0 0
0 0 2 33 196 506 540 182 8 0 0 0 0 8 182 540 506 196 33 2 0 0
22 0 2 35 225 650 825 378 35 0 0 0 0 0 0 35 378 825 650 225 35 2 0
0 2 35 225 650 825 378 35 0 0 0 0 0 0 35 378 825 650 225 35 2 0
23 2 37 256 819 1210 714 112 1 0 0 0 0 0 0 1 112 714 1210 819 256 37 2
2 37 256 819 1210 714 112 1 0 0 0 0 0 0 1 112 714 1210 819 256 37 2
24 39 289 1015 1716 1254 294 9 0 0 0 0 0 0 0 0 9 294 1254 1716 1015 289 39
39 289 1015 1716 1254 294 9 0 0 0 0 0 0 0 0 9 294 1254 1716 1015 289 39
25 324 1240 2366 2079 672 44 0 0 0 0 0 0 0 0 0 0 44 672 2079 2366 1240 324
324 1240 2366 2079 672 44 0 0 0 0 0 0 0 0 0 0 44 672 2079 2366 1240 324
26 1496 3185 3289 1386 156 1 0 0 0 0 0 0 0 0 0 0 1 156 1386 3289 3185 1496
1496 3185 3289 1386 156 1 0 0 0 0 0 0 0 0 0 0 1 156 1386 3289 3185 1496
27 4200 5005 2640 450 10 0 0 0 0 0 0 0 0 0 0 0 0 10 450 2640 5005 4200
4200 5005 2640 450 10 0 0 0 0 0 0 0 0 0 0 0 0 10 450 2640 5005 4200
28 7371 4719 1122 54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 54 1122 4719 7371
7371 4719 1122 54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 54 1122 4719 7371
29 8008 2508 210 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 210 2508 8008
8008 2508 210 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 210 2508 8008
30 5148 660 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 660 5148
5148 660 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 660 5148
31 1782 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 65 1782
1782 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 65 1782
32 275 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 275
275 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 275
33 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
Total 28657 17713 10949 6770 4189 2597 1618 1021 665 466 377 377 466 665 1021 1618 2597 4189 6770 10949 17713 28657
28657 17713 10949 6770 4189 2597 1618 1021 665 466 377 377 466 665 1021 1618 2597 4189 6770 10949 17713 28657
Grand total = 4*377 + 4*466 + 4*665 + 4*1021 + 4*1618 + 4*2597 + 4*4189 + 4*6770 + 4*10949 + 4*17713 + 4*28657
= 300088
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
13 69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
14 101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
15 148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
16 217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
17 318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
18 466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
19 683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
20 1001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1001
1001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1001
21 1467 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1467
1467 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1467
22 2150 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2150
2150 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2150
23 3151 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3151
3151 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3151
24 4616 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4616
4616 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4616
25 6725 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6725
6725 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6725
26 9513 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9513
9513 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9513
27 12305 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12305
12305 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12305
28 13266 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13266
13266 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13266
29 10727 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10727
10727 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10727
30 5819 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5819
5819 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5819
31 1847 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1847
1847 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1847
32 276 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 276
276 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 276
33 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12
Total 75022 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 75022
75022 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 75022
Grand total = 4*75022
= 300088
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
L
3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5
5 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5
6 8 7 6 7 2 0 0 0 0 0 0 0 0 0 0 0 0 2 7 6 7 8
8 7 6 7 2 0 0 0 0 0 0 0 0 0 0 0 0 2 7 6 7 8
7 11 10 8 9 9 2 0 0 0 0 0 0 0 0 0 0 2 9 9 8 10 11
11 10 8 9 9 2 0 0 0 0 0 0 0 0 0 0 2 9 9 8 10 11
8 16 14 12 12 13 11 2 0 0 0 0 0 0 0 0 2 11 13 12 12 14 16
16 14 12 12 13 11 2 0 0 0 0 0 0 0 0 2 11 13 12 12 14 16
9 24 21 18 19 18 20 13 2 0 0 0 0 0 0 2 13 20 18 19 18 21 24
24 21 18 19 18 20 13 2 0 0 0 0 0 0 2 13 20 18 19 18 21 24
10 35 31 26 28 27 27 29 15 2 0 0 0 0 2 15 29 27 27 28 26 31 35
35 31 26 28 27 27 29 15 2 0 0 0 0 2 15 29 27 27 28 26 31 35
11 51 45 38 40 40 39 40 40 17 2 0 0 2 17 40 40 39 40 40 38 45 51
51 45 38 40 40 39 40 40 17 2 0 0 2 17 40 40 39 40 40 38 45 51
12 75 66 56 59 58 59 57 60 53 19 2 2 19 53 60 57 59 58 59 56 66 75
75 66 56 59 58 59 57 60 53 19 2 2 19 53 60 57 59 58 59 56 66 75
13 110 97 82 87 85 86 86 84 89 68 23 23 68 89 84 86 86 85 87 82 97 110
110 97 82 87 85 86 86 84 89 68 23 23 68 89 84 86 86 85 87 82 97 110
14 161 142 120 127 125 125 126 125 124 131 108 108 131 124 125 126 125 125 127 120 142 161
161 142 120 127 125 125 126 125 124 131 108 108 131 124 125 126 125 125 127 120 142 161
15 236 208 176 186 183 184 183 185 184 209 286 286 209 184 185 183 184 183 186 176 208 236
236 208 176 186 183 184 183 185 184 209 286 286 209 184 185 183 184 183 186 176 208 236
16 346 305 258 273 268 270 269 271 298 391 523 523 391 298 271 269 270 268 273 258 305 346
346 305 258 273 268 270 269 271 298 391 523 523 391 298 271 269 270 268 273 258 305 346
17 507 447 378 400 393 395 397 423 543 731 792 792 731 543 423 397 395 393 400 378 447 507
507 447 378 400 393 395 397 423 543 731 792 792 731 543 423 397 395 393 400 378 447 507
18 743 655 554 586 576 581 609 752 1016 1164 1152 1152 1164 1016 752 609 581 576 586 554 655 743
743 655 554 586 576 581 609 752 1016 1164 1152 1152 1164 1016 752 609 581 576 586 554 655 743
19 1089 960 812 859 846 882 1047 1412 1682 1693 1695 1695 1693 1682 1412 1047 882 846 859 812 960 1089
1089 960 812 859 846 882 1047 1412 1682 1693 1695 1695 1693 1682 1412 1047 882 846 859 812 960 1089
20 1596 1407 1190 1261 1272 1473 1954 2411 2492 2476 2488 2488 2476 2492 2411 1954 1473 1272 1261 1190 1407 1596
1596 1407 1190 1261 1272 1473 1954 2411 2492 2476 2488 2488 2476 2492 2411 1954 1473 1272 1261 1190 1407 1596
21 2339 2062 1746 1882 2073 2708 3428 3654 3628 3647 3640 3640 3647 3628 3654 3428 2708 2073 1882 1746 2062 2339
2339 2062 1746 1882 2073 2708 3428 3654 3628 3647 3640 3640 3647 3628 3654 3428 2708 2073 1882 1746 2062 2339
22 3428 3024 2595 2997 3742 4844 5334 5324 5337 5340 5335 5335 5340 5337 5324 5334 4844 3742 2997 2595 3024 3428
3428 3024 2595 2997 3742 4844 5334 5324 5337 5340 5335 5335 5340 5337 5324 5334 4844 3742 2997 2595 3024 3428
23 5026 4470 4074 5277 6778 7752 7813 7814 7830 7816 7823 7823 7816 7830 7814 7813 7752 6778 5277 4074 4470 5026
5026 4470 4074 5277 6778 7752 7813 7814 7830 7816 7823 7823 7816 7830 7814 7813 7752 6778 5277 4074 4470 5026
24 7401 6851 7060 9573 11147 11472 11436 11472 11454 11459 11459 11459 11459 11454 11472 11436 11472 11147 9573 7060 6851 7401
7401 6851 7060 9573 11147 11472 11436 11472 11454 11459 11459 11459 11459 11454 11472 11436 11472 11147 9573 7060 6851 7401
25 11085 11271 12811 16038 16678 16687 16719 16710 16705 16713 16708 16708 16713 16705 16710 16719 16687 16678 16038 12811 11271 11085
11085 11271 12811 16038 16678 16687 16719 16710 16705 16713 16708 16708 16713 16705 16710 16719 16687 16678 16038 12811 11271 11085
26 16948 19068 21423 23828 23642 23757 23737 23728 23739 23733 23735 23735 23733 23739 23728 23737 23757 23642 23828 21423 19068 16948
