Community Detection and Improved Detectability in Multiplex Networks

TL;DR

This paper introduces a probabilistic model for community detection in multiplex networks that leverages community multiplicity across layers, improving detectability without requiring prior community correlation assumptions.

Contribution

The paper proposes a novel generative model with Bayesian priors and localized constraints that enhances community detection in multiplex networks, outperforming existing correlated models.

Findings

Improved community detection in multiplex networks with consistent communities.

Model performs well even without prior community correlation.

Outperforms correlated models in certain SNR ranges.

Abstract

We investigate the widely encountered problem of detecting communities in multiplex networks, such as social networks, with an unknown arbitrary heterogeneous structure. To improve detectability, we propose a generative model that leverages the multiplicity of a single community in multiple layers, with no prior assumption on the relation of communities among different layers. Our model relies on a novel idea of incorporating a large set of generic localized community label constraints across the layers, in conjunction with the celebrated Stochastic Block Model (SBM) in each layer. Accordingly, we build a probabilistic graphical model over the entire multiplex network by treating the constraints as Bayesian priors. We mathematically prove that these constraints/priors promote existence of identical communities across layers without introducing further correlation between individual communities. The constraints are further tailored to render a sparse graphical model and the numerically efficient Belief Propagation algorithm is subsequently employed. We further demonstrate by numerical experiments that in the presence of consistent communities between different layers, consistent communities are matched, and the detectability is improved over a single layer. We compare our model with a "correlated model" which exploits the prior knowledge of community correlation between layers. Similar detectability improvement is obtained under such a correlation, even though our model relies on much milder assumptions than the correlated model. Our model even shows a better detection performance over a certain correlation and signal to noise ratio (SNR) range. In the absence of community correlation, the correlation model naturally fails, while ours maintains its performance.