EXPLOITING THE DISCRIMINATING POWER OF THE EIGENVECTOR CENTRALITY MEASURE TO DETECT GRAPH ISOMORPHISM

Graph Isomorphism is one of the classical problems of graph theory for which no deterministic polynomial-time algorithm is currently known, but has been neither proven to be NP-complete. Several heuristic algorithms have been proposed to determine whether or not two graphs are isomorphic (i.e., structurally the same). In this paper, we analyze the discriminating power of the well-known centrality measures on real-world network graphs and propose to use the sequence (either the non-decreasing or non-increasing order) of eigenvector centrality (EVC) values of the vertices of two graphs as a precursor step to decide whether or not to further conduct tests for graph isomorphism.