16948 19068 21423 23828 23642 23757 23737 23728 23739 23733 23735 23735 23733 23739 23728 23737 23757 23642 23828 21423 19068 16948
27 24958 28912 30031 31217 30935 31070 31005 31032 31025 31024 31026 31026 31024 31025 31032 31005 31070 30935 31217 30031 28912 24958
24958 28912 30031 31217 30935 31070 31005 31032 31025 31024 31026 31026 31024 31025 31032 31005 31070 30935 31217 30031 28912 24958
28 31211 34209 33414 34268 33991 34078 34046 34064 34052 34059 34056 34056 34059 34052 34064 34046 34078 33991 34268 33414 34209 31211
31211 34209 33414 34268 33991 34078 34046 34064 34052 34059 34056 34056 34059 34052 34064 34046 34078 33991 34268 33414 34209 31211
29 28911 28548 27792 28441 28108 28243 28202 28210 28209 28210 28209 28209 28210 28209 28210 28202 28243 28108 28441 27792 28548 28911
28911 28548 27792 28441 28108 28243 28202 28210 28209 28210 28209 28209 28210 28209 28210 28202 28243 28108 28441 27792 28548 28911
30 17544 15345 15785 15789 15672 15776 15715 15741 15734 15734 15735 15735 15734 15734 15741 15715 15776 15672 15789 15785 15345 17544
17544 15345 15785 15789 15672 15776 15715 15741 15734 15734 15735 15735 15734 15734 15741 15715 15776 15672 15789 15785 15345 17544
31 6093 4703 5369 5049 5175 5145 5137 5153 5141 5147 5145 5145 5147 5141 5153 5137 5145 5175 5049 5369 4703 6093
6093 4703 5369 5049 5175 5145 5137 5153 5141 5147 5145 5145 5147 5141 5153 5137 5145 5175 5049 5369 4703 6093
32 982 662 884 732 830 772 802 790 792 794 792 792 794 792 790 802 772 830 732 884 662 982
982 662 884 732 830 772 802 790 792 794 792 792 794 792 790 802 772 830 732 884 662 982
33 46 26 44 28 42 30 40 32 38 34 36 36 34 38 32 40 30 42 28 44 26 46
46 26 44 28 42 30 40 32 38 34 36 36 34 38 32 40 30 42 28 44 26 46
Total 160991 163576 166768 179074 182728 186488 188226 189504 190184 190594 190768 190768 190594 190184 189504 188226 186488 182728 179074 166768 163576 160991
160991 163576 166768 179074 182728 186488 188226 189504 190184 190594 190768 190768 190594 190184 189504 188226 186488 182728 179074 166768 163576 160991
Grand total = 4*160991 + 4*163576 + 4*166768 + 4*179074 + 4*182728 + 4*186488 + 4*188226 + 4*189504 + 4*190184 + 4*190594 + 4*190768
= 7955604
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43
EN
0 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 1293 2091 3382 5472 8855 14329 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494
798 1291 2090 3383 5474 8856 14328
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
21 14329 8855 5472 3382 2091 1293 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0 14328 8856 5474 3383 2090 1291 798 494 306 189 116 71 44 28 18
11 6 3 2 2 2 0
22 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 1291 2090 3383 5474 8856 14328 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493
799 1293 2091 3382 5472 8855 14329
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
43 14328 8856 5474 3383 2090 1291 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0 14329 8855 5472 3382 2091 1293 799 493 304 188 117 73 45 27 16
10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73 + 1*116 + 1*117 + 1*188 + 1*189 + 1*304 + 1*306 + 1*493 + 1*494 + 1*798 + 1*799 +
1*1291 + 1*1293 + 1*2090 + 1*2091 + 1*3382 + 1*3383 + 1*5472 + 1*5474 + 1*8855 + 1*8856 + 1*14328 + 1*14329) +
40(44*0)
= 300088
Value repetition frequencies = 4(36*1 + 1*2 + 2*3) +
40(1*44)
= 1936
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*40
= 44
Number of distinct values = 39
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73 116 117 188
Frequency 1772 4 12 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 189 304 306 493 494 798 799 1291 1293 2090 2091 3382 3383 5472 5474 8855 8856 14328 14329
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 36*4 + 1*8 + 1*12 + 1*1772
= 1936
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*41
= 164
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 1728
Number of possible SN-EN pairs with SN != EN = 43*44
= 1892
a = 23, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 276 138
14 404 202
15 592 296
16 868 434
17 1272 636
18 1864 932
19 2732 1366
20 4004 2002
21 5868 2934
22 8600 4300
23 12604 6302
24 18472 9236
25 27064 13532
26 39496 19748
27 56360 28180
28 74824 37412
29 85132 42566
30 75328 37664
31 46856 23428
32 18264 9132
33 3788 1894
34 308 154
35 4 2
Total 485560 242778
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
L
3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0
0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0
6 0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0
0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0
7 0 0 0 0 5 2 0 0 0 0 0 0 0 0 0 0 0 2 5 0 0 0 0
0 0 0 0 5 2 0 0 0 0 0 0 0 0 0 0 0 2 5 0 0 0 0
8 0 0 0 0 1 7 2 0 0 0 0 0 0 0 0 0 2 7 1 0 0 0 0
0 0 0 0 1 7 2 0 0 0 0 0 0 0 0 0 2 7 1 0 0 0 0
9 0 0 0 0 0 4 9 2 0 0 0 0 0 0 0 2 9 4 0 0 0 0 0
0 0 0 0 0 4 9 2 0 0 0 0 0 0 0 2 9 4 0 0 0 0 0
10 0 0 0 0 0 0 9 11 2 0 0 0 0 0 2 11 9 0 0 0 0 0 0
0 0 0 0 0 0 9 11 2 0 0 0 0 0 2 11 9 0 0 0 0 0 0
11 0 0 0 0 0 0 1 16 13 2 0 0 0 2 13 16 1 0 0 0 0 0 0
0 0 0 0 0 0 1 16 13 2 0 0 0 2 13 16 1 0 0 0 0 0 0
12 0 0 0 0 0 0 0 5 25 15 2 0 2 15 25 5 0 0 0 0 0 0 0
0 0 0 0 0 0 0 5 25 15 2 0 2 15 25 5 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 14 36 17 4 17 36 14 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 14 36 17 4 17 36 14 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 1 30 51 38 51 30 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 30 51 38 51 30 1 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 8 76 128 76 8 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 8 76 128 76 8 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 2 23 101 182 101 23 2 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 2 23 101 182 101 23 2 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 2 25 100 141 100 141 100 25 2 0 0 0 0 0 0 0
0 0 0 0 0 0 0 2 25 100 141 100 141 100 25 2 0 0 0 0 0 0 0
18 0 0 0 0 0 0 2 27 121 204 105 14 105 204 121 27 2 0 0 0 0 0 0
0 0 0 0 0 0 2 27 121 204 105 14 105 204 121 27 2 0 0 0 0 0 0
19 0 0 0 0 0 2 29 144 285 196 27 0 27 196 285 144 29 2 0 0 0 0 0
0 0 0 0 0 2 29 144 285 196 27 0 27 196 285 144 29 2 0 0 0 0 0
20 0 0 0 0 2 31 169 385 336 77 1 0 1 77 336 385 169 31 2 0 0 0 0
0 0 0 0 2 31 169 385 336 77 1 0 1 77 336 385 169 31 2 0 0 0 0
21 0 0 0 2 33 196 506 540 182 8 0 0 0 8 182 540 506 196 33 2 0 0 0
0 0 0 2 33 196 506 540 182 8 0 0 0 8 182 540 506 196 33 2 0 0 0
22 0 0 2 35 225 650 825 378 35 0 0 0 0 0 35 378 825 650 225 35 2 0 0
0 0 2 35 225 650 825 378 35 0 0 0 0 0 35 378 825 650 225 35 2 0 0
23 0 2 37 256 819 1210 714 112 1 0 0 0 0 0 1 112 714 1210 819 256 37 2 0
0 2 37 256 819 1210 714 112 1 0 0 0 0 0 1 112 714 1210 819 256 37 2 0
24 2 39 289 1015 1716 1254 294 9 0 0 0 0 0 0 0 9 294 1254 1716 1015 289 39 2
2 39 289 1015 1716 1254 294 9 0 0 0 0 0 0 0 9 294 1254 1716 1015 289 39 2
25 41 324 1240 2366 2079 672 44 0 0 0 0 0 0 0 0 0 44 672 2079 2366 1240 324 41
41 324 1240 2366 2079 672 44 0 0 0 0 0 0 0 0 0 44 672 2079 2366 1240 324 41
26 361 1496 3185 3289 1386 156 1 0 0 0 0 0 0 0 0 0 1 156 1386 3289 3185 1496 361
361 1496 3185 3289 1386 156 1 0 0 0 0 0 0 0 0 0 1 156 1386 3289 3185 1496 361
27 1785 4200 5005 2640 450 10 0 0 0 0 0 0 0 0 0 0 0 10 450 2640 5005 4200 1785
1785 4200 5005 2640 450 10 0 0 0 0 0 0 0 0 0 0 0 10 450 2640 5005 4200 1785
28 5440 7371 4719 1122 54 0 0 0 0 0 0 0 0 0 0 0 0 0 54 1122 4719 7371 5440
5440 7371 4719 1122 54 0 0 0 0 0 0 0 0 0 0 0 0 0 54 1122 4719 7371 5440
29 10556 8008 2508 210 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 210 2508 8008 10556
10556 8008 2508 210 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 210 2508 8008 10556
30 13013 5148 660 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 660 5148 13013
13013 5148 660 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 660 5148 13013
31 9867 1782 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 65 1782 9867
9867 1782 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 65 1782 9867
32 4290 275 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 275 4290
4290 275 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 275 4290
33 935 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 935
935 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 935
34 77 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 77
