RAwR: Role-Aware Rewiring via Approximate Equitable Partition

2026-05-10

AI Summary

Graph neural networks (GNNs) are fundamentally limited in long-range dependency tasks due to structural bottlenecks such as over-squashing. To address this, this work proposes the RAwR framework, which constructs quotient graphs via approximate equitable partitions to rewire input graphs and enhance communication among structurally equivalent nodes. RAwR unifies role-aware rewiring with a master node strategy and introduces the Spectral Role Lift metric to guide the selection of optimal partitions. By integrating Weisfeiler–Leman coloring, spectral analysis, and quotient graph construction, the method enables efficient graph rewiring. Experiments demonstrate that RAwR achieves state-of-the-art performance on homophilic, heterophilic, and synthetic long-range benchmarks, and its theoretical efficacy is further validated through linear GNN teacher–student models.

Abstract

While Graph Neural Networks (GNNs) have demonstrated significant efficacy in node classification tasks, where predictions rely on local neighborhood information, the performance of GNNs often drops when prediction tasks depend on long-range interactions. These limitations are attributed to phenomena such as oversquashing, where structural bottlenecks restrict signal propagation across the network topology. To address this challenge, we introduce RAwR, a computationally efficient rewiring framework that augments the input graph with a quotient graph derived from equitable partitions. This approach facilitates accelerated communication between nodes that share identical structural roles, as identified by the Weisfeiler-Leman graph coloring, and thereby reduces the total effective resistance of the system. Furthermore, by employing an approximate definition of the equitable partition, RAwR enables a controllable reduction of the quotient graph, which, in its most condensed state, recovers the conventional Master Node rewiring technique. Empirical evaluations across a diverse suite of benchmarks -- including homophilic, heterophilic, and synthetic long-range datasets -- demonstrate that RAwR achieves state-of-the-art results. Our contribution is further supported by an analytical investigation using a teacher-student model of linear GNNs, which elucidates the theoretical foundations of role-based rewiring. This analysis leads to the formulation of Spectral Role Lift (SRL), a metric designed to identify the optimal approximate equitable partition for maximizing predictive performance.

Problem

• Graph Neural Networks
• long-range interactions
• oversquashing
• structural bottlenecks
• signal propagation

Innovation

• equitable partition
• graph rewiring
• Weisfeiler-Leman coloring
• oversquashing
• quotient graph