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.
arXiv:2606. 09100v1 Announce Type: cross Abstract: Community detection is a fundamental problem in the analysis of complex networks.
By Shahin Momenzadeh, Rojiar Pir Mohammadiani
arXiv:2606. 15482v1 Announce Type: cross Abstract: Ricci flow is a curvature-guided diffusion process that deforms space by shrinking regions of high positive curvature and expanding those with negative curvature.
By Tian Qin, Wei-Min Huang
arXiv:2607. 22381v1 Announce Type: new Abstract: Curvature notions on graphs, particularly Ollivier-Ricci and Forman, have emerged as powerful tools for addressing fundamental issues in Graph Neural Networks (GNNs) such as oversmoothing and oversquashing, but rely almost exclusively on local edge-level comparisons and therefore fail to certify how information actually propagates over long distances.
By Rachid Caich, Yassine Abbahaddou
arXiv:2607. 05469v1 Announce Type: cross Abstract: Unsupervised graph clustering is a fundamental technique for uncovering underlying semantic patterns in large-scale networks.
By Jingyun Zhang, Hao Peng, Jianxin Li, Angsheng Li, Philip S. Yu
arXiv:2607. 03145v1 Announce Type: cross Abstract: The informativeness of a training set is as consequential as its size, yet most sampling strategies remain agnostic to the intrinsic geometry of the data distribution.
By Alexandre L. M. Levada