Title: 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.