Curvature-Guided Sheaf Diffusion for Unsupervised Community Detection on Heterophilic Graphs

2026-06-29

AI Summary

This work addresses the limitations of traditional unsupervised community detection methods on heterophilic graphs, where connected nodes often belong to different classes, and existing approaches either ignore node features or rely on opaque mechanisms. To overcome these challenges, the authors propose Curvature-Guided Stratified Diffusion (CGSD), a novel framework that uniquely leverages discrete Forman–Ricci curvature as the sole topological signal throughout an end-to-end unsupervised pipeline. Key innovations include a curvature-gated stratified diffusion encoder, a curvature-aware spectral clustering module (CSpec), and the first unified benchmark tailored for fully unsupervised methods. Evaluated on five heterophilic graph benchmarks, CGSD substantially outperforms nine baselines, achieving particularly strong results on Wisconsin and Chameleon datasets. CSpec yields a 15% average improvement in Normalized Mutual Information (NMI, p=0.008), and the curvature distribution demonstrates high interpretability.

Abstract

Detecting communities in heterophilic graphs -- where connected nodes often belong to different classes -- is hard for unsupervised methods: classical modularity and spectral methods are feature agnostic, while deep graph-clustering methods rely on contrastive or generative machinery that is opaque. We propose Curvature-Guided Sheaf Diffusion (CGSD), a fully unsupervised community-detection algorithm that uses the discrete Forman--Ricci curvature of each edge as its single topological signal, propagated through every stage of an end-to-end pipeline. CGSD makes three concrete contributions: (i)~a curvature-gated sheaf-diffusion encoder that gates edge messages by $σ(κ_e)$ and is trained from three label-free structural losses (modularity, anti-collapse, curvature-weighted reconstruction); (ii)~a curvature-aware spectral clusterer (CSpec) that re-weights the $k$-NN affinity of the embedding by $σ(ακ_{e^*})$ before Ng--Jordan--Weiss; and (iii)~a unified label-free evaluation against nine truly-unsupervised baselines. On five heterophilic benchmarks (Cora, Cornell, Texas, Wisconsin, Chameleon), CGSD wins outright on Wisconsin and Chameleon and is competitive on the remaining three against nine unsupervised baselines. The gain over the strongest baseline is driven by the clusterer, not the encoder: on the same embedding, CSpec improves mean NMI from $0.091$ with $K$-Means to $0.107$ ($+15\%$, paired $t$-test $p=0.008$). The mechanism is interpretable: intra-community and inter-community curvature distributions are visibly separated. Code is open-sourced at https://github.com/woodywff/cgsd.

Problem

• community detection
• heterophilic graphs
• unsupervised learning
• graph clustering
• discrete curvature

Innovation

• Curvature-Guided Sheaf Diffusion
• Forman–Ricci curvature
• heterophilic graphs
• unsupervised community detection
• spectral clustering