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Complete non-self-adjacent paths:Results 02A
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a = 3, b = 3
L C S
3 8 2
4 16 4
5 24 6
6 0 0
7 16 4
Total 64 16
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
L
3 0 0 0
0 8 0
0 0 0
4 0 4 0
4 0 4
0 4 0
5 6 0 6
0 0 0
6 0 6
6 0 0 0
0 0 0
0 0 0
7 2 2 2
2 0 2
2 2 2
Total 8 6 8
6 8 6
8 6 8
Grand total = 4*6 + 5*8
= 64
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
L
3 2 0 2
0 0 0
2 0 2
4 4 0 4
0 0 0
4 0 4
5 6 0 6
0 0 0
6 0 6
6 0 0 0
0 0 0
0 0 0
7 2 2 2
2 0 2
2 2 2
Total 14 2 14
2 0 2
14 2 14
Grand total = 4*2 + 4*14
= 64
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
L
3 2 2 2
2 8 2
2 2 2
4 4 8 4
8 16 8
4 8 4
5 12 12 12
12 24 12
12 12 12
6 0 0 0
0 0 0
0 0 0
7 14 14 14
14 0 14
14 14 14
Total 32 36 32
36 48 36
32 36 32
Grand total = 4*32 + 4*36 + 48
= 320
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8
EN
0 0 0 2 0 2 2 2 2 4
1 0 0 0 1 0 1 0 0 0
2 2 0 0 2 2 0 4 2 2
3 0 1 0 0 0 0 0 1 0
4 0 0 0 0 0 0 0 0 0
5 0 1 0 0 0 0 0 1 0
6 2 2 4 0 2 2 0 0 2
7 0 0 0 1 0 1 0 0 0
8 4 2 2 2 2 0 2 0 0
Sum of all rows = 4(3*0 + 5*2 + 1*4) +
4(7*0 + 2*1) +
1(9*0)
= 56 + 8
= 64
Value repetition frequencies = 4(1*1 + 1*3 + 1*5) +
4(1*2 + 1*7) +
1(1*9)
= 81
Number of distinct row element sets = 3
Number of rows = 1*1 + 2*4
= 9
Number of distinct values = 4
Distinct values 0 1 2 4
Frequency 49 8 20 4
Sum of distinct value frequencies = 1*4 + 1*8 + 1*20 + 1*49
= 81
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*2 + 4*6
= 32
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 40
Number of possible SN-EN pairs with SN != EN = 8*9
= 72
a = 4, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 36 18
7 28 8
8 16 8
9 28 14
Total 164 64
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 0 0 0
0 4 4 0
0 0 0 0
4 0 2 2 0
0 4 4 0
0 2 2 0
5 1 5 5 1
4 0 0 4
1 5 5 1
6 9 0 0 9
0 0 0 0
9 0 0 9
7 1 2 2 1
6 2 2 6
1 2 2 1
8 3 0 0 3
2 0 0 2
3 0 0 3
9 3 3 3 3
2 0 0 2
3 3 3 3
Total 17 12 12 17
14 10 10 14
17 12 12 17
Grand total = 2*10 + 4*12 + 2*14 + 4*17
= 164
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 2
0 0 0 0
2 0 0 2
4 4 0 0 4
0 0 0 0
4 0 0 4
5 8 0 0 8
0 0 0 0
8 0 0 8
6 9 0 0 9
0 0 0 0
9 0 0 9
7 4 2 2 4
2 0 0 2
4 2 2 4
8 3 1 1 3
0 0 0 0
3 1 1 3
9 3 3 3 3
2 0 0 2
3 3 3 3
Total 33 6 6 33
4 0 0 4
33 6 6 33
Grand total = 2*4 + 4*6 + 4*33
= 164
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 2 1 1 2
2 4 4 2
2 1 1 2
4 4 4 4 4
4 12 12 4
4 4 4 4
5 9 12 12 9
12 26 26 12
9 12 12 9
6 18 11 11 18
18 32 32 18
18 11 11 18
7 12 23 23 12
14 14 14 14
12 23 23 12
8 11 11 11 11
12 8 8 12
11 11 11 11
9 24 24 24 24
26 4 4 26
24 24 24 24
Total 80 86 86 80
88 100 100 88
80 86 86 80
Grand total = 4*80 + 4*86 + 2*88 + 2*100
= 1040
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 4 6 0 2 2 4 3 2 4 6
1 0 0 0 2 2 0 1 1 0 0 0 0
2 2 0 0 0 1 1 0 2 0 0 0 0
3 6 4 0 0 4 2 2 0 6 4 2 3
4 0 2 0 0 0 0 0 0 0 2 0 0
5 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
7 0 0 2 0 0 0 0 0 0 0 2 0
8 3 2 4 6 0 2 2 4 0 0 4 6
9 0 0 0 0 2 0 1 1 0 0 0 2
10 0 0 0 0 1 1 0 2 2 0 0 0
11 6 4 2 3 4 2 2 0 6 4 0 0
Sum of all rows = 4(3*0 + 3*2 + 1*3 + 3*4 + 2*6) +
4(8*0 + 2*1 + 2*2) +
2(10*0 + 2*2) +
2(12*0)
= 132 + 24 + 8
= 164
Value repetition frequencies = 4(1*1 + 1*2 + 3*3) +
4(2*2 + 1*8) +
2(1*2 + 1*10) +
2(1*12)
= 144
Number of distinct row element sets = 4
Number of rows = 2*2 + 2*4
= 12
Number of distinct values = 6
Distinct values 0 1 2 3 4 6
Frequency 88 8 24 4 12 8
Sum of distinct value frequencies = 1*4 + 2*8 + 1*12 + 1*24 + 1*88
= 144
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 4*4 + 4*9
= 56
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 76
Number of possible SN-EN pairs with SN != EN = 11*12
= 132
a = 5, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 44 22
7 84 34
8 48 22
9 84 36
10 44 22
11 36 18
Total 396 170
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
L
3 0 0 0 0 0
0 4 0 4 0
0 0 0 0 0
4 0 2 0 2 0
0 0 8 0 0
0 2 0 2 0
5 1 0 10 0 1
0 4 0 4 0
1 0 10 0 1
6 0 9 0 9 0
4 0 0 0 4
0 9 0 9 0
7 14 1 2 1 14
2 6 4 6 2
14 1 2 1 14
8 0 3 0 3 0
16 2 0 2 16
0 3 0 3 0
9 13 3 4 3 13
4 2 0 2 4
13 3 4 3 13
10 4 5 0 5 4
4 0 0 0 4
4 5 0 5 4
11 4 2 4 2 4
2 0 0 0 2
4 2 4 2 4
Total 36 25 20 25 36
32 18 12 18 32
36 25 20 25 36
Grand total = 12 + 2*18 + 2*20 + 4*25 + 2*32 + 4*36
= 396
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
L
3 2 0 0 0 2
0 0 0 0 0
2 0 0 0 2
4 4 0 0 0 4
0 0 0 0 0
4 0 0 0 4
5 8 0 0 0 8
0 0 0 0 0
8 0 0 0 8
6 11 0 0 0 11
0 0 0 0 0
11 0 0 0 11
7 17 2 2 2 17
2 0 0 0 2
17 2 2 2 17
8 10 1 2 1 10
0 0 0 0 0
10 1 2 1 10
9 13 4 6 4 13
2 0 0 0 2
13 4 6 4 13
10 6 4 2 4 6
0 0 0 0 0
6 4 2 4 6
11 4 2 4 2 4
2 0 0 0 2
4 2 4 2 4
Total 75 13 16 13 75
6 0 0 0 6
75 13 16 13 75
Grand total = 2*6 + 4*13 + 2*16 + 4*75
= 396
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
L
3 2 1 0 1 2
2 4 0 4 2
2 1 0 1 2
4 4 4 0 4 4
4 8 8 8 4
4 4 0 4 4
5 9 7 10 7 9
8 20 20 20 8
9 7 10 7 9
6 11 16 10 16 11
16 34 36 34 16
11 16 10 16 11
7 36 34 36 34 36
32 54 64 54 32
36 34 36 34 36
8 18 28 28 28 18
30 32 20 32 30
18 28 28 28 18
9 44 59 60 59 44
48 52 24 52 48
44 59 60 59 44
10 32 30 26 30 32
36 20 28 20 36
32 30 26 30 32
11 32 30 34 30 32
34 4 4 4 34
32 30 34 30 32
Total 188 209 204 209 188
210 228 204 228 210
188 209 204 209 188
Grand total = 4*108 + 3*204 + 4*209 + 2*210 + 2*228
= 2756
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
EN
0 0 0 6 10 14 0 2 2 4 10 4 2 4 7 10
1 0 0 0 3 3 3 0 1 1 1 0 0 0 0 1
2 4 0 0 0 4 2 2 0 2 2 0 0 0 0 0
3 3 3 0 0 0 1 1 1 0 3 1 0 0 0 0
4 14 10 6 0 0 10 4 2 2 0 10 7 4 2 4
5 0 3 0 0 0 0 0 0 0 0 0 3 0 0 0
6 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
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 3 0 0 0 0 0 0 0 0 0 3 0
10 4 2 4 7 10 0 2 2 4 10 0 0 6 10 14
11 0 0 0 0 1 3 0 1 1 1 0 0 0 3 3
12 0 0 0 0 0 2 2 0 2 2 4 0 0 0 4
13 1 0 0 0 0 1 1 1 0 3 3 3 0 0 0
14 10 7 4 2 4 10 4 2 2 0 14 10 6 0 0
Sum of all rows = 4(3*0 + 3*2 + 3*4 + 1*6 + 1*7 + 3*10 + 1*14) +
4(8*0 + 4*1 + 3*3) +
2(9*0 + 4*2 + 2*4) +
2(13*0 + 2*3) +
3(15*0)
= 300 + 52 + 32 + 12
= 396
Value repetition frequencies = 4(3*1 + 4*3) +
4(1*3 + 1*4 + 1*8) +
2(1*2 + 1*4 + 1*9) +
2(1*2 + 1*13) +
3(1*15)
= 225
Number of distinct row element sets = 5
Number of rows = 2*2 + 1*3 + 2*4
= 15
Number of distinct values = 9
Distinct values 0 1 2 3 4 6 7 10 14
Frequency 133 16 20 16 16 4 4 12 4
Sum of distinct value frequencies = 3*4 + 1*12 + 3*16 + 1*20 + 1*133
= 225
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 2*6 + 4*7 + 4*12
= 92
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 118
Number of possible SN-EN pairs with SN != EN = 14*15
= 210
a = 6, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 44 22
7 96 38
8 120 56
9 164 68
10 180 80
11 132 58
12 68 34
13 48 24
14 4 2
Total 912 398
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 0 0 0 0 0
0 4 0 0 4 0
0 0 0 0 0 0
4 0 2 0 0 2 0
0 0 4 4 0 0
0 2 0 0 2 0
5 1 0 5 5 0 1
0 0 4 4 0 0
1 0 5 5 0 1
6 0 0 9 9 0 0
0 4 0 0 4 0
0 0 9 9 0 0
7 1 14 1 1 14 1
6 2 8 8 2 6
1 14 1 1 14 1
8 17 0 3 3 0 17
2 16 2 2 16 2
17 0 3 3 0 17
9 3 13 4 4 13 3
36 4 2 2 4 36
3 13 4 4 13 3
10 32 4 5 5 4 32
4 4 0 0 4 4
32 4 5 5 4 32
11 9 14 3 3 14 9
12 2 0 0 2 12
9 14 3 3 14 9
12 9 0 5 5 0 9
6 0 0 0 0 6
9 0 5 5 0 9
13 5 3 3 3 3 5
2 0 0 0 0 2
5 3 3 3 3 5
14 0 1 0 0 1 0
0 0 0 0 0 0
0 1 0 0 1 0
Total 77 51 38 38 51 77
68 36 20 20 36 68
77 51 38 38 51 77
Grand total = 2*20 + 2*36 + 4*38 + 4*51 + 2*68 + 4*77
= 912
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 2
0 0 0 0 0 0
2 0 0 0 0 2
4 4 0 0 0 0 4
0 0 0 0 0 0
4 0 0 0 0 4
5 8 0 0 0 0 8
0 0 0 0 0 0
8 0 0 0 0 8
6 11 0 0 0 0 11
0 0 0 0 0 0
11 0 0 0 0 11
7 19 2 2 2 2 19
2 0 0 0 0 2
19 2 2 2 2 19
8 27 1 2 2 1 27
0 0 0 0 0 0
27 1 2 2 1 27
9 29 4 7 7 4 29
2 0 0 0 0 2
29 4 7 7 4 29
10 34 5 6 6 5 34
0 0 0 0 0 0
34 5 6 6 5 34
11 17 8 7 7 8 17
2 0 0 0 0 2
17 8 7 7 8 17
12 10 2 5 5 2 10
0 0 0 0 0 0
10 2 5 5 2 10
13 4 4 3 3 4 4
2 0 0 0 0 2
4 4 3 3 4 4
14 0 1 0 0 1 0
0 0 0 0 0 0
0 1 0 0 1 0
Total 165 27 32 32 27 165
8 0 0 0 0 8
165 27 32 32 27 165
Grand total = 2*8 + 4*27 + 4*32 + 4*165
= 912
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 2 1 0 0 1 2
2 4 0 0 4 2
2 1 0 0 1 2
4 4 4 0 0 4 4
4 8 4 4 8 4
4 4 0 0 4 4
5 9 7 5 5 7 9
8 16 14 14 16 8
9 7 5 5 7 9
6 11 7 14 14 7 11
12 26 30 30 26 12
11 7 14 14 7 11
7 25 37 34 34 37 25
30 50 64 64 50 30
25 37 34 34 37 25
8 47 44 45 45 44 47
42 88 78 78 88 42
47 44 45 45 44 47
9 54 83 101 101 83 54
84 100 78 78 100 84
54 83 101 101 83 54
10 89 102 100 100 102 89
96 136 86 86 136 96
89 102 100 100 102 89
11 78 96 85 85 96 78
86 64 58 58 64 86
78 96 85 85 96 78
12 51 46 51 51 46 51
56 28 28 28 28 56
51 46 51 51 46 51
13 44 41 42 42 41 44
46 4 8 8 4 46
44 41 42 42 41 44
14 4 4 2 2 4 4
4 0 4 4 0 4
4 4 2 2 4 4
Total 418 472 479 479 472 418
470 524 452 452 524 470
418 472 479 479 472 418
Grand total = 4*418 + 2*452 + 2*470 + 4*472 + 4*479 + 2*524
= 8368
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 8 14 20 28 0 2 2 4 10 22 5 2 4 8 14 22
1 0 0 0 4 3 4 4 0 1 1 1 3 0 0 0 0 2 4
2 6 0 0 0 6 6 3 3 0 2 2 2 0 0 0 0 0 2
3 6 6 0 0 0 6 2 2 2 0 3 3 2 0 0 0 0 0
4 4 3 4 0 0 0 3 1 1 1 0 4 4 2 0 0 0 0
5 28 20 14 8 0 0 22 10 4 2 2 0 22 14 8 4 2 5
6 0 4 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
7 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
9 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
11 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 0
12 5 2 4 8 14 22 0 2 2 4 10 22 0 0 8 14 20 28
13 0 0 0 0 2 4 4 0 1 1 1 3 0 0 0 4 3 4
14 0 0 0 0 0 2 3 3 0 2 2 2 6 0 0 0 6 6
15 2 0 0 0 0 0 2 2 2 0 3 3 6 6 0 0 0 6
16 4 2 0 0 0 0 3 1 1 1 0 4 4 3 4 0 0 0
17 22 14 8 4 2 5 22 10 4 2 2 0 28 20 14 8 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 1*5 + 2*8 + 1*10 + 2*14 + 1*20 + 2*22 + 1*28) +
4(8*0 + 3*1 + 1*2 + 2*3 + 4*4) +
4(9*0 + 4*2 + 2*3 + 3*6) +
2(16*0 + 2*4) +
4(18*0)
= 660 + 108 + 128 + 16
= 912
Value repetition frequencies = 4(4*1 + 4*2 + 2*3) +
4(1*1 + 1*2 + 1*3 + 1*4 + 1*8) +
4(1*2 + 1*3 + 1*4 + 1*9) +
2(1*2 + 1*16) +
4(1*18)
= 324
Number of distinct row element sets = 5
Number of rows = 1*2 + 4*4
= 18
Number of distinct values = 13
Distinct values 0 1 2 3 4 5 6 8 10 14 20 22 28
Frequency 184 12 32 16 28 4 12 8 4 8 4 8 4
Sum of distinct value frequencies = 4*4 + 3*8 + 2*12 + 1*16 + 1*28 + 1*32 + 1*184
= 324
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 4*9 + 4*10 + 4*15
= 140
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 166
Number of possible SN-EN pairs with SN != EN = 17*18
= 306
a = 7, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 44 22
7 100 38
8 132 60
9 264 110
10 320 138
11 436 188
12 240 106
13 244 108
14 112 54
15 72 36
16 8 4
Total 2028 880
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
L
3 0 0 0 0 0 0 0
0 4 0 0 0 4 0
0 0 0 0 0 0 0
4 0 2 0 0 0 2 0
0 0 4 0 4 0 0
0 2 0 0 0 2 0
5 1 0 5 0 5 0 1
0 0 0 8 0 0 0
1 0 5 0 5 0 1
6 0 0 0 18 0 0 0
0 0 4 0 4 0 0
0 0 0 18 0 0 0
7 1 1 14 0 14 1 1
2 6 4 12 4 6 2
1 1 14 0 14 1 1
8 0 17 0 6 0 17 0
6 2 16 4 16 2 6
0 17 0 6 0 17 0
9 24 3 14 4 14 3 24
4 36 4 4 4 36 4
24 3 14 4 14 3 24
10 4 32 4 10 4 32 4
62 4 4 0 4 4 62
4 32 4 10 4 32 4
11 73 10 15 2 15 10 73
6 12 2 0 2 12 6
73 10 15 2 15 10 73
12 12 22 0 10 0 22 12
36 6 0 0 0 6 36
12 22 0 10 0 22 12
13 31 6 14 2 14 6 31
16 2 0 0 0 2 16
31 6 14 2 14 6 31
14 12 6 1 10 1 6 12
8 0 0 0 0 0 8
12 6 1 10 1 6 12
15 6 6 4 2 4 6 6
2 0 0 0 0 0 2
6 6 4 2 4 6 6
16 0 1 1 0 1 1 0
0 0 0 0 0 0 0
0 1 1 0 1 1 0
Total 164 106 72 64 72 106 164
142 72 38 28 38 72 142
164 106 72 64 72 106 164
Grand total = 28 + 2*38 + 2*64 + 6*72 + 4*106 + 2*142 + 4*164
= 2028
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
L
3 2 0 0 0 0 0 2
0 0 0 0 0 0 0
2 0 0 0 0 0 2
4 4 0 0 0 0 0 4
0 0 0 0 0 0 0
4 0 0 0 0 0 4
5 8 0 0 0 0 0 8
0 0 0 0 0 0 0
8 0 0 0 0 0 8
6 11 0 0 0 0 0 11
0 0 0 0 0 0 0
11 0 0 0 0 0 11
7 19 2 2 2 2 2 19
2 0 0 0 0 0 2
19 2 2 2 2 2 19
8 29 1 2 2 2 1 29
0 0 0 0 0 0 0
29 1 2 2 2 1 29
9 50 4 7 8 7 4 50
2 0 0 0 0 0 2
50 4 7 8 7 4 50
10 63 5 7 10 7 5 63
0 0 0 0 0 0 0
63 5 7 10 7 5 63
11 81 9 13 10 13 9 81
2 0 0 0 0 0 2
81 9 13 10 13 9 81
12 37 10 8 10 8 10 37
0 0 0 0 0 0 0
37 10 8 10 8 10 37
13 33 10 13 8 13 10 33
2 0 0 0 0 0 2
33 10 13 8 13 10 33
14 11 9 4 8 4 9 11
0 0 0 0 0 0 0
11 9 4 8 4 9 11
15 5 6 5 2 5 6 5
2 0 0 0 0 0 2
5 6 5 2 5 6 5
16 0 1 1 0 1 1 0
0 0 0 0 0 0 0
0 1 1 0 1 1 0
Total 353 57 62 60 62 57 353
10 0 0 0 0 0 10
353 57 62 60 62 57 353
Grand total = 2*10 + 4*57 + 2*60 + 4*62 + 4*353
= 2028
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
L
3 2 1 0 0 0 1 2
2 4 0 0 0 4 2
2 1 0 0 0 1 2
4 4 4 0 0 0 4 4
4 8 4 0 4 8 4
4 4 0 0 0 4 4
5 9 7 5 0 5 7 9
8 16 10 8 10 16 8
9 7 5 0 5 7 9
6 11 7 5 18 5 7 11
12 22 22 24 22 22 12
11 7 5 18 5 7 11
7 25 24 36 32 36 24 25
26 42 52 56 52 42 26
25 24 36 32 36 24 25
8 32 44 42 52 42 44 32
40 74 84 84 84 74 40
32 44 42 52 42 44 32
9 87 92 114 136 114 92 87
82 162 144 156 144 162 82
87 92 114 136 114 92 87
10 94 144 159 174 159 144 94
150 222 188 144 188 222 150
94 144 159 174 159 144 94
11 201 221 236 238 236 221 201
208 308 232 192 232 308 208
201 221 236 238 236 221 201
12 125 155 138 138 138 155 125
148 132 124 124 124 132 148
125 155 138 138 138 155 125
13 154 171 173 162 173 171 154
166 118 92 104 92 118 166
154 171 173 162 173 171 154
14 86 87 75 82 75 87 86
92 40 44 60 44 40 92
86 87 75 82 75 87 86
15 68 63 61 52 61 63 68
70 4 20 20 20 4 70
