Non-Dissipative Graph Propagation for Non-Local Community Detection

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.