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. 30249v1 Announce Type: cross 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.
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.
arXiv:2607. 05469v1 Announce Type: cross Abstract: Unsupervised graph clustering is a fundamental technique for uncovering underlying semantic patterns in large-scale networks.
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.
arXiv:2606. 09100v1 Announce Type: cross Abstract: Community detection is a fundamental problem in the analysis of complex networks.
arXiv:2507. 14484v2 Announce Type: replace Abstract: In recent years, graph neural networks (GNN) have achieved unprecedented successes in node classification tasks.
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.
arXiv:2609.26063v1 Announce Type: new Abstract: Federated graph learning (FGL) enables multiple clients to collaboratively train graph models without sharing their private graph data, providing a pro...
arXiv:2608.21466v1 Announce Type: new Abstract: We develop spectral algorithms for selecting state-space partitions that define averaging kernels for finite, ergodic and reversible Markov chains. For...
CurvFlow-DTA introduces a dual-graph discrete Ricci curvature flow framework for drug–target affinity prediction, replacing static curvature with weighted Forman curvature flow on both drug and protein residue–residue contact graphs. The method precomputes a label‑independent flow trajectory for each entity and uses a pair‑conditioned selector to guide a dual‑branch Flow‑GINE, leveraging frozen ESM‑2 residue representations. Experiments on Davis and KIBA datasets show significant improvements over the Ricci‑GraphDTA baseline, with reductions in mean squared error of up to 19.9% in warm‑start and 27.4% in cold‑start settings, and higher concordance indices across benchmarks.
The paper introduces RicciPool, a graph pooling method that incorporates higher‑order connectivity via Ollivier‑Ricci curvature to reweight edges before spectral clustering. Unlike traditional pooling approaches that focus only on rough topology, RicciPool leverages local connection information to improve cluster assignment. Experiments on protein and social network datasets demonstrate its effectiveness.
The paper introduces Omega‑N, a set of ten interpretable node‑level structural descriptors derived from localizing four factors of a composite structural index. By correcting the ill‑conditioned localization with a configuration‑null excess and a multi‑scale personalized‑PageRank neighbourhood, Omega‑N achieves competitive or superior performance in six in‑domain node‑classification tasks compared to a recursive feature engine that uses up to 252 features. In drug‑target prioritisation on protein interaction networks, Omega‑N improves AUPRC by 0.073 to 0.144 over a centrality baseline and remains robust across independent datasets and bias controls, though it offers no benefit when combined with Node2Vec. whyItMatters":"The study demonstrates that a compact, interpretable set of structural features can match or exceed more complex feature sets in practical graph‑based prediction tasks, particularly in biomedical network analysis."