Graph Cascades: Contagion-Based Mesoscopic Rewiring for Structure-Aware Graph Machine Learning
For graph machine learning practitioners, this provides a fast, theoretically grounded method to improve GNN/GT performance by capturing intermediate-scale structure, with clear failure cases identified.
Graph Cascades introduces a mesoscopic rewiring strategy for GNNs and GTs that uses contagion-based diffusion to promote multi-hop reinforced edges, improving node classification accuracy, especially on heterophilic and moderate- to high-degree homophilic graphs, with theoretical guarantees on when reinforcement helps.
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.