77 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 77
35 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Total 46368 28659 17714 10951 6773 4194 2605 1631 1042 699 521 466 521 699 1042 1631 2605 4194 6773 10951 17714 28659 46368
46368 28659 17714 10951 6773 4194 2605 1631 1042 699 521 466 521 699 1042 1631 2605 4194 6773 10951 17714 28659 46368
Grand total = 2*466 + 4*521 + 4*699 + 4*1042 + 4*1631 + 4*2605 + 4*4194 + 4*6773 + 4*10951 + 4*17714 + 4*28659 + 4*46368
= 485560
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
13 69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
14 101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
15 148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
16 217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
17 318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
18 466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
19 683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
20 1001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1001
1001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1001
21 1467 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1467
1467 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1467
22 2150 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2150
2150 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2150
23 3151 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3151
3151 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3151
24 4618 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4618
4618 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4618
25 6766 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6766
6766 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6766
26 9874 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9874
9874 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9874
27 14090 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14090
14090 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14090
28 18706 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18706
18706 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18706
29 21283 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21283
21283 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21283
30 18832 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18832
18832 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18832
31 11714 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11714
11714 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11714
32 4566 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4566
4566 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4566
33 947 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 947
947 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 947
34 77 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 77
77 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 77
35 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Total 121390 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 121390
121390 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 121390
Grand total = 4*121390
= 485560
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
L
3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5
5 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5
6 8 7 6 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 6 7 8
8 7 6 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 6 7 8
7 11 10 8 9 9 2 0 0 0 0 0 0 0 0 0 0 0 2 9 9 8 10 11
11 10 8 9 9 2 0 0 0 0 0 0 0 0 0 0 0 2 9 9 8 10 11
8 16 14 12 12 13 11 2 0 0 0 0 0 0 0 0 0 2 11 13 12 12 14 16
16 14 12 12 13 11 2 0 0 0 0 0 0 0 0 0 2 11 13 12 12 14 16
9 24 21 18 19 18 20 13 2 0 0 0 0 0 0 0 2 13 20 18 19 18 21 24
24 21 18 19 18 20 13 2 0 0 0 0 0 0 0 2 13 20 18 19 18 21 24
10 35 31 26 28 27 27 29 15 2 0 0 0 0 0 2 15 29 27 27 28 26 31 35
35 31 26 28 27 27 29 15 2 0 0 0 0 0 2 15 29 27 27 28 26 31 35
11 51 45 38 40 40 39 40 40 17 2 0 0 0 2 17 40 40 39 40 40 38 45 51
51 45 38 40 40 39 40 40 17 2 0 0 0 2 17 40 40 39 40 40 38 45 51
12 75 66 56 59 58 59 57 60 53 19 2 0 2 19 53 60 57 59 58 59 56 66 75
75 66 56 59 58 59 57 60 53 19 2 0 2 19 53 60 57 59 58 59 56 66 75
13 110 97 82 87 85 86 86 84 89 68 21 4 21 68 89 84 86 86 85 87 82 97 110
110 97 82 87 85 86 86 84 89 68 21 4 21 68 89 84 86 86 85 87 82 97 110
14 161 142 120 127 125 125 126 125 124 129 87 46 87 129 124 125 126 125 125 127 120 142 161
161 142 120 127 125 125 126 125 124 129 87 46 87 129 124 125 126 125 125 127 120 142 161
15 236 208 176 186 183 184 183 185 182 186 207 208 207 186 182 185 183 184 183 186 176 208 236
236 208 176 186 183 184 183 185 182 186 207 208 207 186 182 185 183 184 183 186 176 208 236
16 346 305 258 273 268 270 269 269 273 293 398 500 398 293 273 269 269 270 268 273 258 305 346
346 305 258 273 268 270 269 269 273 293 398 500 398 293 273 269 269 270 268 273 258 305 346
17 507 447 378 400 393 395 395 396 424 544 725 804 725 544 424 396 395 395 393 400 378 447 507
507 447 378 400 393 395 395 396 424 544 725 804 725 544 424 396 395 395 393 400 378 447 507
18 743 655 554 586 576 579 580 610 750 1019 1162 1148 1162 1019 750 610 580 579 576 586 554 655 743
743 655 554 586 576 579 580 610 750 1019 1162 1148 1162 1019 750 610 580 579 576 586 554 655 743
19 1089 960 812 859 844 851 880 1048 1412 1680 1698 1688 1698 1680 1412 1048 880 851 844 859 812 960 1089
1089 960 812 859 844 851 880 1048 1412 1680 1698 1688 1698 1680 1412 1048 880 851 844 859 812 960 1089
20 1596 1407 1190 1259 1239 1279 1471 1954 2412 2491 2475 2494 2475 2491 2412 1954 1471 1279 1239 1259 1190 1407 1596
1596 1407 1190 1259 1239 1279 1471 1954 2412 2491 2475 2494 2475 2491 2412 1954 1471 1279 1239 1259 1190 1407 1596
21 2339 2062 1744 1847 1850 2083 2705 3429 3653 3630 3644 3642 3644 3630 3653 3429 2705 2083 1850 1847 1744 2062 2339
2339 2062 1744 1847 1850 2083 2705 3429 3653 3630 3644 3642 3644 3630 3653 3429 2705 2083 1850 1847 1744 2062 2339
22 3428 3022 2558 2743 2950 3757 4839 5336 5323 5337 5342 5330 5342 5337 5323 5336 4839 3757 2950 2743 2558 3022 3428
3428 3022 2558 2743 2950 3757 4839 5336 5323 5337 5342 5330 5342 5337 5323 5336 4839 3757 2950 2743 2558 3022 3428
23 5024 4431 3787 4291 5208 6800 7745 7815 7814 7829 7817 7824 7817 7829 7814 7815 7745 6800 5208 4291 3787 4431 5024
5024 4431 3787 4291 5208 6800 7745 7815 7814 7829 7817 7824 7817 7829 7814 7815 7745 6800 5208 4291 3787 4431 5024
24 7365 6534 5855 7382 9476 11183 11466 11443 11475 11459 11461 11466 11461 11459 11475 11443 11466 11183 9476 7382 5855 6534 7365
7365 6534 5855 7382 9476 11183 11466 11443 11475 11459 11461 11466 11461 11459 11475 11443 11466 11183 9476 7382 5855 6534 7365
25 10831 9912 9909 13362 15976 16811 16758 16810 16794 16792 16799 16792 16799 16792 16794 16810 16758 16811 15976 13362 9909 9912 10831
10831 9912 9909 13362 15976 16811 16758 16810 16794 16792 16799 16792 16799 16792 16794 16810 16758 16811 15976 13362 9909 9912 10831
26 16145 16023 17867 22881 24404 24503 24527 24536 24518 24531 24526 24526 24526 24531 24518 24536 24527 24503 24404 22881 17867 16023 16145
16145 16023 17867 22881 24404 24503 24527 24536 24518 24531 24526 24526 24526 24531 24518 24536 24527 24503 24404 22881 17867 16023 16145
27 24571 27029 30597 34994 35000 35121 35124 35101 35115 35112 35109 35114 35109 35112 35115 35101 35124 35121 35000 34994 30597 27029 24571
24571 27029 30597 34994 35000 35121 35124 35101 35115 35112 35109 35114 35109 35112 35115 35101 35124 35121 35000 34994 30597 27029 24571
28 36654 42336 44905 47328 46861 47090 46996 47025 47023 47018 47022 47020 47022 47018 47023 47025 46996 47090 46861 47328 44905 42336 36654
36654 42336 44905 47328 46861 47090 46996 47025 47023 47018 47022 47020 47022 47018 47023 47025 46996 47090 46861 47328 44905 42336 36654
29 48099 53710 53222 54667 54234 54391 54321 54359 54339 54347 54346 54344 54346 54347 54339 54359 54321 54391 54234 54667 53222 53710 48099
48099 53710 53222 54667 54234 54391 54321 54359 54339 54347 54346 54344 54346 54347 54339 54359 54321 54391 54234 54667 53222 53710 48099
30 48795 49809 48342 49524 49001 49191 49136 49150 49144 49149 49145 49148 49145 49149 49144 49150 49136 49191 49001 49524 48342 49809 48795
48795 49809 48342 49524 49001 49191 49136 49150 49144 49149 49145 49148 49145 49149 49144 49150 49136 49191 49001 49524 48342 49809 48795
31 34077 31062 31237 31556 31241 31439 31345 31378 31371 31371 31371 31372 31371 31371 31371 31378 31345 31439 31241 31556 31237 31062 34077
34077 31062 31237 31556 31241 31439 31345 31378 31371 31371 31371 31372 31371 31371 31371 31378 31345 31439 31241 31556 31237 31062 34077
32 14588 11805 12905 12472 12585 12598 12555 12590 12571 12578 12577 12576 12577 12578 12571 12590 12555 12598 12585 12472 12905 11805 14588
14588 11805 12905 12472 12585 12598 12555 12590 12571 12578 12577 12576 12577 12578 12571 12590 12555 12598 12585 12472 12905 11805 14588
33 3268 2336 2904 2558 2752 2656 2694 2686 2682 2688 2684 2686 2684 2688 2682 2686 2694 2656 2752 2558 2904 2336 3268
3268 2336 2904 2558 2752 2656 2694 2686 2682 2688 2684 2686 2684 2688 2682 2686 2694 2656 2752 2558 2904 2336 3268
34 285 176 264 194 248 208 236 218 228 224 224 226 224 224 228 218 236 208 248 194 264 176 285
285 176 264 194 248 208 236 218 228 224 224 226 224 224 228 218 236 208 248 194 264 176 285
35 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4
4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4
Total 260492 264674 269840 289754 295670 301760 304582 306666 307792 308498 308846 308960 308846 308498 307792 306666 304582 301760 295670 289754 269840 264674 260492
260492 264674 269840 289754 295670 301760 304582 306666 307792 308498 308846 308960 308846 308498 307792 306666 304582 301760 295670 289754 269840 264674 260492
Grand total = 4*260492 + 4*264674 + 4*269840 + 4*289754 + 4*295670 + 4*301760 + 4*304582 + 4*306666 + 4*307792 + 4*308498 + 4*308846 + 2*308960
= 13492216
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
EN
0 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 1293 2091 3382 5472 8855 14329 23185 0 2 2 2 3 6 11 18 28 44 71 116 189 306
494 798 1291 2090 3383 5474 8856 14328 23183
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
22 23185 14329 8855 5472 3382 2091 1293 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0 23183 14328 8856 5474 3383 2090 1291 798 494 306 189 116 71 44
28 18 11 6 3 2 2 2 0
23 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 1291 2090 3383 5474 8856 14328 23183 0 0 1 3 5 7 10 16 27 45 73 117 188 304
493 799 1293 2091 3382 5472 8855 14329 23185
24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
43 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
45 23183 14328 8856 5474 3383 2090 1291 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0 23185 14329 8855 5472 3382 2091 1293 799 493 304 188 117 73 45
27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73 + 1*116 + 1*117 + 1*188 + 1*189 + 1*304 + 1*306 + 1*493 + 1*494 + 1*798 + 1*799 +
1*1291 + 1*1293 + 1*2090 + 1*2091 + 1*3382 + 1*3383 + 1*5472 + 1*5474 + 1*8855 + 1*8856 + 1*14328 + 1*14329 + 1*23183 + 1*23185) +
42(46*0)
= 485560
Value repetition frequencies = 4(38*1 + 1*2 + 2*3) +
42(1*46)
= 2116
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*42
= 46
Number of distinct values = 41
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73 116 117 188
Frequency 1944 4 12 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 189 304 306 493 494 798 799 1291 1293 2090 2091 3382 3383 5472 5474 8855 8856 14328 14329 23183
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 23185
Frequency 4
Sum of distinct value frequencies = 38*4 + 1*8 + 1*12 + 1*1944
= 2116
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*43
= 172
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 1898
Number of possible SN-EN pairs with SN != EN = 45*46
= 2070
a = 24, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 276 138
14 404 202
15 592 296
16 868 434
17 1272 636
18 1864 932
19 2732 1366
20 4004 2002
21 5868 2934
22 8600 4300
23 12604 6302
24 18472 9236
25 27072 13536
26 39668 19834
27 57960 28980
28 83260 41630
29 112876 56438
30 134352 67176
31 128392 64196
32 89764 44882
33 41540 20770
34 11176 5588
35 1412 706
36 52 26
Total 785660 392828
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
L
3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0
0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0
6 0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0
0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0
7 0 0 0 0 5 2 0 0 0 0 0 0 0 0 0 0 0 0 2 5 0 0 0 0
0 0 0 0 5 2 0 0 0 0 0 0 0 0 0 0 0 0 2 5 0 0 0 0
8 0 0 0 0 1 7 2 0 0 0 0 0 0 0 0 0 0 2 7 1 0 0 0 0
0 0 0 0 1 7 2 0 0 0 0 0 0 0 0 0 0 2 7 1 0 0 0 0
9 0 0 0 0 0 4 9 2 0 0 0 0 0 0 0 0 2 9 4 0 0 0 0 0
0 0 0 0 0 4 9 2 0 0 0 0 0 0 0 0 2 9 4 0 0 0 0 0
10 0 0 0 0 0 0 9 11 2 0 0 0 0 0 0 2 11 9 0 0 0 0 0 0
0 0 0 0 0 0 9 11 2 0 0 0 0 0 0 2 11 9 0 0 0 0 0 0
11 0 0 0 0 0 0 1 16 13 2 0 0 0 0 2 13 16 1 0 0 0 0 0 0
0 0 0 0 0 0 1 16 13 2 0 0 0 0 2 13 16 1 0 0 0 0 0 0
12 0 0 0 0 0 0 0 5 25 15 2 0 0 2 15 25 5 0 0 0 0 0 0 0
0 0 0 0 0 0 0 5 25 15 2 0 0 2 15 25 5 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 14 36 17 2 2 17 36 14 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 14 36 17 2 2 17 36 14 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 1 30 49 21 21 49 30 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 30 49 21 21 49 30 1 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 6 57 85 85 57 6 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 6 57 85 85 57 6 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 2 43 172 172 43 2 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 2 43 172 172 43 2 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 2 25 101 190 190 101 25 2 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 2 25 101 190 190 101 25 2 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 2 27 121 204 112 112 204 121 27 2 0 0 0 0 0 0 0
0 0 0 0 0 0 0 2 27 121 204 112 112 204 121 27 2 0 0 0 0 0 0 0
19 0 0 0 0 0 0 2 29 144 285 196 27 27 196 285 144 29 2 0 0 0 0 0 0
0 0 0 0 0 0 2 29 144 285 196 27 27 196 285 144 29 2 0 0 0 0 0 0
20 0 0 0 0 0 2 31 169 385 336 77 1 1 77 336 385 169 31 2 0 0 0 0 0
0 0 0 0 0 2 31 169 385 336 77 1 1 77 336 385 169 31 2 0 0 0 0 0
21 0 0 0 0 2 33 196 506 540 182 8 0 0 8 182 540 506 196 33 2 0 0 0 0
0 0 0 0 2 33 196 506 540 182 8 0 0 8 182 540 506 196 33 2 0 0 0 0
22 0 0 0 2 35 225 650 825 378 35 0 0 0 0 35 378 825 650 225 35 2 0 0 0
0 0 0 2 35 225 650 825 378 35 0 0 0 0 35 378 825 650 225 35 2 0 0 0
23 0 0 2 37 256 819 1210 714 112 1 0 0 0 0 1 112 714 1210 819 256 37 2 0 0
0 0 2 37 256 819 1210 714 112 1 0 0 0 0 1 112 714 1210 819 256 37 2 0 0
24 0 2 39 289 1015 1716 1254 294 9 0 0 0 0 0 0 9 294 1254 1716 1015 289 39 2 0
0 2 39 289 1015 1716 1254 294 9 0 0 0 0 0 0 9 294 1254 1716 1015 289 39 2 0
25 2 41 324 1240 2366 2079 672 44 0 0 0 0 0 0 0 0 44 672 2079 2366 1240 324 41 2
2 41 324 1240 2366 2079 672 44 0 0 0 0 0 0 0 0 44 672 2079 2366 1240 324 41 2
26 43 361 1496 3185 3289 1386 156 1 0 0 0 0 0 0 0 0 1 156 1386 3289 3185 1496 361 43
43 361 1496 3185 3289 1386 156 1 0 0 0 0 0 0 0 0 1 156 1386 3289 3185 1496 361 43
27 400 1785 4200 5005 2640 450 10 0 0 0 0 0 0 0 0 0 0 10 450 2640 5005 4200 1785 400
400 1785 4200 5005 2640 450 10 0 0 0 0 0 0 0 0 0 0 10 450 2640 5005 4200 1785 400
28 2109 5440 7371 4719 1122 54 0 0 0 0 0 0 0 0 0 0 0 0 54 1122 4719 7371 5440 2109
2109 5440 7371 4719 1122 54 0 0 0 0 0 0 0 0 0 0 0 0 54 1122 4719 7371 5440 2109
29 6936 10556 8008 2508 210 1 0 0 0 0 0 0 0 0 0 0 0 0 1 210 2508 8008 10556 6936
6936 10556 8008 2508 210 1 0 0 0 0 0 0 0 0 0 0 0 0 1 210 2508 8008 10556 6936
30 14756 13013 5148 660 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 660 5148 13013 14756
14756 13013 5148 660 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 660 5148 13013 14756
31 20384 9867 1782 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 65 1782 9867 20384
20384 9867 1782 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 65 1782 9867 20384
32 17875 4290 275 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 275 4290 17875
17875 4290 275 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 275 4290 17875
33 9438 935 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 935 9438
9438 935 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 935 9438
34 2717 77 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 77 2717
2717 77 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 77 2717
35 352 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 352