68 63 61 52 61 63 68
16 8 8 6 4 6 8 8
8 0 4 8 4 0 8
8 8 6 4 6 8 8
Total 906 1028 1050 1088 1050 1028 906
1016 1152 1020 980 1020 1152 1016
906 1028 1050 1088 1050 1028 906
Grand total = 4*906 + 980 + 2*1016 + 2*1020 + 4*1028 + 4*1050 + 2*1088 + 2*1152
= 21468
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
EN
0 0 0 10 18 26 36 54 0 2 2 4 10 22 46 6 2 4 9 18 32 52
1 0 0 0 5 3 5 6 5 0 1 1 1 3 7 0 0 0 0 3 7 10
2 8 0 0 0 8 6 8 4 4 0 2 2 2 6 0 0 0 0 0 4 8
3 9 9 0 0 0 9 9 3 3 3 0 3 3 3 3 0 0 0 0 0 3
4 8 6 8 0 0 0 8 6 2 2 2 0 4 4 8 4 0 0 0 0 0
5 6 5 3 5 0 0 0 7 3 1 1 1 0 5 10 7 3 0 0 0 0
6 54 36 26 18 10 0 0 46 22 10 4 2 2 0 52 32 18 9 4 2 6
7 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 5 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
9 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
11 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
13 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0
14 6 2 4 9 18 32 52 0 2 2 4 10 22 46 0 0 10 18 26 36 54
15 0 0 0 0 3 7 10 5 0 1 1 1 3 7 0 0 0 5 3 5 6
16 0 0 0 0 0 4 8 4 4 0 2 2 2 6 8 0 0 0 8 6 8
17 3 0 0 0 0 0 3 3 3 3 0 3 3 3 9 9 0 0 0 9 9
18 8 4 0 0 0 0 0 6 2 2 2 0 4 4 8 6 8 0 0 0 8
19 10 7 3 0 0 0 0 7 3 1 1 1 0 5 6 5 3 5 0 0 0
20 52 32 18 9 4 2 6 46 22 10 4 2 2 0 54 36 26 18 10 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 1*6 + 1*9 + 2*10 + 2*18 + 1*22 + 1*26 + 1*32 + 1*36 + 1*46 + 1*52 + 1*54) +
4(8*0 + 3*1 + 3*3 + 3*5 + 1*6 + 2*7 + 1*10) +
4(9*0 + 3*2 + 3*4 + 2*6 + 4*8) +
2(9*0 + 8*3 + 4*9) +
2(19*0 + 2*5) +
5(21*0)
= 1412 + 228 + 248 + 120 + 20
= 2028
Value repetition frequencies = 4(9*1 + 3*2 + 2*3) +
4(2*1 + 1*2 + 3*3 + 1*8) +
4(1*2 + 2*3 + 1*4 + 1*9) +
2(1*4 + 1*8 + 1*9) +
2(1*2 + 1*19) +
5(1*21)
= 441
Number of distinct row element sets = 6
Number of rows = 2*2 + 3*4 + 1*5
= 21
Number of distinct values = 19
Distinct values 0 1 2 3 4 5 6 7 8 9 10 18 22 26 32 36 46 52 54
Frequency 241 12 24 28 20 16 16 8 16 12 12 8 4 4 4 4 4 4 4
Sum of distinct value frequencies = 7*4 + 2*8 + 3*12 + 3*16 + 1*20 + 1*24 + 1*28 + 1*241
= 441
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 6*12 + 4*13 + 4*18
= 200
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 220
Number of possible SN-EN pairs with SN != EN = 20*21
= 420
a = 8, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 44 22
7 104 38
8 136 60
9 288 114
10 444 188
11 668 280
12 812 360
13 604 248
14 576 254
15 396 174
16 176 84
17 104 52
18 12 6
Total 4420 1896
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 0 0 0 0 0 0 0
0 4 0 0 0 0 4 0
0 0 0 0 0 0 0 0
4 0 2 0 0 0 0 2 0
0 0 4 0 0 4 0 0
0 2 0 0 0 0 2 0
5 1 0 5 0 0 5 0 1
0 0 0 4 4 0 0 0
1 0 5 0 0 5 0 1
6 0 0 0 9 9 0 0 0
0 0 0 4 4 0 0 0
0 0 0 9 9 0 0 0
7 1 1 1 13 13 1 1 1
2 2 8 8 8 8 2 2
1 1 1 13 13 1 1 1
8 0 0 17 3 3 17 0 0
2 6 2 18 18 2 6 2
0 0 17 3 3 17 0 0
9 3 24 4 14 14 4 24 3
8 4 36 6 6 36 4 8
3 24 4 14 14 4 24 3
10 29 4 32 9 9 32 4 29
4 62 4 4 4 4 62 4
29 4 32 9 9 32 4 29
11 9 74 11 14 14 11 74 9
98 6 12 2 2 12 6 98
9 74 11 14 14 11 74 9
12 138 12 22 5 5 22 12 138
10 36 6 0 0 6 36 10
138 12 22 5 5 22 12 138
13 21 49 8 13 13 8 49 21
102 16 2 0 0 2 16 102
21 49 8 13 13 8 49 21
14 86 13 19 6 6 19 13 86
32 8 0 0 0 0 8 32
86 13 19 6 6 19 13 86
15 33 30 8 13 13 8 30 33
28 2 0 0 0 0 2 28
33 30 8 13 13 8 30 33
16 19 7 7 6 6 7 7 19
10 0 0 0 0 0 0 10
19 7 7 6 6 7 7 19
17 7 8 7 3 3 7 8 7
2 0 0 0 0 0 0 2
7 8 7 3 3 7 8 7
18 0 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 0
Total 347 225 142 109 109 142 225 347
298 146 74 46 46 74 146 298
347 225 142 109 109 142 225 347
Grand total = 2*46 + 2*74 + 4*109 + 4*142 + 2*146 + 4*225 + 2*298 + 4*347
= 4420
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 2
0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 4
5 8 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 8
6 11 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 11
7 19 2 2 2 2 2 2 19
2 0 0 0 0 0 0 2
19 2 2 2 2 2 2 19
8 29 1 2 2 2 2 1 29
0 0 0 0 0 0 0 0
29 1 2 2 2 2 1 29
9 52 4 7 8 8 7 4 52
2 0 0 0 0 0 0 2
52 4 7 8 8 7 4 52
10 88 5 7 11 11 7 5 88
0 0 0 0 0 0 0 0
88 5 7 11 11 7 5 88
11 127 9 14 16 16 14 9 127
2 0 0 0 0 0 0 2
127 9 14 16 16 14 9 127
12 163 11 16 13 13 16 11 163
0 0 0 0 0 0 0 0
163 11 16 13 13 16 11 163
13 92 20 20 18 18 20 20 92
2 0 0 0 0 0 0 2
92 20 20 18 18 20 20 92
14 90 21 20 13 13 20 21 90
0 0 0 0 0 0 0 0
90 21 20 13 13 20 21 90
15 39 28 17 14 14 17 28 39
2 0 0 0 0 0 0 2
39 28 17 14 14 17 28 39
16 17 9 11 7 7 11 9 17
0 0 0 0 0 0 0 0
17 9 11 7 7 11 9 17
17 6 8 7 4 4 7 8 6
2 0 0 0 0 0 0 2
6 8 7 4 4 7 8 6
18 0 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 0
Total 747 119 124 109 109 124 119 747
12 0 0 0 0 0 0 12
747 119 124 109 109 124 119 747
Grand total = 2*12 + 4*109 + 4*119 + 4*124 + 4*747
= 4420
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 2 1 0 0 0 0 1 2
2 4 0 0 0 0 4 2
2 1 0 0 0 0 1 2
4 4 4 0 0 0 0 4 4
4 8 4 0 0 4 8 4
4 4 0 0 0 0 4 4
5 9 7 5 0 0 5 7 9
8 16 10 4 4 10 16 8
9 7 5 0 0 5 7 9
6 11 7 5 9 9 5 7 11
12 22 18 16 16 18 22 12
11 7 5 9 9 5 7 11
7 25 24 23 34 34 23 24 25
26 38 44 44 44 44 38 26
25 24 23 34 34 23 24 25
8 32 27 41 49 49 41 27 32
36 66 62 82 82 62 66 36
32 27 41 49 49 41 27 32
9 68 88 98 135 135 98 88 68
80 130 148 160 160 148 130 80
68 88 98 135 135 98 88 68
10 131 133 175 213 213 175 133 131
126 278 264 248 248 264 278 126
131 133 175 213 213 175 133 131
11 187 281 306 352 352 306 281 187
278 426 394 324 324 394 426 278
187 281 306 352 352 306 281 187
12 361 368 382 403 403 382 368 361
362 598 482 402 402 482 598 362
361 368 382 403 403 382 368 361
13 263 361 362 352 352 362 361 263
332 330 294 294 294 294 330 332
263 361 362 352 352 362 361 263
14 333 366 355 337 337 355 366 333
358 334 256 302 302 256 334 358
333 366 355 337 337 355 366 333
15 264 308 267 250 250 267 308 264
284 166 150 192 192 150 166 284
264 308 267 250 250 267 308 264
16 141 139 132 116 116 132 139 141
148 52 64 88 88 64 52 148
141 139 132 116 116 132 139 141
17 100 93 89 75 75 89 93 100
102 4 28 36 36 28 4 102
100 93 89 75 75 89 93 100
18 12 12 10 8 8 10 12 12
12 0 4 8 8 4 0 12
12 12 10 8 8 10 12 12
Total 1943 2219 2250 2333 2333 2250 2219 1943
2170 2472 2222 2200 2200 2222 2472 2170
1943 2219 2250 2333 2333 2250 2219 1943
Grand total = 4*1943 + 2*2170 + 2*2200 + 4*2219 + 2*2222 + 4*2250 + 4*2333 + 2*2472
= 53108
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 12 22 32 44 70 108 0 2 2 4 10 22 46 96 7 2 4 10 22 42 74 116
1 0 0 0 6 3 6 8 14 6 0 1 1 1 3 7 15 0 0 0 0 4 10 14 20
2 10 0 0 0 10 6 10 12 5 5 0 2 2 2 6 14 0 0 0 0 0 6 14 20
3 12 12 0 0 0 12 9 12 4 4 4 0 3 3 3 9 4 0 0 0 0 0 6 12
4 12 9 12 0 0 0 12 12 9 3 3 3 0 4 4 4 12 6 0 0 0 0 0 4
5 12 10 6 10 0 0 0 10 14 6 2 2 2 0 5 5 20 14 6 0 0 0 0 0
6 14 8 6 3 6 0 0 0 15 7 3 1 1 1 0 6 20 14 10 4 0 0 0 0
7 108 70 44 32 22 12 0 0 96 46 22 10 4 2 2 0 116 74 42 22 10 4 2 7
8 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 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 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
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 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0
16 7 2 4 10 22 42 74 116 0 2 2 4 10 22 46 96 0 0 12 22 32 44 70 108
17 0 0 0 0 4 10 14 20 6 0 1 1 1 3 7 15 0 0 0 6 3 6 8 14
18 0 0 0 0 0 6 14 20 5 5 0 2 2 2 6 14 10 0 0 0 10 6 10 12
19 4 0 0 0 0 0 6 12 4 4 4 0 3 3 3 9 12 12 0 0 0 12 9 12
20 12 6 0 0 0 0 0 4 9 3 3 3 0 4 4 4 12 9 12 0 0 0 12 12
21 20 14 6 0 0 0 0 0 14 6 2 2 2 0 5 5 12 10 6 10 0 0 0 10
22 20 14 10 4 0 0 0 0 15 7 3 1 1 1 0 6 14 8 6 3 6 0 0 0
23 116 74 42 22 10 4 2 7 96 46 22 10 4 2 2 0 108 70 44 32 22 12 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 1*7 + 2*10 + 1*12 + 3*22 + 1*32 + 1*42 + 1*44 + 1*46 + 1*70 + 1*74 + 1*96 + 1*108 + 1*116) +
4(8*0 + 3*1 + 2*3 + 1*4 + 3*6 + 1*7 + 1*8 + 1*10 + 2*14 + 1*15 + 1*20) +
4(9*0 + 3*2 + 2*5 + 3*6 + 3*10 + 1*12 + 2*14 + 1*20) +
4(9*0 + 3*3 + 4*4 + 6 + 2*9 + 5*12) +
2(22*0 + 2*6) +
6(24*0)
= 2988 + 476 + 496 + 436 + 24
= 4420
Value repetition frequencies = 4(11*1 + 2*2 + 3*3) +
4(6*1 + 2*2 + 2*3 + 1*8) +
4(2*1 + 2*2 + 3*3 + 1*9) +
4(1*1 + 1*2 + 1*3 + 1*4 + 1*5 + 1*9) +
2(1*2 + 1*22) +
6(1*24)
= 576
Number of distinct row element sets = 6
Number of rows = 1*2 + 4*4 + 1*6
= 24
Number of distinct values = 25
Distinct values 0 1 2 3 4 5 6 7 8 9 10 12 14 15 20 22 32 42 44 46 70 74 96 108 116
Frequency 304 12 24 20 28 8 32 8 4 8 24 28 16 4 8 12 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 11*4 + 4*8 + 2*12 + 1*16 + 1*20 + 2*24 + 2*28 + 1*32 + 1*304
= 576
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 8*15 + 4*16 + 4*21
= 272
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 280
Number of possible SN-EN pairs with SN != EN = 23*24
= 552
a = 9, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 44 22
7 108 38
8 140 60
9 304 114
10 476 192
11 832 338
12 1148 494
13 1620 694
14 1284 534
15 1520 642
16 912 402
17 640 282
18 272 130
19 144 72
20 16 8
Total 9516 4038
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
L
3 0 0 0 0 0 0 0 0 0
0 4 0 0 0 0 0 4 0
0 0 0 0 0 0 0 0 0
4 0 2 0 0 0 0 0 2 0
0 0 4 0 0 0 4 0 0
0 2 0 0 0 0 0 2 0
5 1 0 5 0 0 0 5 0 1
0 0 0 4 0 4 0 0 0
1 0 5 0 0 0 5 0 1
6 0 0 0 9 0 9 0 0 0
0 0 0 0 8 0 0 0 0
0 0 0 9 0 9 0 0 0
7 1 1 1 0 26 0 1 1 1
2 2 4 12 4 12 4 2 2
1 1 1 0 26 0 1 1 1
8 0 0 0 20 0 20 0 0 0
2 2 6 4 32 4 6 2 2
0 0 0 20 0 20 0 0 0
9 3 3 25 4 24 4 25 3 3
4 8 4 38 8 38 4 8 4
3 3 25 4 24 4 25 3 3
10 4 29 4 37 8 37 4 29 4
8 4 62 4 8 4 62 4 8
4 29 4 37 8 37 4 29 4
11 38 10 75 10 26 10 75 10 38
6 98 6 12 4 12 6 98 6
38 10 75 10 26 10 75 10 38
12 12 138 12 27 0 27 12 138 12
144 10 36 6 0 6 36 10 144
12 138 12 27 0 27 12 138 12
13 243 22 51 7 24 7 51 22 243
20 102 16 2 0 2 16 102 20
243 22 51 7 24 7 51 22 243
14 32 108 13 24 2 24 13 108 32
246 32 8 0 0 0 8 32 246
32 108 13 24 2 24 13 108 32
15 229 38 49 8 24 8 49 38 229
58 28 2 0 0 0 2 28 58
229 38 49 8 24 8 49 38 229
16 68 77 8 25 2 25 8 77 68
88 10 0 0 0 0 0 10 88
68 77 8 25 2 25 8 77 68
17 69 20 33 7 24 7 33 20 69
36 2 0 0 0 0 0 2 36
69 20 33 7 24 7 33 20 69
18 24 17 8 12 2 12 8 17 24
12 0 0 0 0 0 0 0 12
24 17 8 12 2 12 8 17 24
19 8 10 9 6 4 6 9 10 8
2 0 0 0 0 0 0 0 2
8 10 9 6 4 6 9 10 8
20 0 1 1 1 2 1 1 1 0
0 0 0 0 0 0 0 0 0
0 1 1 1 2 1 1 1 0
Total 732 476 294 197 168 197 294 476 732
628 302 148 82 64 82 148 302 628
732 476 294 197 168 197 294 476 732
Grand total = 64 + 2*82 + 2*148 + 2*168 + 4*197 + 4*294 + 2*302 + 4*476 + 2*628 + 4*732
= 9516
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
L
3 2 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 4
5 8 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 8
6 11 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 11
7 19 2 2 2 2 2 2 2 19
2 0 0 0 0 0 0 0 2
19 2 2 2 2 2 2 2 19
8 29 1 2 2 2 2 2 1 29
0 0 0 0 0 0 0 0 0
29 1 2 2 2 2 2 1 29
9 52 4 7 8 8 8 7 4 52
2 0 0 0 0 0 0 0 2
52 4 7 8 8 8 7 4 52
10 90 5 7 11 12 11 7 5 90
0 0 0 0 0 0 0 0 0
90 5 7 11 12 11 7 5 90
11 156 9 14 17 22 17 14 9 156
2 0 0 0 0 0 0 0 2
156 9 14 17 22 17 14 9 156
12 230 11 17 21 16 21 17 11 230
0 0 0 0 0 0 0 0 0
230 11 17 21 16 21 17 11 230
13 314 21 30 25 28 25 30 21 314
2 0 0 0 0 0 0 0 2
314 21 30 25 28 25 30 21 314
14 217 33 33 29 18 29 33 33 217
0 0 0 0 0 0 0 0 0
217 33 33 29 18 29 33 33 217
15 242 48 49 27 26 27 49 48 242
2 0 0 0 0 0 0 0 2
242 48 49 27 26 27 49 48 242
16 107 57 31 25 16 25 31 57 107
0 0 0 0 0 0 0 0 0
107 57 31 25 16 25 31 57 107
17 68 26 37 18 20 18 37 26 68
2 0 0 0 0 0 0 0 2
68 26 37 18 20 18 37 26 68
18 21 19 11 14 6 14 11 19 21
0 0 0 0 0 0 0 0 0
21 19 11 14 6 14 11 19 21
19 7 10 9 6 6 6 9 10 7
2 0 0 0 0 0 0 0 2
7 10 9 6 6 6 9 10 7
20 0 1 1 1 2 1 1 1 0
0 0 0 0 0 0 0 0 0
0 1 1 1 2 1 1 1 0
Total 1577 247 250 206 184 206 250 247 1577
14 0 0 0 0 0 0 0 14
1577 247 250 206 184 206 250 247 1577
Grand total = 2*14 + 2*184 + 4*206 + 4*247 + 4*250 + 4*1577
= 9516
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
L
3 2 1 0 0 0 0 0 1 2
2 4 0 0 0 0 0 4 2
2 1 0 0 0 0 0 1 2
4 4 4 0 0 0 0 0 4 4
4 8 4 0 0 0 4 8 4
4 4 0 0 0 0 0 4 4
5 9 7 5 0 0 0 5 7 9
8 16 10 4 0 4 10 16 8
9 7 5 0 0 0 5 7 9
6 11 7 5 9 0 9 5 7 11
12 22 18 12 8 12 18 22 12
11 7 5 9 0 9 5 7 11
7 25 24 23 21 36 21 23 24 25
26 38 40 36 32 36 40 38 26
25 24 23 21 36 21 23 24 25
8 32 27 24 48 46 48 24 27 32
36 62 54 60 80 60 54 62 36
32 27 24 48 46 48 24 27 32
9 68 67 93 119 134 119 93 67 68
76 122 108 156 156 156 108 122 76
68 67 93 119 134 119 93 67 68
10 108 125 133 211 234 211 133 125 108
124 220 254 254 280 254 254 220 124
108 125 133 211 234 211 133 125 108
11 228 232 322 386 424 386 322 232 228
224 462 458 456 432 456 458 462 224
228 232 322 386 424 386 322 232 228
12 306 451 467 548 550 548 467 451 306
444 736 720 612 564 612 720 736 444
306 451 467 548 550 548 467 451 306
13 669 681 731 798 818 798 731 681 669
654 1118 954 840 776 840 954 1118 654
669 681 731 798 818 798 731 681 669
14 489 707 709 701 666 701 709 707 489
670 774 646 658 724 658 646 774 670
489 707 709 701 666 701 709 707 489
15 791 902 913 851 846 851 913 902 791
840 938 706 736 840 736 706 938 840
791 902 913 851 846 851 913 902 791
16 567 655 563 523 484 523 563 655 567
626 418 416 486 500 486 416 418 626
567 655 563 523 484 523 563 655 567
17 444 490 482 406 406 406 482 490 444
470 254 214 278 348 278 214 254 470
444 490 482 406 406 406 482 490 444
18 228 227 202 189 160 189 202 227 228
236 64 96 140 120 140 96 64 236
228 227 202 189 160 189 202 227 228
19 140 131 125 107 104 107 125 131 140
142 4 36 48 56 48 36 4 142
