Bayesian Community Detection

TL;DR

This paper presents a Bayesian method for detecting communities in networks modeled by the stochastic block model, demonstrating strong consistency under certain degree conditions.

Contribution

It introduces a Bayesian estimator with specific priors for community detection, proving its strong consistency when network degrees grow at least as fast as log-squared of the number of nodes.

Findings

Estimator is strongly consistent for networks with degree at least log^2(n)

Uses Dirichlet, Bernoulli, and Beta priors for class proportions, labels, and edge probabilities

Applicable when the number of classes is known

Abstract

We introduce a Bayesian estimator of the underlying class structure in the stochastic block model, when the number of classes is known. The estimator is the posterior mode corresponding to a Dirichlet prior on the class proportions, a generalized Bernoulli prior on the class labels, and a beta prior on the edge probabilities. We show that this estimator is strongly consistent when the expected degree is at least of order $\log^2{n}$, where $n$ is the number of nodes in the network.