Non-Dissipative Graph Propagation for Non-Local Community Detection

2025-08-15

AI Summary

To address the challenge of community detection in heterophilous graphs—where community structures are non-local and long-range node dependencies are difficult to model—this paper proposes an unsupervised Antisymmetric Graph Neural Network (uAGNN). uAGNN integrates continuous dynamical modeling with graph message passing, leveraging a non-dissipative dynamical system and antisymmetric weight matrices to enable stable, efficient, and globally aware information propagation, thereby overcoming the inherent locality limitation of conventional GNNs. Extensive experiments across ten benchmark datasets demonstrate that uAGNN significantly outperforms state-of-the-art methods under both high- and medium-heterophily regimes, particularly excelling at clustering nodes with long-range structural or semantic similarity. The framework provides a scalable, robust, and theoretically interpretable paradigm for community detection in heterophilous graphs.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning
• Multiagent Systems: Adversarial Agents

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Community detection in graphs aims to cluster nodes into meaningful groups, a task particularly challenging in heterophilic graphs, where nodes sharing similarities and membership to the same community are typically distantly connected. This is particularly evident when this task is tackled by graph neural networks, since they rely on an inherently local message passing scheme to learn the node representations that serve to cluster nodes into communities. In this work, we argue that the ability to propagate long-range information during message passing is key to effectively perform community detection in heterophilic graphs. To this end, we introduce the Unsupervised Antisymmetric Graph Neural Network (uAGNN), a novel unsupervised community detection approach leveraging non-dissipative dynamical systems to ensure stability and to propagate long-range information effectively. By employing antisymmetric weight matrices, uAGNN captures both local and global graph structures, overcoming the limitations posed by heterophilic scenarios. Extensive experiments across ten datasets demonstrate uAGNN's superior performance in high and medium heterophilic settings, where traditional methods fail to exploit long-range dependencies. These results highlight uAGNN's potential as a powerful tool for unsupervised community detection in diverse graph environments.

Problem

• Detecting communities in heterophilic graphs with distant connections
• Overcoming local message passing limitations in graph neural networks
• Propagating long-range information for effective node clustering

Innovation

• Unsupervised Antisymmetric Graph Neural Network
• Non-dissipative dynamical systems propagation
• Antisymmetric weight matrices capture structures