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 TC-15 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)