def EdgeTransitive(path,n): 
    
    # Writes all (not necessarily connected) edge transitive graphs of order n to path/AllETgraphs/ETn.g6
    # Requires: - list of all connected ET graphs of order k <= n, at path/ConnectedETGraphs/ETkc.g6
    #           - list of all (not necessarily connected) ET graphs of order n-1, at path/ConnectedETGraphs/ET(n-1)c.g6
    # All files in graph6 format
    
    # Uses the fact that the (not necessarily connected) edge transitive graphs of order n can be partitioned into three sets:
    #     - Connected
    #     - Disconnected and contain an isolated vertex
    #     - Disconnected, no isolated vertex - in this case, all components are isomorphic and edge transitive
    
    o = open(path+"/AllETGraphs/ET"+str(n)+".g6","w")
    f=open(path+"/ConnectedETGraphs/ET"+str(n)+"c.g6","r")
    g=open(path+"/AllETGraphs/ET"+str(n-1)+".g6","r")
    d = {"h"+str(k) : open(path+"/ConnectedETGraphs/ET"+str(k)+"c.g6","r") for k in range(1,n)}
    
    for line in f.xreadlines(): 
        # First add all connected edge transitive graphs
        o.write(line)
    f.close()
    
    for line in g.xreadlines(): 
        # Next add all disconnected edge transitive graphs that contain an isolated vertex.
        # Obtained by adding an isolated vertex to every (not necessarily connected)
        # edge transitive graph of order n-1
        G=Graph(line)
        G.add_vertex(n-1)
        o.write(G.graph6_string()+"\n")
    
    
    # Finally, add all disconnected edge transitive graphs that do not contain an isolated vertex.
    # All components will be isomorphic and edge transitive.
    for k in range(2,n/2+1): # Run through possible orders k for the components
        if n%k==0:  # k must divide n
            for line in d["h"+str(k)]: 
                G=Graph(line)  # G is a connected edge transitive graph of order k
                H=G.copy()
                for i in range(1,n/k):
                    H=H.disjoint_union(G)
                # H is now the disjoint union of n/k copies of G
                o.write(H.graph6_string()+"\n")
    
    f.close()
    g.close()
    for k in range(1,n):
        d["h"+str(k)].close()
    o.close()
    
def CountLines(path,n):  #Counts number of lines in path/AllETGraphs/ETn.g6
    f=open(path+"/AllETGraphs/ET"+str(n)+".g6")
    i=0
    for line in f.xreadlines():
       i+=1
    return i

# Input path here
p="/Users/lgmol/Desktop/EdgeTransitiveGraphs"

for n in range(2,48):
    EdgeTransitive(p,n)

for n in range(1,48):
    print n, CountLines(p,n)
    
# Output of final loop:
# 1 1
# 2 2
# 3 4
# 4 8
# 5 12
# 6 21
# 7 26
# 8 38
# 9 49
# 10 67
# 11 74
# 12 105
# 13 115
# 14 137
# 15 168
# 16 206
# 17 218
# 18 264
# 19 276
# 20 340
# 21 384
# 22 416
# 23 429
# 24 533
# 25 571
# 26 613
# 27 675
# 28 764
# 29 782
# 30 926
# 31 945
# 32 1066
# 33 1119
# 34 1166
# 35 1242
# 36 1464
# 37 1488
# 38 1537
# 39 1609
# 40 1856
# 41 1882
# 42 2096
# 43 2121
# 44 2244
# 45 2445
# 46 2505
# 47 2530