140 131 125 107 104 107 125 131 140
20 16 16 14 12 12 12 14 16 16
16 0 4 8 8 8 4 0 16
16 16 14 12 12 12 14 16 16
Total 4137 4754 4811 4929 4920 4929 4811 4754 4137
4610 5260 4738 4784 4924 4784 4738 5260 4610
4137 4754 4811 4929 4920 4929 4811 4754 4137
Grand total = 4*4137 + 2*4610 + 2*4738 + 4*4754 + 2*4784 + 4*4811 + 4*4929 + 2*4920 + 4924 + 2*5260
= 128072
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
EN
0 0 0 14 26 38 52 86 146 228 0 2 2 4 10 22 46 96 202 8 2 4 11 26 52 96 160 244
1 0 0 0 7 3 7 10 21 35 7 0 1 1 1 3 7 15 31 0 0 0 0 5 13 18 25 37
2 12 0 0 0 12 6 12 16 28 6 6 0 2 2 2 6 14 30 0 0 0 0 0 8 20 28 40
3 15 15 0 0 0 15 9 15 18 5 5 5 0 3 3 3 9 21 5 0 0 0 0 0 9 21 30
4 16 12 16 0 0 0 16 12 16 12 4 4 4 0 4 4 4 12 16 8 0 0 0 0 0 8 16
5 18 15 9 15 0 0 0 15 15 21 9 3 3 3 0 5 5 5 30 21 9 0 0 0 0 0 5
6 28 16 12 6 12 0 0 0 12 30 14 6 2 2 2 0 6 6 40 28 20 8 0 0 0 0 0
7 35 21 10 7 3 7 0 0 0 31 15 7 3 1 1 1 0 7 37 25 18 13 5 0 0 0 0
8 228 146 86 52 38 26 14 0 0 202 96 46 22 10 4 2 2 0 244 160 96 52 26 11 4 2 8
9 0 7 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
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
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
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
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
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
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
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
17 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 7 0
18 8 2 4 11 26 52 96 160 244 0 2 2 4 10 22 46 96 202 0 0 14 26 38 52 86 146 228
19 0 0 0 0 5 13 18 25 37 7 0 1 1 1 3 7 15 31 0 0 0 7 3 7 10 21 35
20 0 0 0 0 0 8 20 28 40 6 6 0 2 2 2 6 14 30 12 0 0 0 12 6 12 16 28
21 5 0 0 0 0 0 9 21 30 5 5 5 0 3 3 3 9 21 15 15 0 0 0 15 9 15 18
22 16 8 0 0 0 0 0 8 16 12 4 4 4 0 4 4 4 12 16 12 16 0 0 0 16 12 16
23 30 21 9 0 0 0 0 0 5 21 9 3 3 3 0 5 5 5 18 15 9 15 0 0 0 15 15
24 40 28 20 8 0 0 0 0 0 30 14 6 2 2 2 0 6 6 28 16 12 6 12 0 0 0 12
25 37 25 18 13 5 0 0 0 0 31 15 7 3 1 1 1 0 7 35 21 10 7 3 7 0 0 0
26 244 160 96 52 26 11 4 2 8 202 96 46 22 10 4 2 2 0 228 146 86 52 38 26 14 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 1*8 + 1*10 + 1*11 + 1*14 + 1*22 + 2*26 + 1*38 + 1*46 + 2*52 + 1*86 + 2*96 + 1*146 + 1*160 + 1*202 + 1*228 + 1*244) +
4(8*0 + 3*1 + 2*3 + 1*5 + 4*7 + 1*10 + 1*13 + 1*15 + 1*18 + 1*21 + 1*25 + 1*31 + 1*35 + 1*37) +
4(9*0 + 3*2 + 4*6 + 1*8 + 3*12 + 1*14 + 1*16 + 1*20 + 2*28 + 1*30 + 1*40) +
4(9*0 + 3*3 + 4*5 + 3*9 + 4*15 + 1*18 + 2*21 + 1*30) +
2(9*0 + 6*4 + 2*8 + 4*12 + 6*16) +
2(25*0 + 2*7) +
7(27*0)
= 6308 + 988 + 1000 + 824 + 368 + 28
= 9516
Value repetition frequencies = 4(13*1 + 4*2 + 2*3) +
4(10*1 + 1*2 + 1*3 + 1*4 + 1*8) +
4(6*1 + 1*2 + 2*3 + 1*4 + 1*9) +
4(2*1 + 1*2 + 2*3 + 2*4 + 1*9) +
2(1*2 + 1*4 + 2*6 + 1*9) +
2(1*2 + 1*25) +
7(1*27)
= 729
Number of distinct row element sets = 7
Number of rows = 2*2 + 4*4 + 1*7
= 27
Number of distinct values = 39
Distinct values 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 21 22 25 26 28 30 31 35 37 38 40 46 52 86 96 146 160 202 228 244
Frequency 373 12 24 20 20 20 16 20 12 12 8 4 20 4 8 20 16 8 4 12 4 4 8 8 8 4 4 4 4 4 4 8 4 8 4 4 4 4 4
Sum of distinct value frequencies = 17*4 + 8*8 + 4*12 + 2*16 + 6*20 + 1*24 + 1*373
= 729
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 10*18 + 4*19 + 4*24
= 356
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 346
Number of possible SN-EN pairs with SN != EN = 26*27
= 702
a = 10, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 44 22
7 112 38
8 144 60
9 320 114
10 500 192
11 888 342
12 1348 560
13 2116 878
14 2928 1256
15 2920 1186
16 3384 1450
17 2284 960
18 1676 744
19 980 434
20 408 196
21 192 96
22 20 10
Total 20320 8554
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 0 0 0 0 0 0 0 0 0
0 4 0 0 0 0 0 0 4 0
0 0 0 0 0 0 0 0 0 0
4 0 2 0 0 0 0 0 0 2 0
0 0 4 0 0 0 0 4 0 0
0 2 0 0 0 0 0 0 2 0
5 1 0 5 0 0 0 0 5 0 1
0 0 0 4 0 0 4 0 0 0
1 0 5 0 0 0 0 5 0 1
6 0 0 0 9 0 0 9 0 0 0
0 0 0 0 4 4 0 0 0 0
0 0 0 9 0 0 9 0 0 0
7 1 1 1 0 13 13 0 1 1 1
2 2 4 8 8 8 8 4 2 2
1 1 1 0 13 13 0 1 1 1
8 0 0 0 3 17 17 3 0 0 0
2 2 2 8 18 18 8 2 2 2
0 0 0 3 17 17 3 0 0 0
9 3 3 4 25 14 14 25 4 3 3
4 4 8 6 40 40 6 8 4 4
3 3 4 25 14 14 25 4 3 3
10 4 4 29 9 36 36 9 29 4 4
4 8 4 62 8 8 62 4 8 4
4 4 29 9 36 36 9 29 4 4
11 9 39 11 74 22 22 74 11 39 9
10 6 98 6 14 14 6 98 6 10
9 39 11 74 22 22 74 11 39 9
12 45 12 138 17 22 22 17 138 12 45
10 144 10 36 6 6 36 10 144 10
45 12 138 17 22 22 17 138 12 45
13 21 244 24 50 18 18 50 24 244 21
204 20 102 16 2 2 16 102 20 204
21 244 24 50 18 18 50 24 244 21
14 392 33 108 18 20 20 18 108 33 392
36 246 32 8 0 0 8 32 246 36
392 33 108 18 20 20 18 108 33 392
15 57 259 40 49 19 19 49 40 259 57
524 58 28 2 0 0 2 28 58 524
57 259 40 49 19 19 49 40 259 57
16 540 75 99 13 21 21 13 99 75 540
98 88 10 0 0 0 0 10 88 98
540 75 99 13 21 21 13 99 75 540
17 135 191 26 50 19 19 50 26 191 135
262 36 2 0 0 0 0 2 36 262
135 191 26 50 19 19 50 26 191 135
18 212 41 75 14 21 21 14 75 41 212
100 12 0 0 0 0 0 0 12 100
212 41 75 14 21 21 14 75 41 212
19 81 63 24 32 18 18 32 24 63 81
52 2 0 0 0 0 0 0 2 52
81 63 24 32 18 18 32 24 63 81
20 33 23 18 13 8 8 13 18 23 33
14 0 0 0 0 0 0 0 0 14
33 23 18 13 8 8 13 18 23 33
21 9 12 11 8 7 7 8 11 12 9
2 0 0 0 0 0 0 0 0 2
9 12 11 8 7 7 8 11 12 9
22 0 1 1 1 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 1 1 1 0
Total 1543 1003 614 385 277 277 385 614 1003 1543
1324 632 304 156 100 100 156 304 632 1324
1543 1003 614 385 277 277 385 614 1003 1543
Grand total = 2*100 + 2*156 + 4*277 + 2*304 + 4*385 + 4*614 + 2*632 + 4*1003 + 2*1324 + 4*1543
= 20320
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 2
0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 4
5 8 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 8
6 11 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 11
7 19 2 2 2 2 2 2 2 2 19
2 0 0 0 0 0 0 0 0 2
19 2 2 2 2 2 2 2 2 19
8 29 1 2 2 2 2 2 2 1 29
0 0 0 0 0 0 0 0 0 0
29 1 2 2 2 2 2 2 1 29
9 52 4 7 8 8 8 8 7 4 52
2 0 0 0 0 0 0 0 0 2
52 4 7 8 8 8 8 7 4 52
10 90 5 7 11 12 12 11 7 5 90
0 0 0 0 0 0 0 0 0 0
90 5 7 11 12 12 11 7 5 90
11 158 9 14 17 23 23 17 14 9 158
2 0 0 0 0 0 0 0 0 2
158 9 14 17 23 23 17 14 9 158
12 263 11 17 22 24 24 22 17 11 263
0 0 0 0 0 0 0 0 0 0
263 11 17 22 24 24 22 17 11 263
13 406 21 31 35 35 35 35 31 21 406
2 0 0 0 0 0 0 0 0 2
406 21 31 35 35 35 35 31 21 406
14 577 34 45 42 34 34 42 45 34 577
0 0 0 0 0 0 0 0 0 0
577 34 45 42 34 34 42 45 34 577
15 499 62 70 59 39 39 59 70 62 499
2 0 0 0 0 0 0 0 0 2
499 62 70 59 39 39 59 70 62 499
16 588 87 91 46 34 34 46 91 87 588
0 0 0 0 0 0 0 0 0 0
588 87 91 46 34 34 46 91 87 588
17 286 116 75 58 35 35 58 75 116 286
2 0 0 0 0 0 0 0 0 2
286 116 75 58 35 35 58 75 116 286
18 217 61 77 36 28 28 36 77 61 217
0 0 0 0 0 0 0 0 0 0
217 61 77 36 28 28 36 77 61 217
19 81 64 37 38 24 24 38 37 64 81
2 0 0 0 0 0 0 0 0 2
81 64 37 38 24 24 38 37 64 81
20 29 25 21 14 13 13 14 21 25 29
0 0 0 0 0 0 0 0 0 0
29 25 21 14 13 13 14 21 25 29
21 8 12 11 8 8 8 8 11 12 8
2 0 0 0 0 0 0 0 0 2
8 12 11 8 8 8 8 11 12 8
22 0 1 1 1 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 1 1 1 0
Total 3327 515 508 399 323 323 399 508 515 3327
16 0 0 0 0 0 0 0 0 16
3327 515 508 399 323 323 399 508 515 3327
Grand total = 2*16 + 4*323 + 4*399 + 4*508 + 4*515 + 4*3327
= 20320
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 2 1 0 0 0 0 0 0 1 2
2 4 0 0 0 0 0 0 4 2
2 1 0 0 0 0 0 0 1 2
4 4 4 0 0 0 0 0 0 4 4
4 8 4 0 0 0 0 4 8 4
4 4 0 0 0 0 0 0 4 4
5 9 7 5 0 0 0 0 5 7 9
8 16 10 4 0 0 4 10 16 8
9 7 5 0 0 0 0 5 7 9
6 11 7 5 9 0 0 9 5 7 11
12 22 18 12 4 4 12 18 22 12
11 7 5 9 0 0 9 5 7 11
7 25 24 23 21 23 23 21 23 24 25
26 38 40 32 24 24 32 40 38 26
25 24 23 21 23 23 21 23 24 25
8 32 27 24 31 45 45 31 24 27 32
36 62 50 52 58 58 52 50 62 36
32 27 24 31 45 45 31 24 27 32
9 68 67 72 114 118 118 114 72 67 68
76 118 100 116 152 152 116 100 118 76
68 67 72 114 118 118 114 72 67 68
10 108 100 124 169 232 232 169 124 100 108
120 212 188 236 278 278 236 188 212 120
108 100 124 169 232 232 169 124 100 108
11 201 220 236 380 436 436 380 236 220 201
222 370 420 442 484 484 442 420 370 222
201 220 236 380 436 436 380 236 220 201
12 351 338 486 580 629 629 580 486 338 351
352 736 744 772 716 716 772 744 736 352
351 338 486 580 629 629 580 486 338 351
13 543 786 812 979 1028 1028 979 812 786 543
744 1240 1270 1144 1060 1060 1144 1270 1240 744
543 786 812 979 1028 1028 979 812 786 543
14 1131 1139 1247 1372 1387 1387 1372 1247 1139 1131
1088 1996 1752 1590 1518 1518 1590 1752 1996 1088
1131 1139 1247 1372 1387 1387 1372 1247 1139 1131
15 990 1478 1550 1582 1491 1491 1582 1550 1478 990
1404 1772 1506 1436 1600 1600 1436 1506 1772 1404
990 1478 1550 1582 1491 1491 1582 1550 1478 990
16 1667 1859 1864 1788 1720 1720 1788 1864 1859 1667
1746 2260 1690 1682 1898 1898 1682 1690 2260 1746
1667 1859 1864 1788 1720 1720 1788 1864 1859 1667
17 1255 1537 1417 1306 1211 1211 1306 1417 1537 1255
1430 1100 1076 1138 1218 1218 1138 1076 1100 1430
1255 1537 1417 1306 1211 1211 1306 1417 1537 1255
18 1089 1173 1160 1012 940 940 1012 1160 1173 1089
1162 782 654 808 930 930 808 654 782 1162
1089 1173 1160 1012 940 940 1012 1160 1173 1089
19 716 800 712 657 600 600 657 712 800 716
752 334 330 454 470 470 454 330 334 752
716 800 712 657 600 600 657 712 800 716
20 355 347 320 279 257 257 279 320 347 355
364 76 136 196 192 192 196 136 76 364
355 347 320 279 257 257 279 320 347 355
21 188 177 169 147 142 142 147 169 177 188
190 4 44 60 72 72 60 44 4 190
188 177 169 147 142 142 147 169 177 188
22 20 20 18 16 16 16 16 18 20 20
20 0 4 8 8 8 8 4 0 20
20 20 18 16 16 16 16 18 20 20
Total 8765 10111 10244 10442 10275 10275 10442 10244 10111 8765
9758 11150 10036 10182 10682 10682 10182 10036 11150 9758
8765 10111 10244 10442 10275 10275 10442 10244 10111 8765
Grand total = 4*8765 + 2*9758 + 2*10036 + 4*10111 + 2*10182 + 4*10244 + 4*10275 + 4*10442 + 2*10682 + 2*11150
= 302964
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 16 30 44 60 102 184 316 492 0 2 2 4 10 22 46 96 202 426 9 2 4 12 30 62 118 204 330 502
1 0 0 0 8 3 8 12 28 51 80 8 0 1 1 1 3 7 15 31 65 0 0 0 0 6 16 22 30 47 72
2 14 0 0 0 14 6 14 20 42 70 7 7 0 2 2 2 6 14 30 62 0 0 0 0 0 10 26 36 50 74
3 18 18 0 0 0 18 9 18 24 42 6 6 6 0 3 3 3 9 21 45 6 0 0 0 0 0 12 30 42 60
4 20 15 20 0 0 0 20 12 20 24 15 5 5 5 0 4 4 4 12 28 20 10 0 0 0 0 0 12 28 40
5 24 20 12 20 0 0 0 20 15 20 28 12 4 4 4 0 5 5 5 15 40 28 12 0 0 0 0 0 10 20
6 42 24 18 9 18 0 0 0 18 18 45 21 9 3 3 3 0 6 6 6 60 42 30 12 0 0 0 0 0 6
7 70 42 20 14 6 14 0 0 0 14 62 30 14 6 2 2 2 0 7 7 74 50 36 26 10 0 0 0 0 0
8 80 51 28 12 8 3 8 0 0 0 65 31 15 7 3 1 1 1 0 8 72 47 30 22 16 6 0 0 0 0
9 492 316 184 102 60 44 30 16 0 0 426 202 96 46 22 10 4 2 2 0 502 330 204 118 62 30 12 4 2 9
10 0 8 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
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 0 0 0 0 0 0 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
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 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0
20 9 2 4 12 30 62 118 204 330 502 0 2 2 4 10 22 46 96 202 426 0 0 16 30 44 60 102 184 316 492
21 0 0 0 0 6 16 22 30 47 72 8 0 1 1 1 3 7 15 31 65 0 0 0 8 3 8 12 28 51 80
22 0 0 0 0 0 10 26 36 50 74 7 7 0 2 2 2 6 14 30 62 14 0 0 0 14 6 14 20 42 70
23 6 0 0 0 0 0 12 30 42 60 6 6 6 0 3 3 3 9 21 45 18 18 0 0 0 18 9 18 24 42
24 20 10 0 0 0 0 0 12 28 40 15 5 5 5 0 4 4 4 12 28 20 15 20 0 0 0 20 12 20 24
25 40 28 12 0 0 0 0 0 10 20 28 12 4 4 4 0 5 5 5 15 24 20 12 20 0 0 0 20 15 20
26 60 42 30 12 0 0 0 0 0 6 45 21 9 3 3 3 0 6 6 6 42 24 18 9 18 0 0 0 18 18
27 74 50 36 26 10 0 0 0 0 0 62 30 14 6 2 2 2 0 7 7 70 42 20 14 6 14 0 0 0 14
28 72 47 30 22 16 6 0 0 0 0 65 31 15 7 3 1 1 1 0 8 80 51 28 12 8 3 8 0 0 0
29 502 330 204 118 62 30 12 4 2 9 426 202 96 46 22 10 4 2 2 0 492 316 184 102 60 44 30 16 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 1*9 + 1*10 + 1*12 + 1*16 + 1*22 + 2*30 + 1*44 + 1*46 + 1*60 + 1*62 + 1*96 + 1*102 + 1*118 + 1*184 + 1*202 + 1*204 + 1*316 + 1*330 + 1*426 + 1*492 + 1*502) +
4(8*0 + 3*1 + 2*3 + 1*6 + 1*7 + 3*8 + 1*12 + 1*15 + 1*16 + 1*22 + 1*28 + 1*30 + 1*31 + 1*47 + 1*51 + 1*65 + 1*72 + 1*80) +
4(9*0 + 3*2 + 2*6 + 2*7 + 1*10 + 4*14 + 1*20 + 1*26 + 1*30 + 1*36 + 1*42 + 1*50 + 1*62 + 1*70 + 1*74) +
4(9*0 + 3*3 + 4*6 + 2*9 + 1*12 + 4*18 + 1*21 + 1*24 + 1*30 + 2*42 + 1*45 + 1*60) +
4(9*0 + 3*4 + 3*5 + 1*10 + 3*12 + 2*15 + 5*20 + 1*24 + 2*28 + 1*40) +
2(28*0 + 2*8) +
8(30*0)
= 13308 + 2060 + 2032 + 1596 + 1292 + 32
= 20320
Value repetition frequencies = 4(20*1 + 2*2 + 2*3) +
4(14*1 + 1*2 + 2*3 + 1*8) +
4(10*1 + 2*2 + 1*3 + 1*4 + 1*9) +
4(6*1 + 2*2 + 1*3 + 2*4 + 1*9) +
4(3*1 + 2*2 + 3*3 + 1*5 + 1*9) +
2(1*2 + 1*28) +
8(1*30)
= 900
Number of distinct row element sets = 7
Number of rows = 1*2 + 5*4 + 1*8
= 30
Number of distinct values = 51
Distinct values 0 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 22 24 26 28 30 31 36 40
Frequency 448 12 24 20 20 12 28 12 16 12 12 24 16 12 8 16 24 4 8 8 4 12 20 4 4 4
Distinct values 42 44 45 46 47 50 51 60 62 65 70 72 74 80 96 102 118 184 202 204 316 330 426 492 502
Frequency 12 4 4 4 4 4 4 8 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 27*4 + 5*8 + 8*12 + 3*16 + 3*20 + 3*24 + 1*28 + 1*448
= 900
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 12*21 + 4*22 + 4*27
= 452
