Estimating Parameters of a Directed Weighted Graph Model with Beta-Distributed Edge-Weights

Abstract

We introduce a directed, weighted random graph model, where the edge-weights are independent and beta distributed with parameters depending on their endpoints. We will show that the row- and column-sums of the transformed edge-weight matrix are sufficient statistics for the parameters, and use the theory of exponential families to prove that the ML estimate of the parameters exists and is unique. Then an algorithm to find this estimate is introduced together with convergence proof that uses properties of the digamma function. Simulation results and applications are also presented.