Use this if you are using igraph from R
count_isomorphisms {igraph}  R Documentation 
Count the number of isomorphic mappings between two graphs
count_isomorphisms(graph1, graph2, method = "vf2", ...)
graph1 
The first graph. 
graph2 
The second graph. 
method 
Currently only ‘vf2’ is supported, see

... 
Passed to the individual methods. 
Number of isomorphic mappings between the two graphs.
LP Cordella, P Foggia, C Sansone, and M Vento: An improved algorithm for matching large graphs, Proc. of the 3rd IAPR TC15 Workshop on Graphbased Representations in Pattern Recognition, 149–159, 2001.
Other graph isomorphism:
count_subgraph_isomorphisms()
,
graph_from_isomorphism_class()
,
isomorphic()
,
isomorphism_class()
,
isomorphisms()
,
subgraph_isomorphic()
,
subgraph_isomorphisms()
# colored graph isomorphism
g1 < make_ring(10)
g2 < make_ring(10)
isomorphic(g1, g2)
V(g1)$color < rep(1:2, length = vcount(g1))
V(g2)$color < rep(2:1, length = vcount(g2))
# consider colors by default
count_isomorphisms(g1, g2)
# ignore colors
count_isomorphisms(g1, g2, vertex.color1 = NULL,
vertex.color2 = NULL)