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 418
Number of possible SN-EN pairs with SN != EN = 29*30
= 870
a = 11, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 44 22
7 116 38
8 148 60
9 336 114
10 524 192
11 936 342
12 1424 564
13 2392 952
14 3616 1498
15 5488 2284
16 5932 2450
17 7464 3164
18 5076 2134
19 4620 1984
20 2624 1166
21 1496 670
22 592 286
23 248 124
24 24 12
Total 43156 18072
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
L
3 0 0 0 0 0 0 0 0 0 0 0
0 4 0 0 0 0 0 0 0 4 0
0 0 0 0 0 0 0 0 0 0 0
4 0 2 0 0 0 0 0 0 0 2 0
0 0 4 0 0 0 0 0 4 0 0
0 2 0 0 0 0 0 0 0 2 0
5 1 0 5 0 0 0 0 0 5 0 1
0 0 0 4 0 0 0 4 0 0 0
1 0 5 0 0 0 0 0 5 0 1
6 0 0 0 9 0 0 0 9 0 0 0
0 0 0 0 4 0 4 0 0 0 0
0 0 0 9 0 0 0 9 0 0 0
7 1 1 1 0 13 0 13 0 1 1 1
2 2 4 8 4 12 4 8 4 2 2
1 1 1 0 13 0 13 0 1 1 1
8 0 0 0 3 0 34 0 3 0 0 0
2 2 2 4 22 4 22 4 2 2 2
0 0 0 3 0 34 0 3 0 0 0
9 3 3 4 4 35 4 35 4 4 3 3
4 4 4 10 8 72 8 10 4 4 4
3 3 4 4 35 4 35 4 4 3 3
10 4 4 4 34 8 64 8 34 4 4 4
4 4 8 4 66 8 66 4 8 4 4
4 4 4 34 8 64 8 34 4 4 4
11 9 10 40 10 86 18 86 10 40 10 9
6 10 6 98 8 24 8 98 6 10 6
9 10 40 10 86 18 86 10 40 10 9
12 12 45 12 143 12 44 12 143 12 45 12
14 10 144 10 36 12 36 10 144 10 14
12 45 12 143 12 44 12 143 12 45 12
13 58 22 246 23 61 12 61 23 246 22 58
20 204 20 102 16 4 16 102 20 204 20
58 22 246 23 61 12 61 23 246 22 58
14 32 393 33 113 14 38 14 113 33 393 32
278 36 246 32 8 0 8 32 246 36 278
32 393 33 113 14 38 14 113 33 393 32
15 605 62 261 40 60 14 60 40 261 62 605
62 524 58 28 2 0 2 28 58 524 62
605 62 261 40 60 14 60 40 261 62 605
16 96 576 76 104 9 40 9 104 76 576 96
1008 98 88 10 0 0 0 10 88 98 1008
96 576 76 104 9 40 9 104 76 576 96
17 1169 148 222 26 62 14 62 26 222 148 1169
164 262 36 2 0 0 0 2 36 262 164
1169 148 222 26 62 14 62 26 222 148 1169
18 244 430 48 102 10 40 10 102 48 430 244
718 100 12 0 0 0 0 0 12 100 718
244 430 48 102 10 40 10 102 48 430 244
19 617 110 186 28 61 14 61 28 186 110 617
238 52 2 0 0 0 0 0 2 52 238
617 110 186 28 61 14 61 28 186 110 617
20 216 188 40 81 10 40 10 81 40 188 216
188 14 0 0 0 0 0 0 0 14 188
216 188 40 81 10 40 10 81 40 188 216
21 135 66 68 23 43 12 43 23 68 66 135
64 2 0 0 0 0 0 0 0 2 64
135 66 68 23 43 12 43 23 68 66 135
22 40 37 24 23 9 14 9 23 24 37 40
16 0 0 0 0 0 0 0 0 0 16
40 37 24 23 9 14 9 23 24 37 40
23 10 14 13 10 9 10 9 10 13 14 10
2 0 0 0 0 0 0 0 0 0 2
10 14 13 10 9 10 9 10 13 14 10
24 0 1 1 1 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 1 1 1 0
Total 3252 2112 1284 777 504 414 504 777 1284 2112 3252
2790 1328 634 312 174 136 174 312 634 1328 2790
3252 2112 1284 777 504 414 504 777 1284 2112 3252
Grand total = 136 + 2*174 + 2*312 + 2*414 + 4*504 + 2*634 + 4*777 + 4*1284 + 2*1328 + 4*2112 + 2*2790 + 4*3252
= 43156
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
L
3 2 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 4
5 8 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 8
6 11 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 11
7 19 2 2 2 2 2 2 2 2 2 19
2 0 0 0 0 0 0 0 0 0 2
19 2 2 2 2 2 2 2 2 2 19
8 29 1 2 2 2 2 2 2 2 1 29
0 0 0 0 0 0 0 0 0 0 0
29 1 2 2 2 2 2 2 2 1 29
9 52 4 7 8 8 8 8 8 7 4 52
2 0 0 0 0 0 0 0 0 0 2
52 4 7 8 8 8 8 8 7 4 52
10 90 5 7 11 12 12 12 11 7 5 90
0 0 0 0 0 0 0 0 0 0 0
90 5 7 11 12 12 12 11 7 5 90
11 158 9 14 17 23 24 23 17 14 9 158
2 0 0 0 0 0 0 0 0 0 2
158 9 14 17 23 24 23 17 14 9 158
12 265 11 17 22 25 32 25 22 17 11 265
0 0 0 0 0 0 0 0 0 0 0
265 11 17 22 25 32 25 22 17 11 265
13 443 21 31 36 45 42 45 36 31 21 443
2 0 0 0 0 0 0 0 0 0 2
443 21 31 36 45 42 45 36 31 21 443
14 698 34 46 54 47 50 47 54 46 34 698
0 0 0 0 0 0 0 0 0 0 0
698 34 46 54 47 50 47 54 46 34 698
15 1047 63 84 80 71 52 71 80 84 63 1047
2 0 0 0 0 0 0 0 0 0 2
1047 63 84 80 71 52 71 80 84 63 1047
16 1071 103 122 106 55 52 55 106 122 103 1071
0 0 0 0 0 0 0 0 0 0 0
1071 103 122 106 55 52 55 106 122 103 1071
17 1331 158 179 97 75 50 75 97 179 158 1331
2 0 0 0 0 0 0 0 0 0 2
1331 158 179 97 75 50 75 97 179 158 1331
18 717 213 149 114 51 50 51 114 149 213 717
0 0 0 0 0 0 0 0 0 0 0
717 213 149 114 51 50 51 114 149 213 717
19 643 156 181 86 66 44 66 86 181 156 643
2 0 0 0 0 0 0 0 0 0 2
643 156 181 86 66 44 66 86 181 156 643
20 257 171 87 82 39 40 39 82 87 171 257
0 0 0 0 0 0 0 0 0 0 0
257 171 87 82 39 40 39 82 87 171 257
21 126 74 77 38 44 28 44 38 77 74 126
2 0 0 0 0 0 0 0 0 0 2
126 74 77 38 44 28 44 38 77 74 126
22 35 39 27 24 13 20 13 24 27 39 35
0 0 0 0 0 0 0 0 0 0 0
35 39 27 24 13 20 13 24 27 39 35
23 9 14 13 10 10 10 10 10 13 14 9
2 0 0 0 0 0 0 0 0 0 2
9 14 13 10 10 10 10 10 13 14 9
24 0 1 1 1 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 1 1 1 0
Total 7015 1079 1046 790 590 520 590 790 1046 1079 7015
18 0 0 0 0 0 0 0 0 0 18
7015 1079 1046 790 590 520 590 790 1046 1079 7015
Grand total = 2*18 + 2*520 + 4*590 + 4*790 + 4*1046 + 4*1079 + 4*7015
= 43156
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
L
3 2 1 0 0 0 0 0 0 0 1 2
2 4 0 0 0 0 0 0 0 4 2
2 1 0 0 0 0 0 0 0 1 2
4 4 4 0 0 0 0 0 0 0 4 4
4 8 4 0 0 0 0 0 4 8 4
4 4 0 0 0 0 0 0 0 4 4
5 9 7 5 0 0 0 0 0 5 7 9
8 16 10 4 0 0 0 4 10 16 8
9 7 5 0 0 0 0 0 5 7 9
6 11 7 5 9 0 0 0 9 5 7 11
12 22 18 12 4 0 4 12 18 22 12
11 7 5 9 0 0 0 9 5 7 11
7 25 24 23 21 23 10 23 21 23 24 25
26 38 40 32 20 16 20 32 40 38 26
25 24 23 21 23 10 23 21 23 24 25
8 32 27 24 31 28 44 28 31 24 27 32
36 62 50 48 50 36 50 48 50 62 36
32 27 24 31 28 44 28 31 24 27 32
9 68 67 72 93 113 102 113 93 72 67 68
76 118 96 108 112 148 112 108 96 118 76
68 67 72 93 113 102 113 93 72 67 68
10 108 100 99 160 190 230 190 160 99 100 108
120 208 180 170 260 276 260 170 180 208 120
108 100 99 160 190 230 190 160 99 100 108
11 201 191 223 294 430 448 430 294 223 191 201
218 362 320 396 462 528 462 396 320 362 218
201 191 223 294 430 448 430 294 223 191 201
12 320 322 330 573 635 682 635 573 330 322 320
350 602 662 710 788 780 788 710 662 602 350
320 322 330 573 635 682 635 573 330 322 320
13 592 575 831 990 1118 1140 1118 990 831 575 592
606 1188 1202 1318 1256 1252 1256 1318 1202 1188 606
592 575 831 990 1118 1140 1118 990 831 575 592
14 896 1258 1279 1605 1667 1686 1667 1605 1279 1258 896
1182 2030 2142 2010 1920 1864 1920 2010 2142 2030 1182
896 1258 1279 1605 1667 1686 1667 1605 1279 1258 896
15 1942 1982 2286 2554 2608 2548 2608 2554 2286 1982 1942
1862 3526 3188 2970 2878 2888 2878 2970 3188 3526 1862
1942 1982 2286 2554 2608 2548 2608 2554 2286 1982 1942
16 1859 2795 2938 3077 2877 2822 2877 3077 2938 2795 1859
2698 3712 3250 2952 3214 3432 3214 2952 3250 3712 2698
1859 2795 2938 3077 2877 2822 2877 3077 2938 2795 1859
17 3457 3796 3897 3875 3741 3608 3741 3875 3897 3796 3457
3558 5044 3906 3698 4004 4188 4004 3698 3906 5044 3558
3457 3796 3897 3875 3741 3608 3741 3875 3897 3796 3457
18 2515 3209 2998 2826 2583 2544 2583 2826 2998 3209 2515
3008 2660 2460 2588 2760 2804 2760 2588 2460 2660 3008
2515 3209 2998 2826 2583 2544 2583 2826 2998 3209 2515
19 2731 3023 3058 2736 2589 2448 2589 2736 3058 3023 2731
2912 2410 1940 2184 2502 2440 2502 2184 1940 2410 2912
2731 3023 3058 2736 2589 2448 2589 2736 3058 3023 2731
20 1807 2019 1764 1640 1464 1482 1464 1640 1764 2019 1807
1934 1018 1032 1324 1354 1416 1354 1324 1032 1018 1934
1807 2019 1764 1640 1464 1482 1464 1640 1764 2019 1807
21 1142 1222 1162 987 967 890 967 987 1162 1222 1142
1186 454 478 650 762 656 762 650 478 454 1186
1142 1222 1162 987 967 890 967 987 1162 1222 1142
22 530 519 470 421 371 392 371 421 470 519 530
540 88 184 276 260 300 260 276 184 88 540
530 519 470 421 371 392 371 421 470 519 530
23 244 231 221 195 188 186 188 195 221 231 244
246 4 52 72 88 92 88 72 52 4 246
244 231 221 195 188 186 188 195 221 231 244
24 24 24 22 20 20 20 20 20 22 24 24
24 0 4 8 8 8 8 8 4 0 24
24 24 22 20 20 20 20 20 22 24 24
Total 18519 21403 21707 22107 21612 21282 21612 22107 21707 21403 18519
20608 23574 21218 21530 22702 23124 22702 21530 21218 23574 20608
18519 21403 21707 22107 21612 21282 21612 22107 21707 21403 18519
Grand total = 4*18519 + 2*20608 + 2*21218 + 2*21282 + 4*21403 + 2*21530 + 4*21612 + 4*21707 + 4*22107 + 2*22702 + 23124 + 2*23574
= 706344
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
EN
0 0 0 18 34 50 68 118 222 404 682 1054 0 2 2 4 10 22 46 96 202 426 898 10 2 4 13 34 72 140 248 416 678 1040
1 0 0 0 9 3 9 14 35 67 111 168 9 0 1 1 1 3 7 15 31 65 137 0 0 0 0 7 19 26 35 57 97 152
2 16 0 0 0 16 6 16 24 56 102 160 8 8 0 2 2 2 6 14 30 62 130 0 0 0 0 0 12 32 44 60 94 144
3 21 21 0 0 0 21 9 21 30 63 105 7 7 7 0 3 3 3 9 21 45 93 7 0 0 0 0 0 15 39 54 75 111
4 24 18 24 0 0 0 24 12 24 32 56 18 6 6 6 0 4 4 4 12 28 60 24 12 0 0 0 0 0 16 40 56 80
5 30 25 15 25 0 0 0 25 15 25 30 35 15 5 5 5 0 5 5 5 15 35 50 35 15 0 0 0 0 0 15 35 50
6 56 32 24 12 24 0 0 0 24 18 24 60 28 12 4 4 4 0 6 6 6 18 80 56 40 16 0 0 0 0 0 12 24
7 105 63 30 21 9 21 0 0 0 21 21 93 45 21 9 3 3 3 0 7 7 7 111 75 54 39 15 0 0 0 0 0 7
8 160 102 56 24 16 6 16 0 0 0 16 130 62 30 14 6 2 2 2 0 8 8 144 94 60 44 32 12 0 0 0 0 0
9 168 111 67 35 14 9 3 9 0 0 0 137 65 31 15 7 3 1 1 1 0 9 152 97 57 35 26 19 7 0 0 0 0
10 1054 682 404 222 118 68 50 34 18 0 0 898 426 202 96 46 22 10 4 2 2 0 1040 678 416 248 140 72 34 13 4 2 10
11 0 9 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
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
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
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
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
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
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
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
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
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
21 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 9 0
22 10 2 4 13 34 72 140 248 416 678 1040 0 2 2 4 10 22 46 96 202 426 898 0 0 18 34 50 68 118 222 404 682 1054
23 0 0 0 0 7 19 26 35 57 97 152 9 0 1 1 1 3 7 15 31 65 137 0 0 0 9 3 9 14 35 67 111 168
24 0 0 0 0 0 12 32 44 60 94 144 8 8 0 2 2 2 6 14 30 62 130 16 0 0 0 16 6 16 24 56 102 160
25 7 0 0 0 0 0 15 39 54 75 111 7 7 7 0 3 3 3 9 21 45 93 21 21 0 0 0 21 9 21 30 63 105
26 24 12 0 0 0 0 0 16 40 56 80 18 6 6 6 0 4 4 4 12 28 60 24 18 24 0 0 0 24 12 24 32 56
27 50 35 15 0 0 0 0 0 15 35 50 35 15 5 5 5 0 5 5 5 15 35 30 25 15 25 0 0 0 25 15 25 30
28 80 56 40 16 0 0 0 0 0 12 24 60 28 12 4 4 4 0 6 6 6 18 56 32 24 12 24 0 0 0 24 18 24
29 111 75 54 39 15 0 0 0 0 0 7 93 45 21 9 3 3 3 0 7 7 7 105 63 30 21 9 21 0 0 0 21 21
30 144 94 60 44 32 12 0 0 0 0 0 130 62 30 14 6 2 2 2 0 8 8 160 102 56 24 16 6 16 0 0 0 16
31 152 97 57 35 26 19 7 0 0 0 0 137 65 31 15 7 3 1 1 1 0 9 168 111 67 35 14 9 3 9 0 0 0
32 1040 678 416 248 140 72 34 13 4 2 10 898 426 202 96 46 22 10 4 2 2 0 1054 682 404 222 118 68 50 34 18 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 2*10 + 1*13 + 1*18 + 1*22 + 2*34 + 1*46 + 1*50 + 1*68 + 1*72 + 1*96 + 1*118 + 1*140 + 1*202 + 1*222 + 1*248 + 1*404 + 1*416 + 1*426 + 1*682 + 1*678 + 1*898 + 1*1040 +
1*1054) +
4(8*0 + 3*1 + 2*3 + 2*7 + 3*9 + 1*14 + 1*15 + 1*19 + 1*26 + 1*31 + 2*35 + 1*57 + 1*65 + 1*67 + 1*97 + 1*111 + 1*137 + 1*152 + 1*168) +
4(9*0 + 3*2 + 2*6 + 2*8 + 1*12 + 1*14 + 3*16 + 1*24 + 1*30 + 1*32 + 1*44 + 1*56 + 1*60 + 1*62 + 1*94 + 1*102 + 1*130 + 1*144 + 1*160) +
4(9*0 + 3*3 + 4*7 + 2*9 + 1*15 + 5*21 + 1*30 + 1*39 + 1*45 + 1*54 + 1*63 + 1*75 + 1*93 + 1*105 + 1*111) +
4(9*0 + 3*4 + 3*6 + 3*12 + 1*16 + 2*18 + 5*24 + 1*28 + 1*32 + 1*40 + 2*56 + 1*60 + 1*80) +
2(9*0 + 6*5 + 6*15 + 4*25 + 2*30 + 4*35 + 2*50) +
2(31*0 + 2*9) +
9(33*0)
= 28060 + 4316 + 4184 + 3160 + 2360 + 1040 + 36
= 43156
Value repetition frequencies = 4(24*1 + 3*2 + 2*3) +
4(13*1 + 3*2 + 2*3 + 1*8) +
4(14*1 + 2*2 + 2*3 + 1*9) +
4(10*1 + 1*2 + 1*3 + 1*4 + 1*5 + 1*9) +
4(6*1 + 2*2 + 3*3 + 1*5 + 1*9) +
2(2*2 + 2*4 + 2*6 + 1*9) +
2(1*2 + 1*31) +
9(1*33)
= 1089
Number of distinct row element sets = 8
Number of rows = 2*2 + 5*4 + 1*9
= 33
Number of distinct values = 73
Distinct values 0 1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 18 19 21 22 24 25 26 28 30
Frequency 529 12 24 20 20 12 20 24 8 24 8 16 4 8 20 16 12 4 20 4 24 8 4 4 12
Distinct values 31 32 34 35 39 40 44 45 46 50 54 56 57 60 62 63 65 67 68 72 75 80 93 94 96
Frequency 4 8 8 16 4 4 4 4 4 8 4 12 4 8 4 4 4 4 4 4 4 4 4 4 4
Distinct values 97 102 105 111 118 130 137 140 144 152 160 168 202 222 248 404 416 426 678 682 898 1040 1054
Frequency 4 4 4 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 = 46*4 + 9*8 + 5*12 + 3*16 + 5*20 + 4*24 + 1*529
= 1089
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 14*24 + 4*25 + 4*30
= 560
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 496
Number of possible SN-EN pairs with SN != EN = 32*33
= 1056
a = 12, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 44 22
7 120 38
8 152 60
9 352 114
10 548 192
11 984 342
12 1492 564
13 2528 956
14 3984 1580
15 6480 2592
16 9728 4040
17 11928 4896
18 15148 6470
19 11584 4770
20 11396 4900
21 7116 3064
22 4332 1940
23 2204 998
24 832 404
25 312 156
26 28 14
Total 91348 38128
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 0 0 0 0 0 0 0 0 0 0 0
0 4 0 0 0 0 0 0 0 0 4 0
0 0 0 0 0 0 0 0 0 0 0 0
4 0 2 0 0 0 0 0 0 0 0 2 0
0 0 4 0 0 0 0 0 0 4 0 0
0 2 0 0 0 0 0 0 0 0 2 0
5 1 0 5 0 0 0 0 0 0 5 0 1
0 0 0 4 0 0 0 0 4 0 0 0
1 0 5 0 0 0 0 0 0 5 0 1
6 0 0 0 9 0 0 0 0 9 0 0 0
0 0 0 0 4 0 0 4 0 0 0 0
0 0 0 9 0 0 0 0 9 0 0 0
7 1 1 1 0 13 0 0 13 0 1 1 1
