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

Abstract

This paper presents Graph Cascades, a mesoscopic rewiring methodology designed for Graph Neural Networks (GNNs) and Graph Transformers (GTs). This approach addresses structural information at an intermediate scale, moving beyond the limitations of strictly local edges or fully global attention mechanisms. By leveraging contagion-based diffusion processes, Graph Cascades generates an auxiliary graph in O(|V|+|E|) time. Within this structure, node pairs that exhibit repeated multi-hop reinforcement are elevated to direct neighbors.

We provide a theoretical analysis of when reinforcement-based rewiring offers advantages, establishing sufficient conditions where such edge selection proves more aligned with labels than direct adjacency. Our findings include an SBM witness demonstrating that two-hop reinforcement achieves perfect homophily, as well as a formal definition of mesoscopic connectivity grounded in graph effective resistance.

Empirical evaluations on node-classification benchmarks reveal that Graph Cascades enhances the performance of various GNN and sparse-GT backbones. The most consistent improvements are noted in heterophilic graphs and those exhibiting moderate to high-degree homophily. Conversely, our theoretical framework identifies specific scenarios where mesoscopic rewiring is unlikely to yield benefits, such as low-degree regular graphs and networks containing structural bottlenecks. These theoretical predictions align closely with observed empirical failures. Furthermore, we document strong correlations between model performance and the structural characteristics of the rewired graphs.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC