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Re: [igraph] an igraph isomorphism problem

From: Tamás Nepusz
Subject: Re: [igraph] an igraph isomorphism problem
Date: Thu, 22 Aug 2013 10:25:52 +0200

> Thank you very much. 
> but does that mean igraph cannot handle multigraph isomorphism?
It can, with a trick. You have to collapse multiple edges into a single edge 
and assign the original edge count to the new edge as an edge attribute. Then 
you can use the edge_color1 and edge_color2 arguments of isomorphic_vf2 to 
disallow matching an edge to another with a different multiplicity. E.g.:

# Construct the graphs
g1 = igraph.Graph([(0,1),(1,0),(0,0),(1,1)], directed=True)
g2 = igraph.Graph([(0,1),(1,0),(0,1),(1,0)], directed=True)

# Declare that each edge in the graph has a multiplicity of 1 (because we still 
have multiple edges)
g1.es["multiplicity"] = 1
g2.es["multiplicity"] = 1

# Collapse the multiple edges into a single one and sum the multiplicities
g1.simplify(multiple=True, loops=False, combine_edges="sum")
g2.simplify(multiple=True, loops=False, combine_edges="sum")

# Now check whether they are isomorphic, considering the multiplicities
print g1.isomorphic_vf2(g2, edge_color1=g1.es["multiplicity"], 


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