2 2 4 8 4 8 8 4 8 4 2 2
1 1 1 0 13 0 0 13 0 1 1 1
8 0 0 0 3 0 17 17 0 3 0 0 0
2 2 2 4 18 8 8 18 4 2 2 2
0 0 0 3 0 17 17 0 3 0 0 0
9 3 3 4 4 14 25 25 14 4 4 3 3
4 4 4 6 12 40 40 12 6 4 4 4
3 3 4 4 14 25 25 14 4 4 3 3
10 4 4 4 9 33 36 36 33 9 4 4 4
4 4 4 8 8 66 66 8 8 4 4 4
4 4 4 9 33 36 36 33 9 4 4 4
11 9 10 11 39 22 82 82 22 39 11 10 9
6 6 10 6 100 18 18 100 6 10 6 6
9 10 11 39 22 82 82 22 39 11 10 9
12 12 12 45 17 138 34 34 138 17 45 12 12
10 14 10 144 10 42 42 10 144 10 14 10
12 12 45 17 138 34 34 138 17 45 12 12
13 21 59 24 245 34 55 55 34 245 24 59 21
24 20 204 20 102 18 18 102 20 204 20 24
21 59 24 245 34 55 55 34 245 24 59 21
14 73 33 393 38 109 32 32 109 38 393 33 73
36 278 36 246 32 8 8 32 246 36 278 36
73 33 393 38 109 32 32 109 38 393 33 73
15 57 610 64 261 51 55 55 51 261 64 610 57
370 62 524 58 28 2 2 28 58 524 62 370
57 610 64 261 51 55 55 51 261 64 610 57
16 890 103 577 81 100 28 28 100 81 577 103 890
102 1008 98 88 10 0 0 10 88 98 1008 102
890 103 577 81 100 28 28 100 81 577 103 890
17 167 1215 154 222 38 57 57 38 222 154 1215 167
1794 164 262 36 2 0 0 2 36 262 164 1794
167 1215 154 222 38 57 57 38 222 154 1215 167
18 2326 261 466 54 98 29 29 98 54 466 261 2326
276 718 100 12 0 0 0 0 12 100 718 276
2326 261 466 54 98 29 29 98 54 466 261 2326
19 433 981 124 215 40 57 57 40 215 124 981 433
1800 238 52 2 0 0 0 0 2 52 238 1800
433 981 124 215 40 57 57 40 215 124 981 433
20 1646 263 406 52 99 29 29 99 52 406 263 1646
506 188 14 0 0 0 0 0 0 14 188 506
1646 263 406 52 99 29 29 99 52 406 263 1646
21 521 538 96 189 39 56 56 39 189 96 538 521
614 64 2 0 0 0 0 0 0 2 64 614
521 538 96 189 39 56 56 39 189 96 538 521
22 466 153 192 46 77 29 29 77 46 192 153 466
224 16 0 0 0 0 0 0 0 0 16 224
466 153 192 46 77 29 29 77 46 192 153 466
23 161 137 72 67 34 37 37 34 67 72 137 161
84 2 0 0 0 0 0 0 0 0 2 84
161 137 72 67 34 37 37 34 67 72 137 161
24 51 47 38 29 19 15 15 19 29 38 47 51
18 0 0 0 0 0 0 0 0 0 0 18
51 47 38 29 19 15 15 19 29 38 47 51
25 11 16 15 12 11 12 12 11 12 15 16 11
2 0 0 0 0 0 0 0 0 0 0 2
11 16 15 12 11 12 12 11 12 15 16 11
26 0 1 1 1 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 1 1 1 0
Total 6853 4449 2692 1593 971 687 687 971 1593 2692 4449 6853
5878 2794 1330 642 330 210 210 330 642 1330 2794 5878
6853 4449 2692 1593 971 687 687 971 1593 2692 4449 6853
Grand total = 2*210 + 2*330 + 2*642 + 4*687 + 4*971 + 2*1330 + 4*1593 + 4*2692 + 2*2794 + 4*4449 + 2*5878 + 4*6853
= 91348
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 2
0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 4
5 8 0 0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0 0 8
6 11 0 0 0 0 0 0 0 0 0 0 11
0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 11
7 19 2 2 2 2 2 2 2 2 2 2 19
2 0 0 0 0 0 0 0 0 0 0 2
19 2 2 2 2 2 2 2 2 2 2 19
8 29 1 2 2 2 2 2 2 2 2 1 29
0 0 0 0 0 0 0 0 0 0 0 0
29 1 2 2 2 2 2 2 2 2 1 29
9 52 4 7 8 8 8 8 8 8 7 4 52
2 0 0 0 0 0 0 0 0 0 0 2
52 4 7 8 8 8 8 8 8 7 4 52
10 90 5 7 11 12 12 12 12 11 7 5 90
0 0 0 0 0 0 0 0 0 0 0 0
90 5 7 11 12 12 12 12 11 7 5 90
11 158 9 14 17 23 24 24 23 17 14 9 158
2 0 0 0 0 0 0 0 0 0 0 2
158 9 14 17 23 24 24 23 17 14 9 158
12 265 11 17 22 25 33 33 25 22 17 11 265
0 0 0 0 0 0 0 0 0 0 0 0
265 11 17 22 25 33 33 25 22 17 11 265
13 445 21 31 36 46 52 52 46 36 31 21 445
2 0 0 0 0 0 0 0 0 0 0 2
445 21 31 36 46 52 52 46 36 31 21 445
14 739 34 46 55 59 63 63 59 55 46 34 739
0 0 0 0 0 0 0 0 0 0 0 0
739 34 46 55 59 63 63 59 55 46 34 739
15 1201 63 85 94 92 84 84 92 94 85 63 1201
2 0 0 0 0 0 0 0 0 0 0 2
1201 63 85 94 92 84 84 92 94 85 63 1201
16 1865 104 138 137 115 73 73 115 137 138 104 1865
0 0 0 0 0 0 0 0 0 0 0 0
1865 104 138 137 115 73 73 115 137 138 104 1865
17 2178 176 222 201 114 90 90 114 201 222 176 2178
2 0 0 0 0 0 0 0 0 0 0 2
2178 176 222 201 114 90 90 114 201 222 176 2178
18 2812 269 317 187 129 73 73 129 187 317 269 2812
0 0 0 0 0 0 0 0 0 0 0 0
2812 269 317 187 129 73 73 129 187 317 269 2812
19 1741 394 315 244 115 86 86 115 244 315 394 1741
2 0 0 0 0 0 0 0 0 0 0 2
1741 394 315 244 115 86 86 115 244 315 394 1741
20 1745 355 385 178 119 67 67 119 178 385 355 1745
0 0 0 0 0 0 0 0 0 0 0 0
1745 355 385 178 119 67 67 119 178 385 355 1745
21 760 424 231 194 94 75 75 94 194 231 424 760
2 0 0 0 0 0 0 0 0 0 0 2
760 424 231 194 94 75 75 94 194 231 424 760
22 455 189 211 92 85 51 51 85 92 211 189 455
0 0 0 0 0 0 0 0 0 0 0 0
455 189 211 92 85 51 51 85 92 211 189 455
23 151 140 89 78 44 48 48 44 78 89 140 151
2 0 0 0 0 0 0 0 0 0 0 2
151 140 89 78 44 48 48 44 78 89 140 151
24 45 49 41 30 23 20 20 23 30 41 49 45
0 0 0 0 0 0 0 0 0 0 0 0
45 49 41 30 23 20 20 23 30 41 49 45
25 10 16 15 12 12 12 12 12 12 15 16 10
2 0 0 0 0 0 0 0 0 0 0 2
10 16 15 12 12 12 12 12 12 15 16 10
26 0 1 1 1 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 1 1 1 0
Total 14785 2267 2176 1601 1121 877 877 1121 1601 2176 2267 14785
20 0 0 0 0 0 0 0 0 0 0 20
14785 2267 2176 1601 1121 877 877 1121 1601 2176 2267 14785
Grand total = 2*20 + 4*877 + 4*1121 + 4*1601 + 4*2176 + 4*2267 + 4*14785
= 91348
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 2 1 0 0 0 0 0 0 0 0 1 2
2 4 0 0 0 0 0 0 0 0 4 2
2 1 0 0 0 0 0 0 0 0 1 2
4 4 4 0 0 0 0 0 0 0 0 4 4
4 8 4 0 0 0 0 0 0 4 8 4
4 4 0 0 0 0 0 0 0 0 4 4
5 9 7 5 0 0 0 0 0 0 5 7 9
8 16 10 4 0 0 0 0 4 10 16 8
9 7 5 0 0 0 0 0 0 5 7 9
6 11 7 5 9 0 0 0 0 9 5 7 11
12 22 18 12 4 0 0 4 12 18 22 12
11 7 5 9 0 0 0 0 9 5 7 11
7 25 24 23 21 23 10 10 23 21 23 24 25
26 38 40 32 20 12 12 20 32 40 38 26
25 24 23 21 23 10 10 23 21 23 24 25
8 32 27 24 31 28 27 27 28 31 24 27 32
36 62 50 48 46 28 28 46 48 50 62 36
32 27 24 31 28 27 27 28 31 24 27 32
9 68 67 72 93 92 97 97 92 93 72 67 68
76 118 96 104 104 108 108 104 104 96 118 76
68 67 72 93 92 97 97 92 93 72 67 68
10 108 100 99 135 181 188 188 181 135 99 100 108
120 208 176 162 194 258 258 194 162 176 208 120
108 100 99 135 181 188 188 181 135 99 100 108
11 201 191 194 281 344 442 442 344 281 194 191 201
218 358 312 296 416 506 506 416 296 312 358 218
201 191 194 281 344 442 442 344 281 194 191 201
12 320 289 313 417 628 688 688 628 417 313 289 320
346 594 520 620 718 844 844 718 620 520 594 346
320 289 313 417 628 688 688 628 417 313 289 320
13 557 555 571 979 1099 1200 1200 1099 979 571 555 557
604 1004 1060 1156 1334 1352 1352 1334 1156 1060 1004 604
557 555 571 979 1099 1200 1200 1099 979 571 555 557
14 949 907 1288 1550 1784 1835 1835 1784 1550 1288 907 949
990 1910 1894 2178 2166 2124 2124 2166 2178 1894 1910 990
949 907 1288 1550 1784 1835 1835 1784 1550 1288 907 949
15 1552 2099 2167 2832 2998 3010 3010 2998 2832 2167 2099 1552
1956 3348 3618 3496 3472 3394 3394 3472 3496 3618 3348 1956
1552 2099 2167 2832 2998 3010 3010 2998 2832 2167 2099 1552
16 3203 3247 3907 4431 4495 4355 4355 4495 4431 3907 3247 3203
3080 6054 5608 5362 5146 5298 5298 5146 5362 5608 6054 3080
3203 3247 3907 4431 4495 4355 4355 4495 4431 3907 3247 3203
17 3502 5257 5559 6021 5778 5546 5546 5778 6021 5559 5257 3502
5058 7354 6704 5978 6284 6684 6684 6284 5978 6704 7354 5058
3502 5257 5559 6021 5778 5546 5546 5778 6021 5559 5257 3502
18 6697 7168 7447 7593 7366 7050 7050 7366 7593 7447 7168 6697
6776 10394 8318 7670 8012 8520 8520 8012 7670 8318 10394 6776
6697 7168 7447 7593 7366 7050 7050 7366 7593 7447 7168 6697
19 5080 6814 6629 6431 5944 5747 5747 5944 6431 6629 6814 5080
6374 6366 5696 5814 6250 6258 6258 6250 5814 5696 6366 6374
5080 6814 6629 6431 5944 5747 5747 5944 6431 6629 6814 5080
20 6323 7010 7029 6453 6115 5843 5843 6115 6453 7029 7010 6323
6714 6596 5120 5562 6254 6168 6168 6254 5562 5120 6596 6714
6323 7010 7029 6453 6115 5843 5843 6115 6453 7029 7010 6323
21 4477 5193 4658 4307 3915 3852 3852 3915 4307 4658 5193 4477
4890 3020 3016 3528 3706 3754 3754 3706 3528 3016 3020 4890
4477 5193 4658 4307 3915 3852 3852 3915 4307 4658 5193 4477
22 3101 3297 3184 2715 2581 2461 2461 2581 2715 3184 3297 3101
3258 1614 1546 2012 2340 2204 2204 2340 2012 1546 1614 3258
3101 3297 3184 2715 2581 2461 2461 2581 2715 3184 3297 3101
23 1756 1876 1692 1521 1381 1379 1379 1381 1521 1692 1876 1756
1812 566 690 990 1018 1060 1060 1018 990 690 566 1812
1756 1876 1692 1521 1381 1379 1379 1381 1521 1692 1876 1756
24 761 739 684 599 549 544 544 549 599 684 739 761
772 100 240 356 368 396 396 368 356 240 100 772
761 739 684 599 549 544 544 549 599 684 739 761
25 308 293 281 251 242 238 238 242 251 281 293 308
310 4 60 84 104 112 112 104 84 60 4 310
308 293 281 251 242 238 238 242 251 281 293 308
26 28 28 26 24 24 24 24 24 24 26 28 28
28 0 4 8 8 8 8 8 8 4 0 28
28 28 26 24 24 24 24 24 24 26 28 28
Total 39074 45200 45857 46694 45567 44536 44536 45567 46694 45857 45200 39074
43470 49758 44800 45472 47964 49088 49088 47964 45472 44800 49758 43470
39074 45200 45857 46694 45567 44536 44536 45567 46694 45857 45200 39074
Grand total = 4*39074 + 2*43470 + 4*44536 + 2*44800 + 4*45200 + 2*45472 + 4*45567 + 4*45857 + 4*46694 + 2*47964 + 2*49088 + 2*49758
= 1628816
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 20 38 56 76 134 260 492 872 1448 2226 0 2 2 4 10 22 46 96 202 426 898 1892 11 2 4 14 38 82 162 292 502 854 1416 2186
1 0 0 0 10 3 10 16 42 83 142 226 342 10 0 1 1 1 3 7 15 31 65 137 289 0 0 0 0 8 22 30 40 67 122 212 332
2 18 0 0 0 18 6 18 28 70 134 222 336 9 9 0 2 2 2 6 14 30 62 130 274 0 0 0 0 0 14 38 52 70 114 194 304
3 24 24 0 0 0 24 9 24 36 84 153 240 8 8 8 0 3 3 3 9 21 45 93 195 8 0 0 0 0 0 18 48 66 90 141 216
4 28 21 28 0 0 0 28 12 28 40 84 140 21 7 7 7 0 4 4 4 12 28 60 124 28 14 0 0 0 0 0 20 52 72 100 148
5 36 30 18 30 0 0 0 30 15 30 40 70 42 18 6 6 6 0 5 5 5 15 35 75 60 42 18 0 0 0 0 0 20 50 70 100
6 70 40 30 15 30 0 0 0 30 18 30 36 75 35 15 5 5 5 0 6 6 6 18 42 100 70 50 20 0 0 0 0 0 18 42 60
7 140 84 40 28 12 28 0 0 0 28 21 28 124 60 28 12 4 4 4 0 7 7 7 21 148 100 72 52 20 0 0 0 0 0 14 28
8 240 153 84 36 24 9 24 0 0 0 24 24 195 93 45 21 9 3 3 3 0 8 8 8 216 141 90 66 48 18 0 0 0 0 0 8
9 336 222 134 70 28 18 6 18 0 0 0 18 274 130 62 30 14 6 2 2 2 0 9 9 304 194 114 70 52 38 14 0 0 0 0 0
10 342 226 142 83 42 16 10 3 10 0 0 0 289 137 65 31 15 7 3 1 1 1 0 10 332 212 122 67 40 30 22 8 0 0 0 0
11 2226 1448 872 492 260 134 76 56 38 20 0 0 1892 898 426 202 96 46 22 10 4 2 2 0 2186 1416 854 502 292 162 82 38 14 4 2 11
12 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 10 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 0 0 0 0 0 0 0 0 0 0 0 0 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
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 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 0
24 11 2 4 14 38 82 162 292 502 854 1416 2186 0 2 2 4 10 22 46 96 202 426 898 1892 0 0 20 38 56 76 134 260 492 872 1448 2226
25 0 0 0 0 8 22 30 40 67 122 212 332 10 0 1 1 1 3 7 15 31 65 137 289 0 0 0 10 3 10 16 42 83 142 226 342
26 0 0 0 0 0 14 38 52 70 114 194 304 9 9 0 2 2 2 6 14 30 62 130 274 18 0 0 0 18 6 18 28 70 134 222 336
27 8 0 0 0 0 0 18 48 66 90 141 216 8 8 8 0 3 3 3 9 21 45 93 195 24 24 0 0 0 24 9 24 36 84 153 240
28 28 14 0 0 0 0 0 20 52 72 100 148 21 7 7 7 0 4 4 4 12 28 60 124 28 21 28 0 0 0 28 12 28 40 84 140
29 60 42 18 0 0 0 0 0 20 50 70 100 42 18 6 6 6 0 5 5 5 15 35 75 36 30 18 30 0 0 0 30 15 30 40 70
30 100 70 50 20 0 0 0 0 0 18 42 60 75 35 15 5 5 5 0 6 6 6 18 42 70 40 30 15 30 0 0 0 30 18 30 36
31 148 100 72 52 20 0 0 0 0 0 14 28 124 60 28 12 4 4 4 0 7 7 7 21 140 84 40 28 12 28 0 0 0 28 21 28
32 216 141 90 66 48 18 0 0 0 0 0 8 195 93 45 21 9 3 3 3 0 8 8 8 240 153 84 36 24 9 24 0 0 0 24 24
33 304 194 114 70 52 38 14 0 0 0 0 0 274 130 62 30 14 6 2 2 2 0 9 9 336 222 134 70 28 18 6 18 0 0 0 18
34 332 212 122 67 40 30 22 8 0 0 0 0 289 137 65 31 15 7 3 1 1 1 0 10 342 226 142 83 42 16 10 3 10 0 0 0
35 2186 1416 854 502 292 162 82 38 14 4 2 11 1892 898 426 202 96 46 22 10 4 2 2 0 2226 1448 872 492 260 134 76 56 38 20 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 1*10 + 1*11 + 1*14 + 1*20 + 1*22 + 2*38 + 1*46 + 1*56 + 1*76 + 1*82 + 1*96 + 1*134 + 1*162 + 1*202 + 1*260 + 1*292 + 1*426 + 1*492 + 1*502 + 1*854 + 1*872 + 1*898 + 1*1416 +
1*1448 + 1*1892 + 1*2186 + 1*2226) +
4(8*0 + 3*1 + 2*3 + 1*7 + 1*8 + 3*10 + 1*15 + 1*16 + 1*22 + 1*30 + 1*31 + 1*40 + 1*42 + 1*65 + 1*67 + 1*83 + 1*122 + 1*137 + 1*142 + 1*212 + 1*226 + 1*289 + 1*332 + 1*342) +
4(9*0 + 3*2 + 2*6 + 2*9 + 2*14 + 3*18 + 1*28 + 1*30 + 1*38 + 1*52 + 1*62 + 2*70 + 1*114 + 1*130 + 1*134 + 1*194 + 1*222 + 1*274 + 1*304 + 1*336) +
4(9*0 + 3*3 + 4*8 + 2*9 + 1*18 + 1*21 + 4*24 + 1*36 + 1*45 + 1*48 + 1*66 + 1*84 + 1*90 + 1*93 + 1*141 + 1*153 + 1*195 + 1*216 + 1*240) +
4(9*0 + 3*4 + 3*7 + 2*12 + 1*14 + 1*20 + 2*21 + 6*28 + 1*40 + 1*52 + 1*60 + 1*72 + 1*84 + 1*100 + 1*124 + 1*140 + 1*148) +
4(9*0 + 3*5 + 3*6 + 2*15 + 3*18 + 1*20 + 4*30 + 1*35 + 1*36 + 1*40 + 2*42 + 1*50 + 1*60 + 2*70 + 1*75 + 1*100) +
2(34*0 + 2*10) +
10(36*0)
= 59140 + 9068 + 8704 + 6404 + 4484 + 3508 + 40
= 91348
Value repetition frequencies = 4(26*1 + 2*2 + 2*3) +
4(20*1 + 1*2 + 2*3 + 1*8) +
4(13*1 + 4*2 + 2*3 + 1*9) +
4(14*1 + 1*2 + 1*3 + 2*4 + 1*9) +
4(11*1 + 2*2 + 2*3 + 1*6 + 1*9) +
4(8*1 + 3*2 + 3*3 + 1*4 + 1*9) +
2(1*2 + 1*34) +
10(1*36)
= 1296
Number of distinct row element sets = 8
Number of rows = 1*2 + 6*4 + 1*10
= 36
Number of distinct values = 90
Distinct values 0 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 20 21 22 24 28 30 31 35
Frequency 616 12 24 20 20 12 20 16 20 16 20 4 8 16 12 4 28 12 12 8 16 28 24 4 4
Distinct values 36 38 40 42 45 46 48 50 52 56 60 62 65 66 67 70 72 75 76 82 83 84 90 93 96