352 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 352
36 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13
Total 75025 46370 28660 17716 10954 6778 4202 2618 1652 1076 754 610 610 754 1076 1652 2618 4202 6778 10954 17716 28660 46370 75025
75025 46370 28660 17716 10954 6778 4202 2618 1652 1076 754 610 610 754 1076 1652 2618 4202 6778 10954 17716 28660 46370 75025
Grand total = 4*610 + 4*754 + 4*1076 + 4*1652 + 4*2618 + 4*4202 + 4*6778 + 4*10954 + 4*17716 + 4*28660 + 4*46370 + 4*75025
= 785660
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
13 69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
14 101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
15 148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
16 217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
17 318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
18 466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
19 683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
20 1001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1001
1001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1001
21 1467 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1467
1467 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1467
22 2150 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2150
2150 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2150
23 3151 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3151
3151 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3151
24 4618 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4618
4618 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4618
25 6768 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6768
6768 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6768
26 9917 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9917
9917 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9917
27 14490 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14490
14490 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14490
28 20815 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 20815
20815 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 20815
29 28219 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28219
28219 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28219
30 33588 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 33588
33588 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 33588
31 32098 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32098
32098 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32098
32 22441 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22441
22441 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22441
33 10385 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10385
10385 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10385
34 2794 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2794
2794 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2794
35 353 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 353
353 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 353
36 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13
Total 196415 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 196415
196415 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 196415
Grand total = 4*196415
= 785660
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
L
3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5
5 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5
6 8 7 6 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 6 7 8
8 7 6 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 6 7 8
7 11 10 8 9 9 2 0 0 0 0 0 0 0 0 0 0 0 0 2 9 9 8 10 11
11 10 8 9 9 2 0 0 0 0 0 0 0 0 0 0 0 0 2 9 9 8 10 11
8 16 14 12 12 13 11 2 0 0 0 0 0 0 0 0 0 0 2 11 13 12 12 14 16
16 14 12 12 13 11 2 0 0 0 0 0 0 0 0 0 0 2 11 13 12 12 14 16
9 24 21 18 19 18 20 13 2 0 0 0 0 0 0 0 0 2 13 20 18 19 18 21 24
24 21 18 19 18 20 13 2 0 0 0 0 0 0 0 0 2 13 20 18 19 18 21 24
10 35 31 26 28 27 27 29 15 2 0 0 0 0 0 0 2 15 29 27 27 28 26 31 35
35 31 26 28 27 27 29 15 2 0 0 0 0 0 0 2 15 29 27 27 28 26 31 35
11 51 45 38 40 40 39 40 40 17 2 0 0 0 0 2 17 40 40 39 40 40 38 45 51
51 45 38 40 40 39 40 40 17 2 0 0 0 0 2 17 40 40 39 40 40 38 45 51
12 75 66 56 59 58 59 57 60 53 19 2 0 0 2 19 53 60 57 59 58 59 56 66 75
75 66 56 59 58 59 57 60 53 19 2 0 0 2 19 53 60 57 59 58 59 56 66 75
13 110 97 82 87 85 86 86 84 89 68 21 2 2 21 68 89 84 86 86 85 87 82 97 110
110 97 82 87 85 86 86 84 89 68 21 2 2 21 68 89 84 86 86 85 87 82 97 110
14 161 142 120 127 125 125 126 125 124 129 85 25 25 85 129 124 125 126 125 125 127 120 142 161
161 142 120 127 125 125 126 125 124 129 85 25 25 85 129 124 125 126 125 125 127 120 142 161
15 236 208 176 186 183 184 183 185 182 184 184 129 129 184 184 182 185 183 184 183 186 176 208 236
236 208 176 186 183 184 183 185 182 184 184 129 129 184 184 182 185 183 184 183 186 176 208 236
16 346 305 258 273 268 270 269 269 271 268 300 375 375 300 268 271 269 269 270 268 273 258 305 346
346 305 258 273 268 270 269 269 271 268 300 375 375 300 268 271 269 269 270 268 273 258 305 346
17 507 447 378 400 393 395 395 394 397 425 538 737 737 538 425 397 394 395 395 393 400 378 447 507
507 447 378 400 393 395 395 394 397 425 538 737 737 538 425 397 394 395 395 393 400 378 447 507
18 743 655 554 586 576 579 578 581 608 753 1017 1158 1158 1017 753 608 581 578 579 576 586 554 655 743
743 655 554 586 576 579 578 581 608 753 1017 1158 1158 1017 753 608 581 578 579 576 586 554 655 743
19 1089 960 812 859 844 849 849 881 1048 1410 1685 1691 1691 1685 1410 1048 881 849 849 844 859 812 960 1089
1089 960 812 859 844 849 849 881 1048 1410 1685 1691 1691 1685 1410 1048 881 849 849 844 859 812 960 1089
20 1596 1407 1190 1259 1237 1246 1277 1471 1955 2411 2490 2481 2481 2490 2411 1955 1471 1277 1246 1237 1259 1190 1407 1596
1596 1407 1190 1259 1237 1246 1277 1471 1955 2411 2490 2481 2481 2490 2411 1955 1471 1277 1246 1237 1259 1190 1407 1596
21 2339 2062 1744 1845 1815 1860 2080 2706 3428 3655 3627 3646 3646 3627 3655 3428 2706 2080 1860 1815 1845 1744 2062 2339
2339 2062 1744 1845 1815 1860 2080 2706 3428 3655 3627 3646 3646 3627 3655 3428 2706 2080 1860 1815 1845 1744 2062 2339
22 3428 3022 2556 2706 2696 2965 3752 4841 5335 5323 5339 5337 5337 5339 5323 5335 4841 3752 2965 2696 2706 2556 3022 3428
3428 3022 2556 2706 2696 2965 3752 4841 5335 5323 5339 5337 5337 5339 5323 5335 4841 3752 2965 2696 2706 2556 3022 3428
23 5024 4429 3748 4004 4222 5230 6793 7747 7815 7813 7830 7818 7818 7830 7813 7815 7747 6793 5230 4222 4004 3748 4429 5024
5024 4429 3748 4004 4222 5230 6793 7747 7815 7813 7830 7818 7818 7830 7813 7815 7747 6793 5230 4222 4004 3748 4429 5024
24 7363 6493 5533 6173 7281 9508 11173 11469 11442 11476 11457 11464 11464 11457 11476 11442 11469 11173 9508 7281 6173 5533 6493 7363
7363 6493 5533 6173 7281 9508 11173 11469 11442 11476 11457 11464 11464 11457 11476 11442 11469 11173 9508 7281 6173 5533 6493 7363
25 10793 9558 8450 10379 13218 16027 16800 16767 16812 16799 16796 16801 16801 16796 16799 16812 16767 16800 16027 13218 10379 8450 9558 10793
10793 9558 8450 10379 13218 16027 16800 16767 16812 16799 16796 16801 16801 16796 16799 16812 16767 16800 16027 13218 10379 8450 9558 10793
26 15857 14382 13983 18639 22754 24563 24571 24624 24624 24608 24622 24615 24615 24622 24608 24624 24624 24571 24563 22754 18639 13983 14382 15857
15857 14382 13983 18639 22754 24563 24571 24624 24624 24608 24622 24615 24615 24622 24608 24624 24624 24571 24563 22754 18639 13983 14382 15857
27 23546 22874 24927 32454 35551 35975 35963 36008 35972 35990 35985 35985 35985 35985 35990 35972 36008 35963 35975 35551 32454 24927 22874 23546
23546 22874 24927 32454 35551 35975 35963 36008 35972 35990 35985 35985 35985 35985 35990 35972 36008 35963 35975 35551 32454 24927 22874 23546
28 35656 38300 43408 51032 51678 51808 51843 51811 51820 51825 51817 51822 51822 51817 51825 51820 51811 51843 51808 51678 51032 43408 38300 35656
35656 38300 43408 51032 51678 51808 51843 51811 51820 51825 51817 51822 51822 51817 51825 51820 51811 51843 51808 51678 51032 43408 38300 35656
29 53602 61404 66328 71156 70503 70847 70733 70753 70762 70751 70757 70755 70755 70757 70751 70762 70753 70733 70847 70503 71156 66328 61404 53602
