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

Community Detection as Adaptive Diffusion

This work introduces ECHO (Encoding Communities via High-Order Operators), a scalable, self-supervised framework that treats communities as regions of adaptive diffusion on semantic manifolds that recovers communities from topology when node features are weak, while feature isolation is preferable when features are strong.

HeAD-CP: Heterophily-Aware Diffused Conformal Prediction Sets for Graph Neural Networks

Conformal prediction (CP) provides distribution-free uncertainty quantification, and its extension to graphs is an active research direction. Diffused Adaptive Prediction Sets (DAPS) is a widely used graph-aware diffusion baseline, propagating Adaptive Prediction Sets (APS) non-conformity scores along edges with a uniform coefficient $\lambda$. We identify a fundamental shortcoming of this design: the uniform low-pass diffusion presupposes graph homophily and proves detrimental on heterophilic graphs, enlarging the mean prediction-set size by up to 10.6% relative to plain APS. To mitigate this, we propose HeAD-CP, a family of node-wise diffusion variants whose coefficients are determined by a label-free local-homophily estimate derived from the GNN softmax. Three variants, namely signed-$\gamma$, edge-compatibility, and a DAPS-baseline-with-correction, are most effective at extreme heterophily, intermediate heterophily, and moderate-to-high homophily, respectively, and all preserve the marginal coverage guarantee. On ten benchmarks, the HeAD-CP family stays at or below plain APS on every dataset, while DAPS exceeds APS on six. The post-hoc oracle over the family improves over DAPS on 8/10 datasets at $p<0.01$ (paired Wilcoxon), with the largest gains on heterophilic graphs (10.3% on Texas); on the two homophilic datasets where DAPS still wins (CiteSeer, PubMed), it retains a marginal advantage of at most 0.002, statistically insignificant on CiteSeer ($p=0.23$). Designing a calibrated label-free selector that approaches this oracle is the main outstanding empirical question.

Heterophily-Aware Node Classification in Multiplex Graphs

Network Denoising Revisited: A Ricci-Flow-Inspired Graph Diffusion Method

This work proposes Ricci-Diffusion, a curvature-guided graph diffusion method inspired by Ricci flow, which exhibits a Ricci-flow-like evolution, in which relative edge-level curvature modulates local transport in the diffusion kernel and guides edge-weight updates toward a more regular graph geometry.

DiffGCC: diffusion-enhanced global–local graph contrastive clustering

DiffGCC is a generative graph contrastive clustering framework that couples global–local feature encoding with a latent-space diffusion denoising mechanism and substantially outperforms existing methods across ACC, NMI, ARI, and F1, with particularly strong gains on denser, noisier product graphs.

LIGR: Label Informativeness-guided Graph Rewiring

This work proposes LIGR (Label Informativeness-Guided Rewiring), which maximizes an information-theoretic measure quantifying how much neighbors’ labels reveal about node labels, suitable for applications requiring interpretability (biological networks, social graphs).