Ordered community detection in directed networks

TL;DR

This paper introduces a nonparametric Bayesian method for detecting ordered community structures in directed networks, effectively capturing hierarchical relationships and distinguishing them from degree imbalances.

Contribution

It presents a novel modification of the stochastic block model that incorporates hierarchy and directed degree correction for improved community detection.

Findings

Successfully identifies hierarchical community structures in empirical networks.

Distinguishes hierarchical order from degree imbalance effects.

Provides a statistical test for the presence of hierarchy.

Abstract

We develop a method to infer community structure in directed networks where the groups are ordered in a latent one-dimensional hierarchy that determines the preferred edge direction. Our nonparametric Bayesian approach is based on a modification of the stochastic block model (SBM), which can take advantage of rank alignment and coherence to produce parsimonious descriptions of networks that combine ordered hierarchies with arbitrary mixing patterns between groups. Since our model also includes directed degree correction, we can use it to distinguish non-local hierarchical structure from local in- and out-degree imbalance -- thus removing a source of conflation present in most ranking methods. We also demonstrate how we can reliably compare with the results obtained with the unordered SBM variant to determine whether a hierarchical ordering is statistically warranted in the first place. We illustrate the application of our method on a wide variety of empirical networks across several domains.