The Entropy of PageRank Vectors and the Construction of a Discriminatory Statistic for the Identification of Network Topologies

Abstract

The entropy of Brin and Page's PageRank vector scales logarithmically with network size for a number of classic graph topologies. If expressed as a function of the number of edges in the network, E, the scaling may be written as S(E)=log(b,E) for numerical base b. In this article, I demonstrate via a simulation study that numerical base may may be used to characterize the topology of the network. This implies that the sample entropy of a graph, S(E), may be used to form a simple and elegant statistic to characterize the topology of a graph, including modern topologies such as the Barabasi-Albert scale free graphs.