这篇用边的曲率做无监督社区检测，在异质图上赢了九个基线，聚类器部分提升显著，代码也开源了。
提出曲率引导的Sheaf扩散（CGSD），利用离散Forman-Ricci曲率作为拓扑信号进行无监督社区检测。在Cora、Cornell、Texas、Wisconsin、Chameleon五个异质图基准上，CGSD在Wisconsin和Chameleon上优于九个无监督基线，其余三个具竞争力。其曲率感知谱聚类器（CSpec）在相同嵌入下将平均NMI从0.091（K-Means）提升至0.107（+15%，p=0.008）。代码已在GitHub开源。
Curvature-Guided Sheaf Diffusion for Unsupervised Community Detection on Heterophilic Graphs
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.