EXIT analysis for belief propagation in degree-correlated stochastic block models

Abstract

This paper proposes the extrinsic information transfer (EXIT) method for the analysis of belief propagation in community detection on random graphs, specifically under the degree correlated stochastic block model. Belief propagation in community detection has been studied under density evolution; this work for the first time brings EXIT analysis to community detection on random graphs, which has certain advantages that are well documented in the parallel context of error control coding. We show using simulations that in the case of equally-sized communities, when the probability of connectivity in the communities are different, there is only one intersection point on the EXIT curves, hence belief propagation is optimal. When the probability of connectivity in the communities are the same, we show that belief propagation is equivalent to random guessing and the EXIT curves intersect at the trivial zero-zero point. For the roughly equal-sized communities, we show that there is always only one intersection point on the EXIT curves, suggesting that belief propagation is optimal. Finally, for the communities with disparate size, we show that there are multiple intersection points, hence belief propagation is likely to be sub-optimal.