Statistical inference of assortative community structures

TL;DR

This paper introduces a Bayesian method for detecting statistically significant assortative communities in networks, outperforming traditional methods like modularity maximization and avoiding resolution limits.

Contribution

It presents a nonparametric Bayesian approach to infer communities, demonstrating its effectiveness and ability to compare with stochastic block models for assessing assortativity.

Findings

Successfully identifies significant communities in empirical networks.

Avoids overfitting and resolution limit issues of traditional methods.

Reveals more accurate levels of network assortativity.

Abstract

We develop a principled methodology to infer assortative communities in networks based on a nonparametric Bayesian formulation of the planted partition model. We show that this approach succeeds in finding statistically significant assortative modules in networks, unlike alternatives such as modularity maximization, which systematically overfits both in artificial as well as in empirical examples. In addition, we show that our method is not subject to a resolution limit, and can uncover an arbitrarily large number of communities, as long as there is statistical evidence for them. Our formulation is amenable to model selection procedures, which allow us to compare it to more general approaches based on the stochastic block model, and in this way reveal whether assortativity is in fact the dominating large-scale mixing pattern. We perform this comparison with several empirical networks, and identify numerous cases where the network's assortativity is exaggerated by traditional community detection methods, and we show how a more faithful degree of assortativity can be identified.