53602 61404 66328 71156 70503 70847 70733 70753 70762 70751 70757 70755 70755 70757 70751 70762 70753 70733 70847 70503 71156 66328 61404 53602
30 73057 82622 83253 85884 85169 85461 85326 85391 85364 85371 85372 85370 85370 85372 85371 85364 85391 85326 85461 85169 85884 83253 82622 73057
73057 82622 83253 85884 85169 85461 85326 85391 85364 85371 85372 85370 85370 85372 85371 85364 85391 85326 85461 85169 85884 83253 82622 73057
31 80006 84018 81756 83792 82992 83269 83182 83214 83196 83208 83201 83204 83204 83201 83208 83196 83214 83182 83269 82992 83792 81756 84018 80006
80006 84018 81756 83792 82992 83269 83182 83214 83196 83208 83201 83204 83204 83201 83208 83196 83214 83182 83269 82992 83792 81756 84018 80006
32 62988 59610 59029 59997 59349 59682 59547 59588 59580 59581 59580 59581 59581 59580 59581 59580 59588 59547 59682 59349 59997 59029 59610 62988
62988 59610 59029 59997 59349 59682 59547 59588 59580 59581 59580 59581 59581 59580 59581 59580 59588 59547 59682 59349 59997 59029 59610 62988
33 32132 27150 28690 28261 28257 28374 28270 28331 28305 28312 28312 28311 28311 28312 28312 28305 28331 28270 28374 28257 28261 28690 27150 32132
32132 27150 28690 28261 28257 28374 28270 28331 28305 28312 28312 28311 28311 28312 28312 28305 28331 28270 28374 28257 28261 28690 27150 32132
34 9361 7039 8273 7607 7927 7801 7831 7839 7823 7835 7829 7831 7831 7829 7835 7823 7839 7831 7801 7927 7607 8273 7039 9361
9361 7039 8273 7607 7927 7801 7831 7839 7823 7835 7829 7831 7831 7829 7835 7823 7839 7831 7801 7927 7607 8273 7039 9361
35 1267 838 1148 926 1078 980 1038 1008 1020 1018 1016 1018 1018 1016 1018 1020 1008 1038 980 1078 926 1148 838 1267
1267 838 1148 926 1078 980 1038 1008 1020 1018 1016 1018 1018 1016 1018 1020 1008 1038 980 1078 926 1148 838 1267
36 50 28 48 30 46 32 44 34 42 36 40 38 38 40 36 42 34 44 32 46 30 48 28 50
50 28 48 30 46 32 44 34 42 36 40 38 38 40 36 42 34 44 32 46 30 48 28 50
Total 421488 428254 436614 468838 478414 488274 492850 496238 498086 499270 499902 500194 500194 499902 499270 498086 496238 492850 488274 478414 468838 436614 428254 421488
421488 428254 436614 468838 478414 488274 492850 496238 498086 499270 499902 500194 500194 499902 499270 498086 496238 492850 488274 478414 468838 436614 428254 421488
Grand total = 4*421488 + 4*428254 + 4*436614 + 4*468838 + 4*478414 + 4*488274 + 4*492850 + 4*496238 + 4*498086 + 4*499270 + 4*499902 + 4*500194
= 22833688
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46 47
EN
0 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 1293 2091 3382 5472 8855 14329 23185 37513 0 2 2 2 3 6 11 18 28 44 71 116 189
306 494 798 1291 2090 3383 5474 8856 14328 23183 37512
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
23 37513 23185 14329 8855 5472 3382 2091 1293 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0 37512 23183 14328 8856 5474 3383 2090 1291 798 494 306 189 116
71 44 28 18 11 6 3 2 2 2 0
24 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 1291 2090 3383 5474 8856 14328 23183 37512 0 0 1 3 5 7 10 16 27 45 73 117 188
304 493 799 1293 2091 3382 5472 8855 14329 23185 37513
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
43 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
46 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
47 37512 23183 14328 8856 5474 3383 2090 1291 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0 37513 23185 14329 8855 5472 3382 2091 1293 799 493 304 188 117
73 45 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73 + 1*116 + 1*117 + 1*188 + 1*189 + 1*304 + 1*306 + 1*493 + 1*494 + 1*798 + 1*799 +
1*1291 + 1*1293 + 1*2090 + 1*2091 + 1*3382 + 1*3383 + 1*5472 + 1*5474 + 1*8855 + 1*8856 + 1*14328 + 1*14329 + 1*23183 + 1*23185 + 1*37512 + 1*37513) +
44(48*0)
= 785660
Value repetition frequencies = 4(40*1 + 1*2 + 2*3) +
44(1*48)
= 2304
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*44
= 48
Number of distinct values = 43
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73 116 117 188
Frequency 2124 4 12 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 189 304 306 493 494 798 799 1291 1293 2090 2091 3382 3383 5472 5474 8855 8856 14328 14329 23183
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 23185 37512 37513
Frequency 4 4 4
Sum of distinct value frequencies = 40*4 + 1*8 + 1*12 + 1*2124
= 2304
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*45
= 180
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 2076
Number of possible SN-EN pairs with SN != EN = 47*48
= 2256
a = 25, b = 2
L C S
3 8 2
4 8 4
5 12 6
6 20 10
7 28 14
8 40 20
9 60 30
10 88 44
11 128 64
12 188 94
13 276 138
14 404 202
15 592 296
16 868 434
17 1272 636
18 1864 932
19 2732 1366
20 4004 2002
21 5868 2934
22 8600 4300
23 12604 6302
24 18472 9236
25 27072 13536
26 39676 19838
27 58140 29070
28 85024 42512
29 122756 61378
30 169236 84618
31 209176 104588
32 213524 106762
33 165092 82546
34 88396 44198
35 29440 14720
36 5200 2600
37 360 180
38 4 2
Total 1271232 635614
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
L
3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
4 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
5 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0
0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0
6 0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0
0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0
7 0 0 0 0 5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 5 0 0 0 0
0 0 0 0 5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 5 0 0 0 0
8 0 0 0 0 1 7 2 0 0 0 0 0 0 0 0 0 0 0 2 7 1 0 0 0 0
0 0 0 0 1 7 2 0 0 0 0 0 0 0 0 0 0 0 2 7 1 0 0 0 0
9 0 0 0 0 0 4 9 2 0 0 0 0 0 0 0 0 0 2 9 4 0 0 0 0 0
0 0 0 0 0 4 9 2 0 0 0 0 0 0 0 0 0 2 9 4 0 0 0 0 0
10 0 0 0 0 0 0 9 11 2 0 0 0 0 0 0 0 2 11 9 0 0 0 0 0 0
0 0 0 0 0 0 9 11 2 0 0 0 0 0 0 0 2 11 9 0 0 0 0 0 0
11 0 0 0 0 0 0 1 16 13 2 0 0 0 0 0 2 13 16 1 0 0 0 0 0 0
0 0 0 0 0 0 1 16 13 2 0 0 0 0 0 2 13 16 1 0 0 0 0 0 0
12 0 0 0 0 0 0 0 5 25 15 2 0 0 0 2 15 25 5 0 0 0 0 0 0 0
0 0 0 0 0 0 0 5 25 15 2 0 0 0 2 15 25 5 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 14 36 17 2 0 2 17 36 14 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 14 36 17 2 0 2 17 36 14 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 1 30 49 19 4 19 49 30 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 30 49 19 4 19 49 30 1 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 6 55 66 42 66 55 6 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 6 55 66 42 66 55 6 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 22 114 162 114 22 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 22 114 162 114 22 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 2 26 150 280 150 26 2 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 2 26 150 280 150 26 2 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 2 27 121 211 210 211 121 27 2 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 2 27 121 211 210 211 121 27 2 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 2 29 144 285 196 54 196 285 144 29 2 0 0 0 0 0 0 0
0 0 0 0 0 0 0 2 29 144 285 196 54 196 285 144 29 2 0 0 0 0 0 0 0
20 0 0 0 0 0 0 2 31 169 385 336 77 2 77 336 385 169 31 2 0 0 0 0 0 0
0 0 0 0 0 0 2 31 169 385 336 77 2 77 336 385 169 31 2 0 0 0 0 0 0
21 0 0 0 0 0 2 33 196 506 540 182 8 0 8 182 540 506 196 33 2 0 0 0 0 0
0 0 0 0 0 2 33 196 506 540 182 8 0 8 182 540 506 196 33 2 0 0 0 0 0
22 0 0 0 0 2 35 225 650 825 378 35 0 0 0 35 378 825 650 225 35 2 0 0 0 0
0 0 0 0 2 35 225 650 825 378 35 0 0 0 35 378 825 650 225 35 2 0 0 0 0
23 0 0 0 2 37 256 819 1210 714 112 1 0 0 0 1 112 714 1210 819 256 37 2 0 0 0
0 0 0 2 37 256 819 1210 714 112 1 0 0 0 1 112 714 1210 819 256 37 2 0 0 0
24 0 0 2 39 289 1015 1716 1254 294 9 0 0 0 0 0 9 294 1254 1716 1015 289 39 2 0 0
0 0 2 39 289 1015 1716 1254 294 9 0 0 0 0 0 9 294 1254 1716 1015 289 39 2 0 0
25 0 2 41 324 1240 2366 2079 672 44 0 0 0 0 0 0 0 44 672 2079 2366 1240 324 41 2 0
0 2 41 324 1240 2366 2079 672 44 0 0 0 0 0 0 0 44 672 2079 2366 1240 324 41 2 0
26 2 43 361 1496 3185 3289 1386 156 1 0 0 0 0 0 0 0 1 156 1386 3289 3185 1496 361 43 2
2 43 361 1496 3185 3289 1386 156 1 0 0 0 0 0 0 0 1 156 1386 3289 3185 1496 361 43 2
27 45 400 1785 4200 5005 2640 450 10 0 0 0 0 0 0 0 0 0 10 450 2640 5005 4200 1785 400 45
45 400 1785 4200 5005 2640 450 10 0 0 0 0 0 0 0 0 0 10 450 2640 5005 4200 1785 400 45
