Graph Cascades: Contagion-Based Mesoscopic Rewiring for Structure-Aware Graph Machine Learning

2026-06-03

AI Summary

Existing graph neural networks and sparse graph Transformers struggle to effectively capture mesoscale structures, leading to limited performance on heterophilic graphs and medium-to-high-density homophilic graphs. This work proposes a mesoscale rewiring strategy grounded in an epidemic diffusion process, which constructs an auxiliary graph in O(|V|+|E|) time by promoting repeatedly reinforced multi-hop node pairs to direct neighbors, thereby enhancing structural awareness. Theoretical analysis provides the first sufficient conditions under which rewiring outperforms the original adjacency, demonstrates the efficacy of two-hop reinforcement in fully assortative stochastic block models, formalizes mesoscale connectivity via effective graph resistance, and identifies graph structures where rewiring offers no benefit. Experiments show that the method consistently improves performance across diverse GNNs and sparse graph Transformers on multiple node classification benchmarks, particularly excelling on heterophilic and medium-to-high-density homophilic graphs, with post-rewiring structural properties strongly correlated with model performance.

Abstract

We introduce Graph Cascades, a mesoscopic rewiring strategy for Graph Neural Networks (GNNs) and Graph Transformers (GTs) that captures intermediate-scale graph structure beyond purely local edges or fully global attention. Using contagion-based diffusion processes, Graph Cascades constructs, in O(|V|+|E|) time, an auxiliary graph where node pairs supported by repeated multi-hop reinforcement are promoted to direct neighbors. We theoretically characterize when reinforcement-based rewiring helps: sufficient conditions under which reinforcement-based edge selection is more label-aligned than direct adjacency, an SBM witness in which two-hop reinforcement is perfectly homophilic, and a formalization of mesoscopic connectivity via graph effective resistance. Empirically, across node-classification benchmarks, Graph Cascades improves multiple GNN and sparse-GT backbones, with the most reliable gains observed on heterophilic and moderate- to high-degree homophilic graphs. The theoretical conditions also identify regimes where mesoscopic rewiring is unlikely to be beneficial -- low-degree regular graphs and graphs with structural bottlenecks -- and these predictions match the observed failures. We additionally observe tight correlations between performance and structural properties in the rewired graphs.

Problem

• Graph Neural Networks
• mesoscopic structure
• graph rewiring
• heterophilic graphs
• structure-aware learning

Innovation

• Graph Rewiring
• Mesoscopic Structure
• Contagion-Based Diffusion
• Graph Neural Networks
• Effective Resistance