Efficient Curvature-aware Graph Network

TL;DR

This paper introduces Effective Resistance Curvature, a computationally efficient alternative to Ollivier-Ricci curvature for graph neural networks, maintaining geometric expressiveness while enabling large-scale applications.

Contribution

We propose a novel Effective Resistance Curvature measure that reduces computational complexity and retains geometric interpretability, addressing limitations of existing curvature methods in GNNs.

Findings

Effective Resistance Curvature outperforms Ollivier-Ricci in efficiency.

Our method achieves comparable GNN performance with lower computational cost.

Theoretically proven to be a suitable substitute for Ollivier-Ricci curvature.

Abstract

Graph curvature provides geometric priors for Graph Neural Networks (GNNs), enhancing their ability to model complex graph structures, particularly in terms of structural awareness, robustness, and theoretical interpretability. Among existing methods, Ollivier-Ricci curvature has been extensively studied due to its strong geometric interpretability, effectively characterizing the local geometric distribution between nodes. However, its prohibitively high computational complexity limits its applicability to large-scale graph datasets. To address this challenge, we propose a novel graph curvature measure--Effective Resistance Curvature--which quantifies the ease of message passing along graph edges using the effective resistance between node pairs, instead of the optimal transport distance. This method significantly outperforms Ollivier-Ricci curvature in computational efficiency while preserving comparable geometric expressiveness. Theoretically, we prove the low computational complexity of effective resistance curvature and establish its substitutability for Ollivier-Ricci curvature. Furthermore, extensive experiments on diverse GNN tasks demonstrate that our method achieves competitive performance with Ollivier-Ricci curvature while drastically reducing computational overhead.