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

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.

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2606.05046 [cs.LG]

(or arXiv:2606.05046v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.05046 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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