Frequency 8 12 12 12 4 4 4 4 8 4 8 4 4 4 4 16 4 4 4 4 4 8 4 4 4
Distinct values 100 114 122 124 130 134 137 140 141 142 148 153 162 194 195 202 212 216 222 226 240 260 274 289 292
Frequency 8 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 304 332 336 342 426 492 502 854 872 898 1416 1448 1892 2186 2226
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 59*4 + 9*8 + 7*12 + 5*16 + 5*20 + 2*24 + 2*28 + 1*616
= 1296
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 16*27 + 4*28 + 4*33
= 680
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 580
Number of possible SN-EN pairs with SN != EN = 35*36
= 1260
a = 13, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 44 22
7 124 38
8 156 60
9 368 114
10 572 192
11 1032 342
12 1560 564
13 2656 956
14 4196 1584
15 7036 2682
16 11112 4422
17 17432 7110
18 22520 9310
19 30180 12782
20 25140 10362
21 27380 11654
22 17444 7466
23 12620 5512
24 6592 2970
25 3200 1466
26 1136 554
27 384 192
28 32 16
Total 192972 80386
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
L
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 4 0
0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 2 0 0 0 0 0 0 0 0 0 2 0
0 0 4 0 0 0 0 0 0 0 4 0 0
0 2 0 0 0 0 0 0 0 0 0 2 0
5 1 0 5 0 0 0 0 0 0 0 5 0 1
0 0 0 4 0 0 0 0 0 4 0 0 0
1 0 5 0 0 0 0 0 0 0 5 0 1
6 0 0 0 9 0 0 0 0 0 9 0 0 0
0 0 0 0 4 0 0 0 4 0 0 0 0
0 0 0 9 0 0 0 0 0 9 0 0 0
7 1 1 1 0 13 0 0 0 13 0 1 1 1
2 2 4 8 4 8 4 8 4 8 4 2 2
1 1 1 0 13 0 0 0 13 0 1 1 1
8 0 0 0 3 0 17 0 17 0 3 0 0 0
2 2 2 4 18 4 12 4 18 4 2 2 2
0 0 0 3 0 17 0 17 0 3 0 0 0
9 3 3 4 4 14 4 46 4 14 4 4 3 3
4 4 4 6 8 44 8 44 8 6 4 4 4
3 3 4 4 14 4 46 4 14 4 4 3 3
10 4 4 4 9 8 61 8 61 8 9 4 4 4
4 4 4 4 12 8 124 8 12 4 4 4 4
4 4 4 9 8 61 8 61 8 9 4 4 4
11 9 10 11 10 51 18 146 18 51 10 11 10 9
6 6 6 10 8 110 12 110 8 10 6 6 6
9 10 11 10 51 18 146 18 51 10 11 10 9
12 12 12 12 50 12 160 24 160 12 50 12 12 12
10 10 14 10 144 16 72 16 144 10 14 10 10
12 12 12 50 12 160 24 160 12 50 12 12 12
13 21 22 61 23 256 28 98 28 256 23 61 22 21
20 24 20 204 20 104 32 104 20 204 20 24 20
21 22 61 23 256 28 98 28 256 23 61 22 21
14 32 74 33 398 34 127 26 127 34 398 33 74 32
40 36 278 36 246 32 16 32 246 36 278 36 40
32 74 33 398 34 127 26 127 34 398 33 74 32
15 102 62 612 64 272 46 96 46 272 64 612 62 102
62 370 62 524 58 28 4 28 58 524 62 370 62
102 62 612 64 272 46 96 46 272 64 612 62 102
16 96 897 104 582 77 119 16 119 77 582 104 897 96
484 102 1008 98 88 10 0 10 88 98 1008 102 484
96 897 104 582 77 119 16 119 77 582 104 897 96
17 1273 180 1221 154 234 33 100 33 234 154 1221 180 1273
168 1794 164 262 36 2 0 2 36 262 164 1794 168
1273 180 1221 154 234 33 100 33 234 154 1221 180 1273
18 280 2380 268 472 50 117 18 117 50 472 268 2380 280
3002 276 718 100 12 0 0 0 12 100 718 276 3002
280 2380 268 472 50 117 18 117 50 472 268 2380 280
19 4333 462 1028 128 227 36 100 36 227 128 1028 462 4333
470 1800 238 52 2 0 0 0 2 52 238 1800 470
4333 462 1028 128 227 36 100 36 227 128 1028 462 4333
20 748 2212 280 447 49 118 18 118 49 447 280 2212 748
4136 506 188 14 0 0 0 0 0 14 188 506 4136
748 2212 280 447 49 118 18 118 49 447 280 2212 748
21 4075 606 903 108 230 35 100 35 230 108 903 606 4075
996 614 64 2 0 0 0 0 0 2 64 614 996
4075 606 903 108 230 35 100 35 230 108 903 606 4075
22 1136 1391 200 415 49 118 18 118 49 415 200 1391 1136
1846 224 16 0 0 0 0 0 0 0 16 224 1846
1136 1391 200 415 49 118 18 118 49 415 200 1391 1136
23 1485 374 541 100 200 34 98 34 200 100 541 374 1485
658 84 2 0 0 0 0 0 0 0 2 84 658
1485 374 541 100 200 34 98 34 200 100 541 374 1485
24 520 438 160 198 42 96 18 96 42 198 160 438 520
352 18 0 0 0 0 0 0 0 0 0 18 352
520 438 160 198 42 96 18 96 42 198 160 438 520
25 237 160 144 71 78 28 62 28 78 71 144 160 237
100 2 0 0 0 0 0 0 0 0 0 2 100
237 160 144 71 78 28 62 28 78 71 144 160 237
26 60 65 48 43 25 25 16 25 25 43 48 65 60
20 0 0 0 0 0 0 0 0 0 0 0 20
60 65 48 43 25 25 16 25 25 43 48 65 60
27 12 18 17 14 13 14 14 14 13 14 17 18 12
2 0 0 0 0 0 0 0 0 0 0 0 2
12 18 17 14 13 14 14 14 13 14 17 18 12
28 0 1 1 1 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 1 1 1 0
Total 14440 9374 5658 3303 1936 1236 1024 1236 1936 3303 5658 9374 14440
12384 5882 2796 1338 660 366 284 366 660 1338 2796 5882 12384
14440 9374 5658 3303 1936 1236 1024 1236 1936 3303 5658 9374 14440
Grand total = 284 + 2*366 + 2*660 + 2*1024 + 4*1236 + 2*1338 + 4*1936 + 2*2796 + 4*3303 + 4*5658 + 2*5882 + 4*9374 + 2*12384 + 4*14440
= 192972
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
L
3 2 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
2 0 0 0 0 0 0 0 0 0 0 0 2
4 4 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
4 0 0 0 0 0 0 0 0 0 0 0 4
5 8 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
8 0 0 0 0 0 0 0 0 0 0 0 8
6 11 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
11 0 0 0 0 0 0 0 0 0 0 0 11
7 19 2 2 2 2 2 2 2 2 2 2 2 19
2 0 0 0 0 0 0 0 0 0 0 0 2
19 2 2 2 2 2 2 2 2 2 2 2 19
8 29 1 2 2 2 2 2 2 2 2 2 1 29
0 0 0 0 0 0 0 0 0 0 0 0 0
29 1 2 2 2 2 2 2 2 2 2 1 29
9 52 4 7 8 8 8 8 8 8 8 7 4 52
2 0 0 0 0 0 0 0 0 0 0 0 2
52 4 7 8 8 8 8 8 8 8 7 4 52
10 90 5 7 11 12 12 12 12 12 11 7 5 90
0 0 0 0 0 0 0 0 0 0 0 0 0
90 5 7 11 12 12 12 12 12 11 7 5 90
11 158 9 14 17 23 24 24 24 23 17 14 9 158
2 0 0 0 0 0 0 0 0 0 0 0 2
158 9 14 17 23 24 24 24 23 17 14 9 158
12 265 11 17 22 25 33 34 33 25 22 17 11 265
0 0 0 0 0 0 0 0 0 0 0 0 0
265 11 17 22 25 33 34 33 25 22 17 11 265
13 445 21 31 36 46 53 62 53 46 36 31 21 445
2 0 0 0 0 0 0 0 0 0 0 0 2
445 21 31 36 46 53 62 53 46 36 31 21 445
14 741 34 46 55 60 75 76 75 60 55 46 34 741
0 0 0 0 0 0 0 0 0 0 0 0 0
741 34 46 55 60 75 76 75 60 55 46 34 741
15 1246 63 85 95 106 105 116 105 106 95 85 63 1246
2 0 0 0 0 0 0 0 0 0 0 0 2
1246 63 85 95 106 105 116 105 106 95 85 63 1246
16 2056 104 139 153 146 133 94 133 146 153 139 104 2056
0 0 0 0 0 0 0 0 0 0 0 0 0
2056 104 139 153 146 133 94 133 146 153 139 104 2056
17 3284 177 240 244 218 129 130 129 218 244 240 177 3284
2 0 0 0 0 0 0 0 0 0 0 0 2
3284 177 240 244 218 129 130 129 218 244 240 177 3284
18 4211 289 374 355 202 151 96 151 202 355 374 289 4211
0 0 0 0 0 0 0 0 0 0 0 0 0
4211 289 374 355 202 151 96 151 202 355 374 289 4211
19 5656 466 571 379 273 135 128 135 273 379 571 466 5656
2 0 0 0 0 0 0 0 0 0 0 0 2
5656 466 571 379 273 135 128 135 273 379 571 466 5656
20 4051 707 625 492 216 147 94 147 216 492 625 707 4051
0 0 0 0 0 0 0 0 0 0 0 0 0
4051 707 625 492 216 147 94 147 216 492 625 707 4051
21 4422 762 819 390 264 126 122 126 264 390 819 762 4422
2 0 0 0 0 0 0 0 0 0 0 0 2
4422 762 819 390 264 126 122 126 264 390 819 762 4422
22 2085 943 545 428 183 135 84 135 183 428 545 943 2085
0 0 0 0 0 0 0 0 0 0 0 0 0
2085 943 545 428 183 135 84 135 183 428 545 943 2085
23 1497 488 565 246 202 103 106 103 202 246 565 488 1497
2 0 0 0 0 0 0 0 0 0 0 0 2
1497 488 565 246 202 103 106 103 202 246 565 488 1497
24 543 427 239 216 95 97 62 97 95 216 239 427 543
0 0 0 0 0 0 0 0 0 0 0 0 0
543 427 239 216 95 97 62 97 95 216 239 427 543
25 216 170 157 90 84 48 68 48 84 90 157 170 216
2 0 0 0 0 0 0 0 0 0 0 0 2
216 170 157 90 84 48 68 48 84 90 157 170 216
26 53 67 51 44 29 30 20 30 29 44 51 67 53
0 0 0 0 0 0 0 0 0 0 0 0 0
53 67 51 44 29 30 20 30 29 44 51 67 53
27 11 18 17 14 14 14 14 14 14 14 17 18 11
2 0 0 0 0 0 0 0 0 0 0 0 2
11 18 17 14 14 14 14 14 14 14 17 18 11
28 0 1 1 1 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 1 1 1 0
Total 31155 4769 4554 3300 2212 1564 1356 1564 2212 3300 4554 4769 31155
22 0 0 0 0 0 0 0 0 0 0 0 22
31155 4769 4554 3300 2212 1564 1356 1564 2212 3300 4554 4769 31155
Grand total = 2*22 + 2*1356 + 4*1564 + 4*2212 + 4*3300 + 4*4554 + 4*4769 + 4*31155
= 192972
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
L
3 2 1 0 0 0 0 0 0 0 0 0 1 2
2 4 0 0 0 0 0 0 0 0 0 4 2
2 1 0 0 0 0 0 0 0 0 0 1 2
4 4 4 0 0 0 0 0 0 0 0 0 4 4
4 8 4 0 0 0 0 0 0 0 4 8 4
4 4 0 0 0 0 0 0 0 0 0 4 4
5 9 7 5 0 0 0 0 0 0 0 5 7 9
8 16 10 4 0 0 0 0 0 4 10 16 8
9 7 5 0 0 0 0 0 0 0 5 7 9
6 11 7 5 9 0 0 0 0 0 9 5 7 11
12 22 18 12 4 0 0 0 4 12 18 22 12
11 7 5 9 0 0 0 0 0 9 5 7 11
7 25 24 23 21 23 10 10 10 23 21 23 24 25
26 38 40 32 20 12 8 12 20 32 40 38 26
25 24 23 21 23 10 10 10 23 21 23 24 25
8 32 27 24 31 28 27 10 27 28 31 24 27 32
36 62 50 48 46 24 20 24 46 48 50 62 36
32 27 24 31 28 27 10 27 28 31 24 27 32
9 68 67 72 93 92 76 92 76 92 93 72 67 68
76 118 96 104 100 100 68 100 100 104 96 118 76
68 67 72 93 92 76 92 76 92 93 72 67 68
10 108 100 99 135 156 179 146 179 156 135 99 100 108
120 208 176 158 186 192 240 192 186 158 176 208 120
108 100 99 135 156 179 146 179 156 135 99 100 108
11 201 191 194 252 331 356 436 356 331 252 194 191 201
218 358 308 288 316 460 484 460 316 288 308 358 218
201 191 194 252 331 356 436 356 331 252 194 191 201
12 320 289 280 400 472 681 694 681 472 400 280 289 320
346 590 512 478 628 774 908 774 628 478 512 590 346
320 289 280 400 472 681 694 681 472 400 280 289 320
13 557 518 550 719 1088 1181 1260 1181 1088 719 550 518 557
600 996 868 1006 1164 1422 1444 1422 1164 1006 868 996 600
557 518 550 719 1088 1181 1260 1181 1088 719 550 518 557
14 910 883 882 1525 1695 1918 1950 1918 1695 1525 882 883 910
988 1668 1676 1828 2230 2266 2280 2266 2230 1828 1676 1668 988
910 883 882 1525 1695 1918 1950 1918 1695 1525 882 883 910
15 1609 1558 2148 2609 3135 3236 3300 3236 3135 2609 2148 1558 1609
1702 3144 3050 3608 3742 3780 3708 3780 3742 3608 3050 3144 1702
1609 1558 2148 2609 3135 3236 3300 3236 3135 2609 2148 1558 1609
16 2604 3338 3439 4745 5032 5041 4912 5041 5032 4745 3439 3338 2604
3170 5472 5986 5938 6046 5976 5996 5976 6046 5938 5986 5472 3170
2604 3338 3439 4745 5032 5041 4912 5041 5032 4745 3439 3338 2604
17 5328 5397 6796 7802 8063 7789 7716 7789 8063 7802 6796 5397 5328
5172 10268 9734 9570 9178 9414 9540 9414 9178 9570 9734 10268 5172
5328 5397 6796 7802 8063 7789 7716 7789 8063 7802 6796 5397 5328
18 6305 9356 9814 10982 10668 10263 9974 10263 10668 10982 9814 9356 6305
9000 13734 12982 11598 11768 12460 12776 12460 11768 11598 12982 13734 9000
6305 9356 9814 10982 10668 10263 9974 10263 10668 10982 9814 9356 6305
19 12600 13297 14152 14818 14609 13909 13732 13909 14609 14818 14152 13297 12600
12562 20432 16924 15502 15768 16550 16940 16550 15768 15502 16924 20432 12562
12600 13297 14152 14818 14609 13909 13732 13909 14609 14818 14152 13297 12600
20 9943 13833 13769 13632 12626 12253 12038 12253 12626 13632 13769 13833 9943
13056 14522 12784 12608 13666 13856 13516 13856 13666 12608 12784 14522 13056
9943 13833 13769 13632 12626 12253 12038 12253 12626 13632 13769 13833 9943
21 14223 15805 15972 15078 14404 13746 13760 13746 14404 15078 15972 15805 14223
14974 16816 12972 13426 14904 14832 14700 14832 14904 13426 12972 16816 14974
14223 15805 15972 15078 14404 13746 13760 13746 14404 15078 15972 15805 14223
22 10171 12127 10943 10165 9225 9086 8932 9086 9225 10165 10943 12127 10171
11420 8056 7816 8826 9300 9450 9300 9450 9300 8826 7816 8056 11420
10171 12127 10943 10165 9225 9086 8932 9086 9225 10165 10943 12127 10171
23 8303 9011 8928 7737 7338 6929 7072 6929 7338 7737 8928 9011 8303
8780 5498 4832 5840 6824 6496 6592 6496 6824 5840 4832 5498 8780
8303 9011 8928 7737 7338 6929 7072 6929 7338 7737 8928 9011 8303
24 4951 5351 4752 4326 3845 3887 3744 3887 3845 4326 4752 5351 4951
5186 2066 2332 3180 3242 3466 3328 3466 3242 3180 2332 2066 5186
4951 5351 4752 4326 3845 3887 3744 3887 3845 4326 4752 5351 4951
25 2636 2738 2570 2207 2103 1963 2064 1963 2103 2207 2570 2738 2636
2702 718 950 1346 1530 1436 1640 1436 1530 1346 950 718 2702
2636 2738 2570 2207 2103 1963 2064 1963 2103 2207 2570 2738 2636
26 1056 1027 946 845 763 772 734 772 763 845 946 1027 1056
1068 112 304 460 468 548 512 548 468 460 304 112 1068
1056 1027 946 845 763 772 734 772 763 845 946 1027 1056
27 380 363 349 315 304 298 296 298 304 315 349 363 380
382 4 68 96 120 132 136 132 120 96 68 4 382
380 363 349 315 304 298 296 298 304 315 349 363 380
28 32 32 30 28 28 28 28 28 28 28 30 32 32
32 0 4 8 8 8 8 8 8 8 4 0 32
32 32 30 28 28 28 28 28 28 28 30 32 32
Total 82388 95351 96742 98474 96028 93628 92900 93628 96028 98474 96742 95351 82388
91642 104930 94496 95964 101258 103654 104144 103654 101258 95964 94496 104930 91642
82388 95351 96742 98474 96028 93628 92900 93628 96028 98474 96742 95351 82388
Grand total = 4*82388 + 2*91642 + 2*92900 + 4*93628 + 2*94496 + 4*95351 + 2*95964 + 4*96028 + 4*96742 + 4*98474 + 2*101258 + 2*103654 + 104144 + 2*104930
= 3724276
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
EN
0 0 0 22 42 62 84 150 298 580 1062 1842 3038 4666 0 2 2 4 10 22 46 96 202 426 898 1892 3986 12 2 4 15 42 92 184 336 588 1030 1792 2996 4630
1 0 0 0 11 3 11 18 49 99 173 284 459 703 11 0 1 1 1 3 7 15 31 65 137 289 609 0 0 0 0 9 25 34 45 77 147 272 463 717
2 20 0 0 0 20 6 20 32 84 166 284 452 684 10 10 0 2 2 2 6 14 30 62 130 274 578 0 0 0 0 0 16 44 60 80 134 244 424 664
3 27 27 0 0 0 27 9 27 42 105 201 333 504 9 9 9 0 3 3 3 9 21 45 93 195 411 9 0 0 0 0 0 21 57 78 105 171 291 456
4 32 24 32 0 0 0 32 12 32 48 112 204 320 24 8 8 8 0 4 4 4 12 28 60 124 260 32 16 0 0 0 0 0 24 64 88 120 188 288
5 42 35 21 35 0 0 0 35 15 35 50 105 175 49 21 7 7 7 0 5 5 5 15 35 75 155 70 49 21 0 0 0 0 0 25 65 90 125 185
6 84 48 36 18 36 0 0 0 36 18 36 48 84 90 42 18 6 6 6 0 6 6 6 18 42 90 120 84 60 24 0 0 0 0 0 24 60 84 120
7 175 105 50 35 15 35 0 0 0 35 21 35 42 155 75 35 15 5 5 5 0 7 7 7 21 49 185 125 90 65 25 0 0 0 0 0 21 49 70
8 320 204 112 48 32 12 32 0 0 0 32 24 32 260 124 60 28 12 4 4 4 0 8 8 8 24 288 188 120 88 64 24 0 0 0 0 0 16 32
9 504 333 201 105 42 27 9 27 0 0 0 27 27 411 195 93 45 21 9 3 3 3 0 9 9 9 456 291 171 105 78 57 21 0 0 0 0 0 9
10 684 452 284 166 84 32 20 6 20 0 0 0 20 578 274 130 62 30 14 6 2 2 2 0 10 10 664 424 244 134 80 60 44 16 0 0 0 0 0
11 703 459 284 173 99 49 18 11 3 11 0 0 0 609 289 137 65 31 15 7 3 1 1 1 0 11 717 463 272 147 77 45 34 25 9 0 0 0 0
12 4666 3038 1842 1062 580 298 150 84 62 42 22 0 0 3986 1892 898 426 202 96 46 22 10 4 2 2 0 4630 2996 1792 1030 588 336 184 92 42 15 4 2 12
13 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 11 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
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
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
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
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
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
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
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
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
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
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
25 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 11 0
26 12 2 4 15 42 92 184 336 588 1030 1792 2996 4630 0 2 2 4 10 22 46 96 202 426 898 1892 3986 0 0 22 42 62 84 150 298 580 1062 1842 3038 4666
27 0 0 0 0 9 25 34 45 77 147 272 463 717 11 0 1 1 1 3 7 15 31 65 137 289 609 0 0 0 11 3 11 18 49 99 173 284 459 703
28 0 0 0 0 0 16 44 60 80 134 244 424 664 10 10 0 2 2 2 6 14 30 62 130 274 578 20 0 0 0 20 6 20 32 84 166 284 452 684
29 9 0 0 0 0 0 21 57 78 105 171 291 456 9 9 9 0 3 3 3 9 21 45 93 195 411 27 27 0 0 0 27 9 27 42 105 201 333 504
30 32 16 0 0 0 0 0 24 64 88 120 188 288 24 8 8 8 0 4 4 4 12 28 60 124 260 32 24 32 0 0 0 32 12 32 48 112 204 320
31 70 49 21 0 0 0 0 0 25 65 90 125 185 49 21 7 7 7 0 5 5 5 15 35 75 155 42 35 21 35 0 0 0 35 15 35 50 105 175
32 120 84 60 24 0 0 0 0 0 24 60 84 120 90 42 18 6 6 6 0 6 6 6 18 42 90 84 48 36 18 36 0 0 0 36 18 36 48 84
33 185 125 90 65 25 0 0 0 0 0 21 49 70 155 75 35 15 5 5 5 0 7 7 7 21 49 175 105 50 35 15 35 0 0 0 35 21 35 42
34 288 188 120 88 64 24 0 0 0 0 0 16 32 260 124 60 28 12 4 4 4 0 8 8 8 24 320 204 112 48 32 12 32 0 0 0 32 24 32
35 456 291 171 105 78 57 21 0 0 0 0 0 9 411 195 93 45 21 9 3 3 3 0 9 9 9 504 333 201 105 42 27 9 27 0 0 0 27 27
36 664 424 244 134 80 60 44 16 0 0 0 0 0 578 274 130 62 30 14 6 2 2 2 0 10 10 684 452 284 166 84 32 20 6 20 0 0 0 20
37 717 463 272 147 77 45 34 25 9 0 0 0 0 609 289 137 65 31 15 7 3 1 1 1 0 11 703 459 284 173 99 49 18 11 3 11 0 0 0
38 4630 2996 1792 1030 588 336 184 92 42 15 4 2 12 3986 1892 898 426 202 96 46 22 10 4 2 2 0 4666 3038 1842 1062 580 298 150 84 62 42 22 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 1*10 + 1*12 + 1*15 + 2*22 + 2*42 + 1*46 + 1*62 + 1*84 + 1*92 + 1*96 + 1*150 + 1*184 + 1*202 + 1*298 + 1*336 + 1*426 + 1*580 + 1*588 + 1*898 + 1*1030 + 1*1062 + 1*1792 +
1*1842 + 1*1892 + 1*2996 + 1*3038 + 1*3986 + 1*4630 + 1*4666) +
4(8*0 + 3*1 + 2*3 + 1*7 + 1*9 + 3*11 + 1*15 + 1*18 + 1*25 + 1*31 + 1*34 + 1*45 + 1*49 + 1*65 + 1*77 + 1*99 + 1*137 + 1*147 + 1*173 + 1*272 + 1*284 + 1*289 + 1*459 + 1*463 + 1*609 + 1*703 +
1*717) +
4(9*0 + 3*2 + 2*6 + 2*10 + 1*14 + 1*16 + 3*20 + 1*30 + 1*32 + 1*44 + 1*60 + 1*62 + 1*80 + 1*84 + 1*130 + 1*134 + 1*166 + 1*244 + 1*274 + 1*284 + 1*424 + 1*452 + 1*578 + 1*664 + 1*684) +
4(9*0 + 3*3 + 6*9 + 2*21 + 4*27 + 1*42 + 1*45 + 1*57 + 1*78 + 1*93 + 2*105 + 1*171 + 1*195 + 1*201 + 1*291 + 1*333 + 1*411 + 1*456 + 1*504) +
4(9*0 + 3*4 + 3*8 + 2*12 + 1*16 + 3*24 + 1*28 + 5*32 + 1*48 + 1*60 + 1*64 + 1*88 + 1*112 + 1*120 + 1*124 + 1*188 + 1*204 + 1*260 + 1*288 + 1*320) +
4(9*0 + 3*5 + 3*7 + 2*15 + 3*21 + 1*25 + 5*35 + 1*42 + 2*49 + 1*50 + 1*65 + 1*70 + 1*75 + 1*90 + 1*105 + 1*125 + 1*155 + 1*175 + 1*185) +
2(9*0 + 6*6 + 4*18 + 2*24 + 4*36 + 2*42 + 2*48 + 2*60 + 4*84 + 2*90 + 2*120) +
2(37*0 + 2*11) +
11(39*0)
= 124620 + 19076 + 18216 + 13200 + 8848 + 6256 + 2712 + 44
= 192972
Value repetition frequencies = 4(27*1 + 3*2 + 2*3) +
4(23*1 + 1*2 + 2*3 + 1*8) +
4(20*1 + 2*2 + 2*3 + 1*9) +
4(19*1 + 2*2 + 1*3 + 1*4 + 1*9) +
4(14*1 + 1*2 + 3*3 + 1*5 + 1*9) +
4(12*1 + 2*2 + 3*3 + 1*5 + 1*9) +
2(6*2 + 3*4 + 1*6 + 1*9) +
2(1*2 + 1*37) +
11(1*39)
= 1521
Number of distinct row element sets = 9
Number of rows = 2*2 + 6*4 + 1*11
= 39
Number of distinct values = 115
Distinct values 0 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 20 21 22 24 25 27 28 30
Frequency 709 12 24 20 20 12 20 16 12 28 12 16 12 4 16 8 12 12 20 8 16 8 16 4 4
Distinct values 31 32 34 35 36 42 44 45 46 48 49 50 57 60 62 64 65 70 75 77 78 80 84 88 90
Frequency 4 24 4 20 8 20 4 8 4 8 12 4 4 12 8 4 8 4 4 4 4 4 16 4 8
Distinct values 92 93 96 99 105 112 120 124 125 130 134 137 147 150 155 166 171 173 175 184 185 188 195 201 202
Frequency 4 4 4 4 12 4 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 204 244 260 272 274 284 288 289 291 298 320 333 336 411 424 426 452 456 459 463 504 578 580 588 609
Frequency 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 664 684 703 717 898 1030 1062 1792 1842 1892 2996 3038 3986 4630 4666
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 78*4 + 11*8 + 10*12 + 6*16 + 6*20 + 2*24 + 1*28 + 1*709
= 1521
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 18*30 + 4*31 + 4*36
= 812
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 670
Number of possible SN-EN pairs with SN != EN = 38*39
= 1482
a = 14, b = 3
L C S
3 8 2
4 16 4
5 32 10
6 44 22
7 128 38
8 160 60
9 384 114
10 596 192
11 1080 342
12 1628 564
13 2784 956
14 4400 1584
15 7420 2686
16 11928 4520
17 19440 7574
18 30268 12296
19 41996 17222
20 57660 24362
21 53824 22068
22 61696 26296
23 41896 17634
24 33804 14692
25 19292 8480
26 10172 4624
27 4516 2090
28 1512 740
29 464 232
30 36 18
Total 407184 169422
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 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 4 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 2 0 0 0 0 0 0 0 0 0 0 2 0
0 0 4 0 0 0 0 0 0 0 0 4 0 0
0 2 0 0 0 0 0 0 0 0 0 0 2 0
5 1 0 5 0 0 0 0 0 0 0 0 5 0 1
0 0 0 4 0 0 0 0 0 0 4 0 0 0
1 0 5 0 0 0 0 0 0 0 0 5 0 1
6 0 0 0 9 0 0 0 0 0 0 9 0 0 0
0 0 0 0 4 0 0 0 0 4 0 0 0 0
0 0 0 9 0 0 0 0 0 0 9 0 0 0
7 1 1 1 0 13 0 0 0 0 13 0 1 1 1
2 2 4 8 4 8 4 4 8 4 8 4 2 2
1 1 1 0 13 0 0 0 0 13 0 1 1 1
8 0 0 0 3 0 17 0 0 17 0 3 0 0 0
2 2 2 4 18 4 8 8 4 18 4 2 2 2
0 0 0 3 0 17 0 0 17 0 3 0 0 0
9 3 3 4 4 14 4 25 25 4 14 4 4 3 3
4 4 4 6 8 40 12 12 40 8 6 4 4 4
3 3 4 4 14 4 25 25 4 14 4 4 3 3
10 4 4 4 9 8 36 33 33 36 8 9 4 4 4
4 4 4 4 8 12 66 66 12 8 4 4 4 4
4 4 4 9 8 36 33 33 36 8 9 4 4 4
11 9 10 11 10 22 47 82 82 47 22 10 11 10 9
6 6 6 6 12 18 104 104 18 12 6 6 6 6
9 10 11 10 22 47 82 82 47 22 10 11 10 9
12 12 12 12 17 45 34 150 150 34 45 17 12 12 12
10 10 10 14 10 150 46 46 150 10 14 10 10 10
12 12 12 17 45 34 150 150 34 45 17 12 12 12
13 21 22 24 60 34 250 71 71 250 34 60 24 22 21
20 20 24 20 204 22 118 118 22 204 20 24 20 20
21 22 24 60 34 250 71 71 250 34 60 24 22 21
14 32 33 74 38 394 52 121 121 52 394 38 74 33 32
36 40 36 278 36 246 40 40 246 36 278 36 40 36
32 33 74 38 394 52 121 121 52 394 38 74 33 32
15 57 107 64 612 75 267 87 87 267 75 612 64 107 57
66 62 370 62 524 58 30 30 58 524 62 370 62 66
57 107 64 612 75 267 87 87 267 75 612 64 107 57
16 145 103 898 109 578 96 107 107 96 578 109 898 103 145
102 484 102 1008 98 88 10 10 88 98 1008 102 484 102
145 103 898 109 578 96 107 107 96 578 109 898 103 145
17 167 1286 186 1221 166 229 76 76 229 166 1221 186 1286 167
632 168 1794 164 262 36 2 2 36 262 164 1794 168 632
167 1286 186 1221 166 229 76 76 229 166 1221 186 1286 167
18 1772 297 2387 274 468 69 106 106 69 468 274 2387 297 1772
280 3002 276 718 100 12 0 0 12 100 718 276 3002 280
1772 297 2387 274 468 69 106 106 69 468 274 2387 297 1772
19 473 4403 476 1032 140 223 79 79 223 140 1032 476 4403 473
4784 470 1800 238 52 2 0 0 2 52 238 1800 470 4784
473 4403 476 1032 140 223 79 79 223 140 1032 476 4403 473
20 7620 795 2266 292 444 68 107 107 68 444 292 2266 795 7620
802 4136 506 188 14 0 0 0 0 14 188 506 4136 802
7620 795 2266 292 444 68 107 107 68 444 292 2266 795 7620
21 1289 4921 636 948 124 226 79 79 226 124 948 636 4921 1289
8790 996 614 64 2 0 0 0 0 2 64 614 996 8790
1289 4921 636 948 124 226 79 79 226 124 948 636 4921 1289
22 9368 1281 1957 222 447 69 107 107 69 447 222 1957 1281 9368
1860 1846 224 16 0 0 0 0 0 0 16 224 1846 1860
9368 1281 1957 222 447 69 107 107 69 447 222 1957 1281 9368
23 2321 3420 460 904 124 225 78 78 225 124 904 460 3420 2321
5140 658 84 2 0 0 0 0 0 0 2 84 658 5140
2321 3420 460 904 124 225 78 78 225 124 904 460 3420 2321
24 4360 895 1363 212 412 68 107 107 68 412 212 1363 895 4360
1698 352 18 0 0 0 0 0 0 0 0 18 352 1698
4360 895 1363 212 412 68 107 107 68 412 212 1363 895 4360
25 1483 1344 374 546 111 195 76 76 195 111 546 374 1344 1483
1286 100 2 0 0 0 0 0 0 0 0 2 100 1286
1483 1344 374 546 111 195 76 76 195 111 546 374 1344 1483
26 920 445 452 166 194 61 85 85 61 194 166 452 445 920
420 20 0 0 0 0 0 0 0 0 0 0 20 420
920 445 452 166 194 61 85 85 61 194 166 452 445 920
27 281 267 168 143 82 72 53 53 72 82 143 168 267 281
124 2 0 0 0 0 0 0 0 0 0 0 2 124
281 267 168 143 82 72 53 53 72 82 143 168 267 281
28 73 79 66 53 39 31 26 26 31 39 53 66 79 73
22 0 0 0 0 0 0 0 0 0 0 0 0 22
73 79 66 53 39 31 26 26 31 39 53 66 79 73
29 13 20 19 16 15 16 16 16 16 15 16 19 20 13
2 0 0 0 0 0 0 0 0 0 0 0 0 2
13 20 19 16 15 16 16 16 16 15 16 19 20 13
30 0 1 1 1 2 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 2 1 1 1 0
Total 30425 19751 11908 6901 3951 2357 1673 1673 2357 3951 6901 11908 19751 30425
26092 12388 5884 2804 1356 696 440 440 696 1356 2804 5884 12388 26092
30425 19751 11908 6901 3951 2357 1673 1673 2357 3951 6901 11908 19751 30425
Grand total = 2*440 + 2*696 + 2*1356 + 4*1673 + 4*2357 + 2*2804 + 4*3951 + 2*5884 + 4*6901 + 4*11908 + 2*12388 + 4*19751 + 2*26092 + 4*30425
= 407184
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 2
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 2
4 4 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
4 0 0 0 0 0 0 0 0 0 0 0 0 4
5 8 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
8 0 0 0 0 0 0 0 0 0 0 0 0 8
6 11 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
11 0 0 0 0 0 0 0 0 0 0 0 0 11
7 19 2 2 2 2 2 2 2 2 2 2 2 2 19
2 0 0 0 0 0 0 0 0 0 0 0 0 2
19 2 2 2 2 2 2 2 2 2 2 2 2 19
8 29 1 2 2 2 2 2 2 2 2 2 2 1 29
0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 1 2 2 2 2 2 2 2 2 2 2 1 29
9 52 4 7 8 8 8 8 8 8 8 8 7 4 52
2 0 0 0 0 0 0 0 0 0 0 0 0 2
52 4 7 8 8 8 8 8 8 8 8 7 4 52
10 90 5 7 11 12 12 12 12 12 12 11 7 5 90
0 0 0 0 0 0 0 0 0 0 0 0 0 0
90 5 7 11 12 12 12 12 12 12 11 7 5 90
11 158 9 14 17 23 24 24 24 24 23 17 14 9 158
2 0 0 0 0 0 0 0 0 0 0 0 0 2
158 9 14 17 23 24 24 24 24 23 17 14 9 158
12 265 11 17 22 25 33 34 34 33 25 22 17 11 265
0 0 0 0 0 0 0 0 0 0 0 0 0 0
265 11 17 22 25 33 34 34 33 25 22 17 11 265
13 445 21 31 36 46 53 63 63 53 46 36 31 21 445
2 0 0 0 0 0 0 0 0 0 0 0 0 2
445 21 31 36 46 53 63 63 53 46 36 31 21 445
14 741 34 46 55 60 76 88 88 76 60 55 46 34 741
0 0 0 0 0 0 0 0 0 0 0 0 0 0
741 34 46 55 60 76 88 88 76 60 55 46 34 741
15 1248 63 85 95 107 119 137 137 119 107 95 85 63 1248
2 0 0 0 0 0 0 0 0 0 0 0 0 2
1248 63 85 95 107 119 137 137 119 107 95 85 63 1248
16 2105 104 139 154 162 164 154 154 164 162 154 139 104 2105
0 0 0 0 0 0 0 0 0 0 0 0 0 0
2105 104 139 154 162 164 154 154 164 162 154 139 104 2105
17 3516 177 241 262 261 233 169 169 233 261 262 241 177 3516
2 0 0 0 0 0 0 0 0 0 0 0 0 2
3516 177 241 262 261 233 169 169 233 261 262 241 177 3516
18 5703 290 394 412 370 224 174 174 224 370 412 394 290 5703
0 0 0 0 0 0 0 0 0 0 0 0 0 0
5703 290 394 412 370 224 174 174 224 370 412 394 290 5703
19 7853 488 644 635 408 293 177 177 293 408 635 644 488 7853
2 0 0 0 0 0 0 0 0 0 0 0 0 2
7853 488 644 635 408 293 177 177 293 408 635 644 488 7853
20 10940 797 997 733 530 244 174 174 244 530 733 997 797 10940
0 0 0 0 0 0 0 0 0 0 0 0 0 0
10940 797 997 733 530 244 174 174 244 530 733 997 797 10940
21 9040 1260 1229 996 461 296 173 173 296 461 996 1229 1260 9040
2 0 0 0 0 0 0 0 0 0 0 0 0 2
9040 1260 1229 996 461 296 173 173 296 461 996 1229 1260 9040
22 10497 1521 1651 818 535 234 168 168 234 535 818 1651 1521 10497
0 0 0 0 0 0 0 0 0 0 0 0 0 0
10497 1521 1651 818 535 234 168 168 234 535 818 1651 1521 10497
23 5439 1974 1251 960 412 275 162 162 275 412 960 1251 1974 5439
2 0 0 0 0 0 0 0 0 0 0 0 0 2
5439 1974 1251 960 412 275 162 162 275 412 960 1251 1974 5439
24 4499 1199 1371 598 433 199 152 152 199 433 598 1371 1199 4499
0 0 0 0 0 0 0 0 0 0 0 0 0 0
4499 1199 1371 598 433 199 152 152 199 433 598 1371 1199 4499
25 1778 1204 659 582 254 211 134 134 211 254 582 659 1204 1778
2 0 0 0 0 0 0 0 0 0 0 0 0 2
1778 1204 659 582 254 211 134 134 211 254 582 659 1204 1778
26 869 501 495 244 219 107 108 108 107 219 244 495 501 869
0 0 0 0 0 0 0 0 0 0 0 0 0 0
869 501 495 244 219 107 108 108 107 219 244 495 501 869
27 257 272 189 158 96 88 68 68 88 96 158 189 272 257
2 0 0 0 0 0 0 0 0 0 0 0 0 2
257 272 189 158 96 88 68 68 88 96 158 189 272 257
28 65 81 69 54 43 36 30 30 36 43 54 69 81 65
0 0 0 0 0 0 0 0 0 0 0 0 0 0
65 81 69 54 43 36 30 30 36 43 54 69 81 65
29 12 20 19 16 16 16 16 16 16 16 16 19 20 12