28 441 2109 5440 7371 4719 1122 54 0 0 0 0 0 0 0 0 0 0 0 54 1122 4719 7371 5440 2109 441
441 2109 5440 7371 4719 1122 54 0 0 0 0 0 0 0 0 0 0 0 54 1122 4719 7371 5440 2109 441
29 2470 6936 10556 8008 2508 210 1 0 0 0 0 0 0 0 0 0 0 0 1 210 2508 8008 10556 6936 2470
2470 6936 10556 8008 2508 210 1 0 0 0 0 0 0 0 0 0 0 0 1 210 2508 8008 10556 6936 2470
30 8721 14756 13013 5148 660 11 0 0 0 0 0 0 0 0 0 0 0 0 0 11 660 5148 13013 14756 8721
8721 14756 13013 5148 660 11 0 0 0 0 0 0 0 0 0 0 0 0 0 11 660 5148 13013 14756 8721
31 20196 20384 9867 1782 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 65 1782 9867 20384 20196
20196 20384 9867 1782 65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 65 1782 9867 20384 20196
32 30940 17875 4290 275 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 275 4290 17875 30940
30940 17875 4290 275 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 275 4290 17875 30940
33 30888 9438 935 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 935 9438 30888
30888 9438 935 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 935 9438 30888
34 19305 2717 77 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 77 2717 19305
19305 2717 77 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 77 2717 19305
35 7007 352 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 352 7007
7007 352 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 352 7007
36 1287 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 1287
1287 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 1287
37 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90
90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90
38 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Total 121393 75027 46371 28662 17719 10959 6786 4215 2639 1686 1131 843 754 843 1131 1686 2639 4215 6786 10959 17719 28662 46371 75027 121393
121393 75027 46371 28662 17719 10959 6786 4215 2639 1686 1131 843 754 843 1131 1686 2639 4215 6786 10959 17719 28662 46371 75027 121393
Grand total = 2*754 + 4*843 + 4*1131 + 4*1686 + 4*2639 + 4*4215 + 4*6786 + 4*10959 + 4*17719 + 4*28662 + 4*46371 + 4*75027 + 4*121393
= 1271232
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
L
3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
6 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7
8 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
9 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15
10 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22
11 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
12 47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47
13 69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 69
14 101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101
15 148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
148 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148
16 217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 217
17 318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 318
18 466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
466 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 466
19 683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 683
20 1001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1001
1001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1001
21 1467 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1467
1467 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1467
22 2150 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2150
2150 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2150
23 3151 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3151
3151 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3151
24 4618 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4618
4618 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4618
25 6768 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6768
6768 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6768
26 9919 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9919
9919 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9919
27 14535 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14535
14535 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14535
28 21256 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21256
21256 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21256
29 30689 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 30689
30689 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 30689
30 42309 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 42309
42309 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 42309
31 52294 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 52294
52294 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 52294
32 53381 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 53381
53381 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 53381
33 41273 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 41273
41273 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 41273
34 22099 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22099
22099 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22099
35 7360 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7360
7360 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7360
36 1300 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1300
1300 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1300
37 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90
90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90
38 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Total 317808 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 317808
317808 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 317808
Grand total = 4*317808
= 1271232
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
L
3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
4 3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3
5 5 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5
5 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5
6 8 7 6 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 6 7 8
8 7 6 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 6 7 8
7 11 10 8 9 9 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 9 9 8 10 11
11 10 8 9 9 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 9 9 8 10 11
8 16 14 12 12 13 11 2 0 0 0 0 0 0 0 0 0 0 0 2 11 13 12 12 14 16
16 14 12 12 13 11 2 0 0 0 0 0 0 0 0 0 0 0 2 11 13 12 12 14 16
9 24 21 18 19 18 20 13 2 0 0 0 0 0 0 0 0 0 2 13 20 18 19 18 21 24
24 21 18 19 18 20 13 2 0 0 0 0 0 0 0 0 0 2 13 20 18 19 18 21 24
10 35 31 26 28 27 27 29 15 2 0 0 0 0 0 0 0 2 15 29 27 27 28 26 31 35
35 31 26 28 27 27 29 15 2 0 0 0 0 0 0 0 2 15 29 27 27 28 26 31 35
11 51 45 38 40 40 39 40 40 17 2 0 0 0 0 0 2 17 40 40 39 40 40 38 45 51
51 45 38 40 40 39 40 40 17 2 0 0 0 0 0 2 17 40 40 39 40 40 38 45 51
12 75 66 56 59 58 59 57 60 53 19 2 0 0 0 2 19 53 60 57 59 58 59 56 66 75
75 66 56 59 58 59 57 60 53 19 2 0 0 0 2 19 53 60 57 59 58 59 56 66 75
13 110 97 82 87 85 86 86 84 89 68 21 2 0 2 21 68 89 84 86 86 85 87 82 97 110
110 97 82 87 85 86 86 84 89 68 21 2 0 2 21 68 89 84 86 86 85 87 82 97 110
14 161 142 120 127 125 125 126 125 124 129 85 23 4 23 85 129 124 125 126 125 125 127 120 142 161
161 142 120 127 125 125 126 125 124 129 85 23 4 23 85 129 124 125 126 125 125 127 120 142 161
15 236 208 176 186 183 184 183 185 182 184 182 106 50 106 182 184 182 185 183 184 183 186 176 208 236
236 208 176 186 183 184 183 185 182 184 182 106 50 106 182 184 182 185 183 184 183 186 176 208 236
16 346 305 258 273 268 270 269 269 271 266 275 277 250 277 275 266 271 269 269 270 268 273 258 305 346
346 305 258 273 268 270 269 269 271 266 275 277 250 277 275 266 271 269 269 270 268 273 258 305 346
17 507 447 378 400 393 395 395 394 395 398 419 550 670 550 419 398 395 394 395 395 393 400 378 447 507
507 447 378 400 393 395 395 394 395 398 419 550 670 550 419 398 395 394 395 395 393 400 378 447 507
18 743 655 554 586 576 579 578 579 579 611 751 1013 1168 1013 751 611 579 579 578 579 576 586 554 655 743
743 655 554 586 576 579 578 579 579 611 751 1013 1168 1013 751 611 579 579 578 579 576 586 554 655 743
19 1089 960 812 859 844 849 847 850 881 1046 1415 1678 1694 1678 1415 1046 881 850 847 849 844 859 812 960 1089
