A Performance Comparison of Five Algorithms for Graph Isomorphism

Despite the significant number of isomorphism algorithms presented in the literature, till now no efforts have been done for characterizing their performance. Consequently, it is not clear how the behavior of those algorithms varies as the type and the size of the graphs to be matched varies in case of real applications. In this paper we present a benchmarking activity for characterizing the performance of a bunch of algorithms for exact graph isomorphism. To this purpose we use a large database containing 10,000 couples of isomorphic graphs with different topologies (regular graphs, randomly connected graphs, bounded valence graph), enriched with suitably modified versions of them for simulating distortions occurring in real cases. The size of the considered graphs ranges from a few nodes to about 1000 nodes.