Graph Isomorphism Detection Using Vertex Similarity Measure

Abstract

Measures of vertex similarity have been incorporated in graph matching algorithms. Graph matching tries to retrieve a 1-1 correspondence between vertices of two given graphs. In this paper, the vertex similarity measure of Blondel et al. is studied for its usefulness in detecting graph isomorphism. Firstly, the applicability of this measure to distinguish similar pairs from dissimilar pairs is shown to be limited in scope even for small graphs. In a preliminary experiment, we show that Blondel’s vertex similarity measure does not retrieve the isomorphism within a graph of 14 nodes. We propose a refinement of Blondel’s measure. Zager et al. also refine Blondel’s measure and further propose a graph matching algorithm. We propose a graph matching algorithm based on the lines of Zager et al. and test our algorithm against Zager’s as well as Blondel’s and show that the proposed refinement performs better than both the measures with regard to graph isomorphism problem. The performance is evaluated systematically on a large bench mark data set made available by Foggia et al. The proposed algorithm performs with 90.10% accuracy on all of the 18,200 pairs of isomorphic graphs available in the benchmark dataset.