1089 960 812 859 844 849 847 850 881 1046 1415 1678 1694 1678 1415 1046 881 850 847 849 844 859 812 960 1089
20 1596 1407 1190 1259 1237 1244 1244 1277 1472 1954 2410 2496 2468 2496 2410 1954 1472 1277 1244 1244 1237 1259 1190 1407 1596
1596 1407 1190 1259 1237 1244 1244 1277 1472 1954 2410 2496 2468 2496 2410 1954 1472 1277 1244 1244 1237 1259 1190 1407 1596
21 2339 2062 1744 1845 1813 1825 1857 2081 2705 3430 3652 3629 3650 3629 3652 3430 2705 2081 1857 1825 1813 1845 1744 2062 2339
2339 2062 1744 1845 1813 1825 1857 2081 2705 3430 3652 3629 3650 3629 3652 3430 2705 2081 1857 1825 1813 1845 1744 2062 2339
22 3428 3022 2556 2704 2659 2711 2960 3754 4840 5335 5325 5334 5344 5334 5325 5335 4840 3754 2960 2711 2659 2704 2556 3022 3428
3428 3022 2556 2704 2659 2711 2960 3754 4840 5335 5325 5334 5344 5334 5325 5335 4840 3754 2960 2711 2659 2704 2556 3022 3428
23 5024 4429 3746 3965 3935 4244 5223 6795 7747 7814 7814 7831 7812 7831 7814 7814 7747 6795 5223 4244 3935 3965 3746 4429 5024
5024 4429 3746 3965 3935 4244 5223 6795 7747 7814 7814 7831 7812 7831 7814 7814 7747 6795 5223 4244 3935 3965 3746 4429 5024
24 7363 6491 5492 5851 6072 7313 9498 11176 11468 11443 11474 11460 11462 11460 11474 11443 11468 11176 9498 7313 6072 5851 5492 6491 7363
7363 6491 5492 5851 6072 7313 9498 11176 11468 11443 11474 11460 11462 11460 11474 11443 11468 11176 9498 7313 6072 5851 5492 6491 7363
25 10791 9515 8091 8916 10231 13265 16012 16805 16765 16813 16799 16794 16806 16794 16799 16813 16765 16805 16012 13265 10231 8916 8091 9515 10791
10791 9515 8091 8916 10231 13265 16012 16805 16765 16813 16799 16794 16806 16794 16799 16813 16765 16805 16012 13265 10231 8916 8091 9515 10791
26 15817 13989 12237 14670 18426 22827 24545 24582 24626 24628 24613 24625 24618 24625 24613 24628 24626 24582 24545 22827 18426 14670 12237 13989 15817
15817 13989 12237 14670 18426 22827 24545 24582 24626 24628 24613 24625 24618 24625 24613 24628 24626 24582 24545 22827 18426 14670 12237 13989 15817
27 23222 20916 19838 26021 32230 35746 36037 36067 36099 36067 36083 36081 36076 36081 36083 36067 36099 36067 36037 35746 32230 26021 19838 20916 23222
23222 20916 19838 26021 32230 35746 36037 36067 36099 36067 36083 36081 36076 36081 36083 36067 36099 36067 36037 35746 32230 26021 19838 20916 23222
28 34377 32786 34836 45816 51527 52786 52721 52818 52766 52782 52784 52777 52784 52777 52784 52782 52766 52818 52721 52786 51527 45816 34836 32786 34377
34377 32786 34836 45816 51527 52786 52721 52818 52766 52782 52784 52777 52784 52777 52784 52782 52766 52818 52721 52786 51527 45816 34836 32786 34377
29 51801 54323 61275 73913 76082 76311 76370 76347 76338 76356 76343 76348 76348 76348 76343 76356 76338 76347 76370 76311 76082 73913 61275 54323 51801
51801 54323 61275 73913 76082 76311 76370 76347 76338 76356 76343 76348 76348 76348 76343 76356 76338 76347 76370 76311 76082 73913 61275 54323 51801
30 78173 88433 96925 106150 105503 105968 105857 105854 105877 105863 105866 105869 105864 105869 105866 105863 105877 105854 105857 105968 105503 106150 96925 88433 78173
78173 88433 96925 106150 105503 105968 105857 105854 105877 105863 105866 105869 105864 105869 105866 105863 105877 105854 105857 105968 105503 106150 96925 88433 78173
31 109711 124958 128158 133212 132030 132551 132322 132416 132387 132389 132394 132390 132392 132390 132394 132389 132387 132416 132322 132551 132030 133212 128158 124958 109711
109711 124958 128158 133212 132030 132551 132322 132416 132387 132389 132394 132390 132392 132390 132394 132389 132387 132416 132322 132551 132030 133212 128158 124958 109711
32 128105 137728 134978 138459 137226 137660 137503 137573 137535 137555 137547 137548 137550 137548 137547 137555 137535 137573 137503 137660 137226 138459 134978 137728 128105
128105 137728 134978 138459 137226 137660 137503 137573 137535 137555 137547 137548 137550 137548 137547 137555 137535 137573 137503 137660 137226 138459 134978 137728 128105
33 111783 109419 107371 109521 108350 108873 108683 108738 108724 108730 108725 108729 108726 108729 108725 108730 108724 108738 108683 108873 108350 109521 107371 109419 111783
111783 109419 107371 109521 108350 108873 108683 108738 108724 108730 108725 108729 108726 108729 108725 108730 108724 108738 108683 108873 108350 109521 107371 109419 111783
34 66209 58212 59927 59817 59498 59813 59615 59709 59676 59683 59683 59683 59682 59683 59683 59683 59676 59709 59615 59813 59498 59817 59927 58212 66209
66209 58212 59927 59817 59498 59813 59615 59709 59676 59683 59683 59683 59682 59683 59683 59683 59676 59709 59615 59813 59498 59817 59927 58212 66209
35 23949 18844 21178 20079 20512 20399 20386 20429 20394 20413 20406 20407 20408 20407 20406 20413 20394 20429 20386 20399 20512 20079 21178 18844 23949
23949 18844 21178 20079 20512 20399 20386 20429 20394 20413 20406 20407 20408 20407 20406 20413 20394 20429 20386 20399 20512 20079 21178 18844 23949
36 4535 3174 4052 3484 3830 3636 3732 3694 3702 3706 3700 3704 3702 3704 3700 3706 3702 3694 3732 3636 3830 3484 4052 3174 4535
4535 3174 4052 3484 3830 3636 3732 3694 3702 3706 3700 3704 3702 3704 3700 3706 3702 3694 3732 3636 3830 3484 4052 3174 4535
37 335 204 312 224 294 240 280 252 270 260 264 264 262 264 264 260 270 252 280 240 294 224 312 204 335
335 204 312 224 294 240 280 252 270 260 264 264 262 264 264 260 270 252 280 240 294 224 312 204 335
38 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4
4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4
Total 681985 692932 706460 758602 774100 790060 797474 802972 805988 807946 809036 809620 809794 809620 809036 807946 805988 802972 797474 790060 774100 758602 706460 692932 681985
681985 692932 706460 758602 774100 790060 797474 802972 805988 807946 809036 809620 809794 809620 809036 807946 805988 802972 797474 790060 774100 758602 706460 692932 681985
Grand total = 4*681985 + 4*692932 + 4*706460 + 4*758602 + 4*774100 + 4*790060 + 4*797474 + 4*802972 + 4*805988 + 4*807946 + 4*809036 + 4*809620 + 2*809794
= 38568288
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46 47 48 49
EN
0 0 0 1 3 5 7 10 16 27 45 73 117 188 304 493 799 1293 2091 3382 5472 8855 14329 23185 37513 60696 0 2 2 2 3 6 11 18 28 44 71 116
189 306 494 798 1291 2090 3383 5474 8856 14328 23183 37512 60697
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
24 60696 37513 23185 14329 8855 5472 3382 2091 1293 799 493 304 188 117 73 45 27 16 10 7 5 3 1 0 0 60697 37512 23183 14328 8856 5474 3383 2090 1291 798 494 306
189 116 71 44 28 18 11 6 3 2 2 2 0
25 0 2 2 2 3 6 11 18 28 44 71 116 189 306 494 798 1291 2090 3383 5474 8856 14328 23183 37512 60697 0 0 1 3 5 7 10 16 27 45 73 117
188 304 493 799 1293 2091 3382 5472 8855 14329 23185 37513 60696
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
43 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
46 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
48 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
49 60697 37512 23183 14328 8856 5474 3383 2090 1291 798 494 306 189 116 71 44 28 18 11 6 3 2 2 2 0 60696 37513 23185 14329 8855 5472 3382 2091 1293 799 493 304
188 117 73 45 27 16 10 7 5 3 1 0 0
Sum of all rows = 4(3*0 + 1*1 + 3*2 + 2*3 + 1*5 + 1*6 + 1*7 + 1*10 + 1*11 + 1*16 + 1*18 + 1*27 + 1*28 + 1*44 + 1*45 + 1*71 + 1*73 + 1*116 + 1*117 + 1*188 + 1*189 + 1*304 + 1*306 + 1*493 + 1*494 + 1*798 + 1*799 +
1*1291 + 1*1293 + 1*2090 + 1*2091 + 1*3382 + 1*3383 + 1*5472 + 1*5474 + 1*8855 + 1*8856 + 1*14328 + 1*14329 + 1*23183 + 1*23185 + 1*37512 + 1*37513 + 1*60696 + 1*60697) +
46(50*0)
= 1271232
Value repetition frequencies = 4(42*1 + 1*2 + 2*3) +
46(1*50)
= 2500
Number of distinct row element sets = 2
Number of rows = 1*4 + 1*46
= 50
Number of distinct values = 45
Distinct values 0 1 2 3 5 6 7 10 11 16 18 27 28 44 45 71 73 116 117 188
Frequency 2124 4 12 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 189 304 306 493 494 798 799 1291 1293 2090 2091 3382 3383 5472 5474 8855 8856 14328 14329 23183
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 23185 37512 37513 60696 60697
Frequency 4 4 4 4 4
Sum of distinct value frequencies = 42*4 + 1*8 + 1*12 + 1*2312
= 2500
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*47
= 188
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 2262
Number of possible SN-EN pairs with SN != EN = 49*50
= 2450
