RAwR: Role-Aware Rewiring via Approximate Equitable Partition
Authors: Riccardo Porcedda, Giuseppe Squillace, Bastian Epping, Andrea Vandin, Michael Schaub, Mirco Tribastone, Francesca Chiaromonte
Organizations: Department of Excellence L’EMbeDS, Sant’Anna School of Advanced Studies, Pisa, Italy · Department of Computer Science, University of Pisa, Italy · IMT School for Advanced Studies, Lucca, Italy · Computational Network Science, RWTH Aachen University, Aachen, Germany · DTU Technical University of Denmark, Lyngby, Denmark · Department of Statistics, The Pennsylvania State University, USA · Huck Institutes of the Life Sciences, The Pennsylvania State University, USA
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.
The information flow in the graph neural networks (GNNs) is fundamentally constrained by over-squashing, where structural bottlenecks impede long range information propagation. Graph-rewiring methods, which modify graph topology, have been extensively used to alleviate this. However, existing approaches often introduce prohibitive structural and computational bottlenecks, fail to preserve the critical properties of original graphs, and increase the edge counts massively. We introduce a novel method Schreier-Coset Graph Rewiring , a group-theoretic rewiring method that augments the input graph with a Schreier-Coset graph derived from a special linear group. Our method provides theoretical guarantees, a graph that exhibits spectral gap and a bounded effective resistance, creating a low-resistance bypass for long-range communication. Empirical evaluations demonstrate that SCGR reduces effective resistance by 5-40% across various learning tasks, effectively mitigating connectivity bottlenecks while maintaining competitive accuracy.
Graph Neural Networks (GNNs) have emerged as a powerful paradigm for learning on graph-structured data by iteratively propagating and aggregating information across edges. However, conventional message passing schemes often suffer from over-squashing, whereby exponentially large neighborhoods are compressed into fixed-dimensional embeddings, impeding effective long-range dependency learning. In this work, we introduce Ramanujan Propagation, a graph rewiring strategy that leverages Ramanujan graphs to alleviate topological bottlenecks in GNNs. We first establish that suitably chosen Ramanujan graphs guarantee non-negative resistance curvature, which mitigates over-squashing and facilitates efficient information flow. We then propose an algorithmic framework to construct a Ramanujan rewired graph that preserves the local connectivity of the original graph. Our experiments demonstrate that our method outperforms nine state-of-the-art rewiring techniques. These results establish Ramanujan graphs as a rigorous structural prior for scalable, topology-aware message passing in GNNs.
Graph Neural Networks are powerful models for learning from graph-structured data, yet their effectiveness is often limited by two critical challenges: over-squashing, where information from distant nodes is excessively compressed, and over-smoothing, where repeated propagation makes node representations indistinguishable. Both phenomena stem from the interaction between message passing and the input topology, ultimately degrading information flow and limiting the performance of GNNs. In this survey, we examine graph rewiring techniques, a class of methods designed to modify the graph topology to enhance information propagation in GNNs. We provide a comprehensive review of state-of-the-art rewiring approaches, delving into their theoretical underpinnings, practical implementations, and performance trade-offs.
Hugo Attali, Nathalie Pernelle, Davide Buscaldi +1