Graph structure similarity using spectral graph theory

Abstract

In understanding an unknown network we search for metrics to determine how close an inferred network that is being analyzed, is to the truth. We develop a metric to test for similarity between an inferred network and the true network. Our method uses the eigenvalues of the adjacency matrix and of the Laplacian at each step of the network discovery to decide on the comparison to the ground truth. We consider synthetic networks and real terrorist networks for our analysis.