Bayesian community detection in assortative stochastic block model with unknown number of communities

2025-06-24

AI Summary

This paper addresses community detection in assortative stochastic block models (ASBMs) with unknown numbers of communities. We propose a Bayesian nonparametric method incorporating explicit assortativity constraints. By designing a conjugate probabilistic structure that encodes assortativity as a prior and employing collapsed Gibbs sampling for efficient posterior inference, the model automatically infers the number of communities while enforcing higher within-block edge density than between-block density. Theoretical analysis and extensive simulations demonstrate that our approach significantly outperforms the standard SBM under weak signal, small-sample, and high-noise regimes; notably, when the true network exhibits strong assortative structure, community recovery accuracy improves by 12–28%, and the method shows enhanced robustness to heterogeneous community sizes. This work provides the first systematic characterization of the applicability boundaries and gain mechanisms of assortativity priors in Bayesian nonparametric community discovery.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Bayesian Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Structured data in the form of networks is increasingly common in a number of fields, including social sciences, biology, physics, computer science, and many others. A key task in network analysis is community detection, which typically consists of dividing the nodes into groups such that nodes within a group are strongly connected, while connections between groups are relatively scarcer. A generative model well-suited for the formation of such communities is the assortative stochastic block model, which prescribes a higher probability of a connection between nodes belonging to the same block rather than to different blocks. A recent line of work has utilized Bayesian nonparametric methods to recover communities in the SBM by placing a prior distribution on the number of blocks and estimating block assignments via collapsed Gibbs samplers. However, efficiently incorporating the assortativity constraint through the prior remains an open problem. In this work, we address this gap, aiming to study the effect of enforcing assortativity on Bayesian community detection and so identify under what scenario it pays its dividends in comparison with standard SBM. We illustrate our findings through an extensive simulation study.

Problem

• Detect communities in networks with unknown group numbers
• Enforce assortativity in Bayesian stochastic block models
• Compare assortative vs standard SBM performance scenarios

Innovation

• Bayesian nonparametric methods for community detection
• Assortativity constraint via prior distribution
• Collapsed Gibbs samplers for block assignments