Maximum likelihood rumor source detection in a star network

Abstract

Here we examine the problem of rumor source identification in star networks. We assume the SI model for rumor propagation with exponential waiting times. We consider the case where a rumor originates from a single source, and find an explicit, non-iterative, maximum likelihood estimate for the source given the observed infection pattern. The theoretical derivation is supported by computational data. We contrast this estimator with the "rumor center" estimator of Shah and Zaman. Unlike rumor centrality, our ML estimator admits the possibility of more than two equiprobable maxima for a given infection pattern, and while a unique rumor center is always equivalent to the distance center, we show that this is not the case for our ML estimator.