Rejecting isomorphisms from collection of graphs

Question

I have a collection of 15M (Million) DAGs (directed acyclic graphs - directed hypercubes actually) that I would like to remove isomorphisms from. What is the common algorith

Answer 1

This is indeed an interesting problem.

I would approach it from the adjacency matrix angle. Two isomorphic graphs will have adjacency matrices where the rows / columns are in a different order. So my idea is to compute for each graph several matrix properties which are invariant to row/column swaps, off the top of my head:

numVerts, min, max, sum/mean, trace (probably not useful if there are no reflexive edges), norm, rank, min/max/mean column/row sums, min/max/mean column/row norm

and any pair of isomorphic graphs will be the same on all properties.

You could make a hash function which takes in a graph and spits out a hash string like

string hashstr = str(numVerts)+str(min)+str(max)+str(sum)+...

then sort all graphs by hash string and you only need to do full isomorphism checks for graphs which hash the same.

Given that you have 15 million graphs on 36 nodes, I'm assuming that you're dealing with weighted graphs, for unweighted undirected graphs this technique will be way less effective.