2 0 0 0 0 0 0 0 0 0 0 0 0 2
12 20 19 16 16 16 16 16 16 16 16 19 20 12
30 0 1 1 1 2 2 2 2 2 2 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 2 2 2 2 2 2 1 1 1 0
Total 65645 10039 9560 6871 4487 2951 2231 2231 2951 4487 6871 9560 10039 65645
24 0 0 0 0 0 0 0 0 0 0 0 0 24
65645 10039 9560 6871 4487 2951 2231 2231 2951 4487 6871 9560 10039 65645
Grand total = 2*24 + 4*2231 + 4*2951 + 4*4487 + 4*6871 + 4*9560 + 4*10039 + 4*65645
= 407184
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 2 1 0 0 0 0 0 0 0 0 0 0 1 2
2 4 0 0 0 0 0 0 0 0 0 0 4 2
2 1 0 0 0 0 0 0 0 0 0 0 1 2
4 4 4 0 0 0 0 0 0 0 0 0 0 4 4
4 8 4 0 0 0 0 0 0 0 0 4 8 4
4 4 0 0 0 0 0 0 0 0 0 0 4 4
5 9 7 5 0 0 0 0 0 0 0 0 5 7 9
8 16 10 4 0 0 0 0 0 0 4 10 16 8
9 7 5 0 0 0 0 0 0 0 0 5 7 9
6 11 7 5 9 0 0 0 0 0 0 9 5 7 11
12 22 18 12 4 0 0 0 0 4 12 18 22 12
11 7 5 9 0 0 0 0 0 0 9 5 7 11
7 25 24 23 21 23 10 10 10 10 23 21 23 24 25
26 38 40 32 20 12 8 8 12 20 32 40 38 26
25 24 23 21 23 10 10 10 10 23 21 23 24 25
8 32 27 24 31 28 27 10 10 27 28 31 24 27 32
36 62 50 48 46 24 16 16 24 46 48 50 62 36
32 27 24 31 28 27 10 10 27 28 31 24 27 32
9 68 67 72 93 92 76 71 71 76 92 93 72 67 68
76 118 96 104 100 96 60 60 96 100 104 96 118 76
68 67 72 93 92 76 71 71 76 92 93 72 67 68
10 108 100 99 135 156 154 137 137 154 156 135 99 100 108
120 208 176 158 182 184 174 174 184 182 158 176 208 120
108 100 99 135 156 154 137 137 154 156 135 99 100 108
11 201 191 194 252 302 343 350 350 343 302 252 194 191 201
218 358 308 284 308 360 438 438 360 308 284 308 358 218
201 191 194 252 302 343 350 350 343 302 252 194 191 201
12 320 289 280 367 455 525 687 687 525 455 367 280 289 320
346 590 508 470 486 684 838 838 684 486 470 508 590 346
320 289 280 367 455 525 687 687 525 455 367 280 289 320
13 557 518 513 698 828 1170 1241 1241 1170 828 698 513 518 557
600 992 860 814 1014 1252 1514 1514 1252 1014 814 860 992 600
557 518 513 698 828 1170 1241 1241 1170 828 698 513 518 557
14 910 842 857 1119 1670 1829 2033 2033 1829 1670 1119 857 842 910
984 1660 1426 1602 1872 2322 2414 2414 2322 1872 1602 1426 1660 984
910 842 857 1119 1670 1829 2033 2033 1829 1670 1119 857 842 910
15 1566 1530 1546 2552 2874 3335 3488 3488 3335 2874 2552 1546 1530 1566
1700 2836 2740 2930 3742 3938 3982 3982 3938 3742 2930 2740 2836 1700
1566 1530 1546 2552 2874 3335 3488 3488 3335 2874 2552 1546 1530 1566
16 2665 2549 3366 4156 5180 5381 5385 5385 5381 5180 4156 3366 2549 2665
2846 5168 4890 5886 6268 6586 6416 6416 6586 6268 5886 4890 5168 2846
2665 2549 3366 4156 5180 5381 5385 5385 5381 5180 4156 3366 2549 2665
17 4458 5430 5633 8135 8740 8813 8610 8610 8813 8740 8135 5633 5430 4458
5254 9006 9880 10020 10514 10396 10532 10532 10396 10514 10020 9880 9006 5254
4458 5430 5633 8135 8740 8813 8610 8610 8813 8740 8135 5633 5430 4458
18 8711 8720 11347 13167 13824 13404 13091 13091 13404 13824 13167 11347 8720 8711
8562 17100 16460 16700 16030 16366 16666 16666 16366 16030 16700 16460 17100 8562
8711 8720 11347 13167 13824 13404 13091 13091 13404 13824 13167 11347 8720 8711
19 11255 16434 17186 19909 19780 19135 18480 18480 19135 19780 19909 17186 16434 11255
15694 24746 24200 21908 21882 22700 23474 23474 22700 21882 21908 24200 24746 15694
11255 16434 17186 19909 19780 19135 18480 18480 19135 19780 19909 17186 16434 11255
20 22787 23724 25873 27672 27462 26248 25655 25655 26248 27462 27672 25873 23724 22787
22464 38484 32846 30252 30116 31458 32138 32138 31458 30116 30252 32846 38484 22464
22787 23724 25873 27672 27462 26248 25655 25655 26248 27462 27672 25873 23724 22787
21 19358 27697 28180 28622 26807 25895 25526 25526 25895 26807 28622 28180 27697 19358
26260 31856 28142 26872 29068 29746 29038 29038 29746 29068 26872 28142 31856 26260
19358 27697 28180 28622 26807 25895 25526 25526 25895 26807 28622 28180 27697 19358
22 30429 33523 34064 32868 31521 30160 30002 30002 30160 31521 32868 34064 33523 30429
31696 39646 30780 30594 33454 33974 33378 33378 33974 33454 30594 30780 39646 31696
30429 33523 34064 32868 31521 30160 30002 30002 30160 31521 32868 34064 33523 30429
23 22268 27538 25460 23974 21896 21361 21140 21140 21361 21896 23974 25460 27538 22268
25822 20618 19456 21136 22414 22636 22448 22448 22636 22414 21136 19456 20618 25822
22268 27538 25460 23974 21896 21361 21140 21140 21361 21896 23974 25460 27538 22268
24 20851 22788 22667 20042 18916 17946 18078 18078 17946 18916 20042 22667 22788 20851
22110 16708 13824 16058 18476 17956 17940 17940 17956 18476 16058 13824 16708 22110
20851 22788 22667 20042 18916 17946 18078 18078 17946 18916 20042 22667 22788 20851
25 13415 14961 13388 12271 10996 10911 10698 10698 10911 10996 12271 13388 14961 13415
14278 6988 7392 9356 9698 10120 10038 10038 10120 9698 9356 7392 6988 14278
13415 14961 13388 12271 10996 10911 10698 10698 10911 10996 12271 13388 14961 13415
26 7893 8237 7816 6669 6309 5932 6000 6000 5932 6309 6669 7816 8237 7893
8178 2958 3350 4556 5216 4964 5302 5302 4964 5216 4556 3350 2958 8178
7893 8237 7816 6669 6309 5932 6000 6000 5932 6309 6669 7816 8237 7893
27 3832 3968 3624 3233 2945 2907 2844 2844 2907 2945 3233 3624 3968 3832
3912 862 1290 1894 1986 2148 2168 2168 2148 1986 1894 1290 862 3912
3832 3968 3624 3233 2945 2907 2844 2844 2907 2945 3233 3624 3968 3832
28 1423 1379 1288 1143 1057 1036 1012 1012 1036 1057 1143 1288 1379 1423
1436 124 376 564 608 684 700 700 684 608 564 376 124 1436
1423 1379 1288 1143 1057 1036 1012 1012 1036 1057 1143 1288 1379 1423
29 460 441 425 387 374 366 362 362 366 374 387 425 441 460
462 4 76 108 136 152 160 160 152 136 108 76 4 462
460 441 425 387 374 366 362 362 366 374 387 425 441 460
30 36 36 34 32 32 32 32 32 32 32 32 34 36 36
36 0 4 8 8 8 8 8 8 8 8 4 0 36
36 36 34 32 32 32 32 32 32 32 32 34 36 36
Total 173654 201032 203969 207557 202267 196996 194942 194942 196996 202267 207557 203969 201032 173654
193142 221180 199202 202370 213648 218766 219850 219850 218766 213648 202370 199202 221180 193142
173654 201032 203969 207557 202267 196996 194942 194942 196996 202267 207557 203969 201032 173654
Grand total = 4*173654 + 2*193142 + 4*194942 + 4*196996 + 2*199202 + 4*201032 + 4*202267 + 2*202370 + 4*203969 + 4*207557 + 2*213648 + 2*218766 + 2*219850 + 2*221180
= 8457984
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 24 46 68 92 166 336 668 1252 2236 3850 6360 9784 0 2 2 4 10 22 46 96 202 426 898 1892 3986 8398 13 2 4 16 46 102 206 380 674 1206 2168 3806 6354 9802
1 0 0 0 12 3 12 20 56 115 204 342 576 955 1476 12 0 1 1 1 3 7 15 31 65 137 289 609 1283 0 0 0 0 10 28 38 50 87 172 332 594 987 1516
2 22 0 0 0 22 6 22 36 98 198 346 568 918 1406 11 11 0 2 2 2 6 14 30 62 130 274 578 1218 0 0 0 0 0 18 50 68 90 154 294 544 926 1434
3 30 30 0 0 0 30 9 30 48 126 249 426 678 1026 10 10 10 0 3 3 3 9 21 45 93 195 411 867 10 0 0 0 0 0 24 66 90 120 201 366 636 996
4 36 27 36 0 0 0 36 12 36 56 140 268 444 672 27 9 9 9 0 4 4 4 12 28 60 124 260 548 36 18 0 0 0 0 0 28 76 104 140 228 388 608
5 48 40 24 40 0 0 0 40 15 40 60 140 255 400 56 24 8 8 8 0 5 5 5 15 35 75 155 325 80 56 24 0 0 0 0 0 30 80 110 150 235 360
6 98 56 42 21 42 0 0 0 42 18 42 60 126 210 105 49 21 7 7 7 0 6 6 6 18 42 90 186 140 98 70 28 0 0 0 0 0 30 78 108 150 222
7 210 126 60 42 18 42 0 0 0 42 21 42 56 98 186 90 42 18 6 6 6 0 7 7 7 21 49 105 222 150 108 78 30 0 0 0 0 0 28 70 98 140
8 400 255 140 60 40 15 40 0 0 0 40 24 40 48 325 155 75 35 15 5 5 5 0 8 8 8 24 56 360 235 150 110 80 30 0 0 0 0 0 24 56 80
9 672 444 268 140 56 36 12 36 0 0 0 36 27 36 548 260 124 60 28 12 4 4 4 0 9 9 9 27 608 388 228 140 104 76 28 0 0 0 0 0 18 36
10 1026 678 426 249 126 48 30 9 30 0 0 0 30 30 867 411 195 93 45 21 9 3 3 3 0 10 10 10 996 636 366 201 120 90 66 24 0 0 0 0 0 10
11 1406 918 568 346 198 98 36 22 6 22 0 0 0 22 1218 578 274 130 62 30 14 6 2 2 2 0 11 11 1434 926 544 294 154 90 68 50 18 0 0 0 0 0
12 1476 955 576 342 204 115 56 20 12 3 12 0 0 0 1283 609 289 137 65 31 15 7 3 1 1 1 0 12 1516 987 594 332 172 87 50 38 28 10 0 0 0 0
13 9784 6360 3850 2236 1252 668 336 166 92 68 46 24 0 0 8398 3986 1892 898 426 202 96 46 22 10 4 2 2 0 9802 6354 3806 2168 1206 674 380 206 102 46 16 4 2 13
14 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 12 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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
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 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 12 0
28 13 2 4 16 46 102 206 380 674 1206 2168 3806 6354 9802 0 2 2 4 10 22 46 96 202 426 898 1892 3986 8398 0 0 24 46 68 92 166 336 668 1252 2236 3850 6360 9784
29 0 0 0 0 10 28 38 50 87 172 332 594 987 1516 12 0 1 1 1 3 7 15 31 65 137 289 609 1283 0 0 0 12 3 12 20 56 115 204 342 576 955 1476
30 0 0 0 0 0 18 50 68 90 154 294 544 926 1434 11 11 0 2 2 2 6 14 30 62 130 274 578 1218 22 0 0 0 22 6 22 36 98 198 346 568 918 1406
31 10 0 0 0 0 0 24 66 90 120 201 366 636 996 10 10 10 0 3 3 3 9 21 45 93 195 411 867 30 30 0 0 0 30 9 30 48 126 249 426 678 1026
32 36 18 0 0 0 0 0 28 76 104 140 228 388 608 27 9 9 9 0 4 4 4 12 28 60 124 260 548 36 27 36 0 0 0 36 12 36 56 140 268 444 672
33 80 56 24 0 0 0 0 0 30 80 110 150 235 360 56 24 8 8 8 0 5 5 5 15 35 75 155 325 48 40 24 40 0 0 0 40 15 40 60 140 255 400
34 140 98 70 28 0 0 0 0 0 30 78 108 150 222 105 49 21 7 7 7 0 6 6 6 18 42 90 186 98 56 42 21 42 0 0 0 42 18 42 60 126 210
35 222 150 108 78 30 0 0 0 0 0 28 70 98 140 186 90 42 18 6 6 6 0 7 7 7 21 49 105 210 126 60 42 18 42 0 0 0 42 21 42 56 98
36 360 235 150 110 80 30 0 0 0 0 0 24 56 80 325 155 75 35 15 5 5 5 0 8 8 8 24 56 400 255 140 60 40 15 40 0 0 0 40 24 40 48
37 608 388 228 140 104 76 28 0 0 0 0 0 18 36 548 260 124 60 28 12 4 4 4 0 9 9 9 27 672 444 268 140 56 36 12 36 0 0 0 36 27 36
38 996 636 366 201 120 90 66 24 0 0 0 0 0 10 867 411 195 93 45 21 9 3 3 3 0 10 10 10 1026 678 426 249 126 48 30 9 30 0 0 0 30 30
39 1434 926 544 294 154 90 68 50 18 0 0 0 0 0 1218 578 274 130 62 30 14 6 2 2 2 0 11 11 1406 918 568 346 198 98 36 22 6 22 0 0 0 22
40 1516 987 594 332 172 87 50 38 28 10 0 0 0 0 1283 609 289 137 65 31 15 7 3 1 1 1 0 12 1476 955 576 342 204 115 56 20 12 3 12 0 0 0
41 9802 6354 3806 2168 1206 674 380 206 102 46 16 4 2 13 8398 3986 1892 898 426 202 96 46 22 10 4 2 2 0 9784 6360 3850 2236 1252 668 336 166 92 68 46 24 0 0
Sum of all rows = 4(3*0 + 3*2 + 2*4 + 1*10 + 1*13 + 1*16 + 1*22 + 1*24 + 3*46 + 1*68 + 1*92 + 1*96 + 1*102 + 1*166 + 1*202 + 1*206 + 1*336 + 1*380 + 1*426 + 1*668 + 1*674 + 1*898 + 1*1206 + 1*1252 + 1*1892 +
1*2168 + 1*2236 + 1*3806 + 1*3850 + 1*3986 + 1*6354 + 1*6360 + 1*8398 + 1*9784 + 1*9802) +
4(8*0 + 3*1 + 2*3 + 1*7 + 1*10 + 3*12 + 1*15 + 1*20 + 1*28 + 1*31 + 1*38 + 1*50 + 1*56 + 1*65 + 1*87 + 1*115 + 1*137 + 1*172 + 1*204 + 1*289 + 1*332 + 1*342 + 1*576 + 1*594 + 1*609 + 1*955 +
1*987 + 1*1283 + 1*1476 + 1*1516) +
4(9*0 + 3*2 + 2*6 + 2*11 + 1*14 + 1*18 + 3*22 + 1*30 + 1*36 + 1*50 + 1*62 + 1*68 + 1*90 + 1*98 + 1*130 + 1*154 + 1*198 + 1*274 + 1*294 + 1*346 + 1*544 + 1*568 + 1*578 + 1*918 + 1*926 + 1*1218 +
1*1406 + 1*1434) +
4(9*0 + 3*3 + 2*9 + 4*10 + 1*21 + 1*24 + 4*30 + 1*45 + 1*48 + 1*66 + 1*90 + 1*93 + 1*120 + 1*126 + 1*195 + 1*201 + 1*249 + 1*366 + 1*411 + 1*426 + 1*636 + 1*678 + 1*867 + 1*996 + 1*1026) +
4(9*0 + 3*4 + 3*9 + 2*12 + 1*18 + 2*27 + 2*28 + 5*36 + 1*56 + 1*60 + 1*76 + 1*104 + 1*124 + 2*140 + 1*228 + 1*260 + 1*268 + 1*388 + 1*444 + 1*548 + 1*608 + 1*672) +
4(9*0 + 3*5 + 3*8 + 2*15 + 3*24 + 1*30 + 1*35 + 4*40 + 1*48 + 2*56 + 1*60 + 1*75 + 2*80 + 1*110 + 1*140 + 1*150 + 1*155 + 1*235 + 1*255 + 1*325 + 1*360 + 1*400) +
4(9*0 + 3*6 + 3*7 + 2*18 + 2*21 + 1*28 + 1*30 + 5*42 + 1*49 + 1*56 + 1*60 + 1*70 + 1*78 + 1*90 + 2*98 + 1*105 + 1*108 + 1*126 + 1*140 + 1*150 + 1*186 + 1*210 + 1*222) +
2(40*0 + 2*12) +
12(42*0)
= 262580 + 40156 + 38240 + 27484 + 17948 + 11804 + 8924 + 48
= 407184
Value repetition frequencies = 4(31*1 + 1*2 + 3*3) +
4(26*1 + 1*2 + 2*3 + 1*8) +
4(23*1 + 2*2 + 2*3 + 1*9) +
4(20*1 + 1*2 + 1*3 + 2*4 + 1*9) +
4(14*1 + 4*2 + 2*3 + 1*5 + 1*9) +
4(14*1 + 3*2 + 3*3 + 1*4 + 1*9) +
4(16*1 + 3*2 + 2*3 + 1*5 + 1*9) +
2(1*2 + 1*40) +
12(1*42)
= 1764
Number of distinct row element sets = 9
Number of rows = 1*2 + 7*4 + 1*12
= 42
Number of distinct values = 141
Distinct values 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 21 22 24 27 28 30
Frequency 728 12 24 20 20 12 20 16 12 20 24 8 24 4 4 12 4 16 4 12 16 20 8 16 28
Distinct values 31 35 36 38 40 42 45 46 48 49 50 56 60 62 65 66 68 70 75 76 78 80 87 90 92
Frequency 4 4 24 4 16 20 4 12 8 4 8 20 12 4 4 4 8 4 4 4 4 8 4 12 4
Distinct values 93 96 98 102 104 105 108 110 115 120 124 126 130 137 140 150 154 155 166 172 186 195 198 201 202
Frequency 4 4 12 4 4 4 4 4 4 4 4 8 4 4 16 8 4 4 4 4 4 4 4 4 4
Distinct values 204 206 210 222 228 235 249 255 260 268 274 289 294 325 332 336 342 346 360 366 380 388 400 411 426
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 8
Distinct values 444 544 548 568 576 578 594 608 609 636 668 672 674 678 867 898 918 926 955 987 996 1026 1206 1218 1252
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 1283 1406 1434 1476 1516 1892 2168 2236 3806 3850 3986 6354 6360 8398 9784 9802
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 104*4 + 9*8 + 9*12 + 6*16 + 7*20 + 4*24 + 1*28 + 1*808
= 1764
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 2*2 + 20*33 + 4*34 + 4*39
= 956
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 766
Number of possible SN-EN pairs with SN != EN = 41*42
= 1722
