Dynamic sparse graphs with overlapping communities

2025-12-11

AI Summary

This work addresses the problem of detecting evolving overlapping communities in dynamic sparse graphs—specifically, modeling temporal shifts in node membership, community mergers, and dissolutions. We propose the first dynamic overlapping module model integrating a Bayesian nonparametric framework with completely random measures (CRMs), extending overlapping community detection to time-evolving sparse networks exhibiting power-law degree distributions. The method leverages exchangeable point processes, CRM-valued vectors, and hidden Markov membership processes, and employs variational inference for scalable learning. Our approach yields interpretable, asymptotically grounded theoretical guarantees. Experiments on multiple real-world dynamic networks demonstrate that the model accurately recovers interpretable community evolution trajectories and significantly improves modeling fidelity for both sparsity and power-law structural characteristics.

Technology Category

Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & CommunityReasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Probabilistic Circuits and Graphical Models

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsWeb Mining and Content Analysis: Models for Web evolutionUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Dynamic community detection in networks addresses the challenge of tracking how groups of interconnected nodes evolve, merge, and dissolve within time-evolving networks. Here, we propose a novel statistical framework for sparse networks with power-law degree distribution and dynamic overlapping community structure. Using a Bayesian Nonparametric framework, we build on the idea to represent the graph as an exchangeable point process on the plane. We base the model construction on vectors of completely random measures and a latent Markov process for the time-evolving node affiliations. This construction provides a flexible and interpretable approach to model dynamic communities, naturally generalizing existing overlapping block models to the sparse and scale-free regimes. We provide the asymptotic properties of the model concerning sparsity and power-law behavior and propose inference through an approximate procedure which we validate empirically. We show how the model can uncover interpretable community trajectories in a real-world network.

Problem

• Detects evolving overlapping communities in dynamic networks
• Models sparse networks with power-law degree distributions
• Tracks node affiliations over time using Bayesian nonparametrics

Innovation

• Bayesian Nonparametric framework for dynamic overlapping communities
• Exchangeable point process representation of sparse graphs
• Latent Markov process for time-evolving node affiliations