Graph representation using mutual information for graph model discrimination

We present a novel approach of graph representation based on mutual information of a random walk in a graph. This representation, as any global metric of a graph, can be used to identify the model generator of the observed network. In this study, we use our graph representation combined with Random Forest (RF) to discriminate between Erdos-Renyi (ER), Stochastic Block Model (SBM) and Planted Clique (PC) models. We also combine our graph representation with a Squared Mahalanobis Distance (SMD)-based test to reject a model given an observed network. We test the proposed method with computer simulations.