# Generating Isomorphic Graphs

Is there a way of generating random isomorphic graphs for the purposes of testing tools like Nauty or BLISS? Every paper I've found says the authors had a database of certain isomorphic graphs, but I don't know how they constructed them or where I find test sets for graph isomorphism algorithms. I expect the answer to this question is no.

Is there a way to generate graphs that are likely to be isomorphic?

1. create a graph $$G = (V, E)$$ as you like
2. generate a random permutation $$\sigma\in \mathfrak{S}(V)$$, for example with Knuth's algorithm
3. create the graph $$G' = (V, E')$$ where $$E' = \{(\sigma(u), \sigma(v))\mid (u, v)\in E\}$$
4. Tada! $$G$$ and $$G'$$ are isomorphic!