Structural Invariance Matters: Rethinking Graph Rewiring through Graph Metrics

TL;DR

This paper systematically analyzes how different graph rewiring strategies impact structural properties and task performance in GNNs, emphasizing the importance of preserving local structure for effective rewiring.

Contribution

It provides the first comprehensive study linking structural metric changes due to rewiring with downstream GNN performance, guiding better rewiring strategy design.

Findings

Successful rewiring preserves local structure

Global connectivity can be more flexible

Structural fidelity correlates with accuracy

Abstract

Graph rewiring has emerged as a key technique to alleviate over-squashing in Graph Neural Networks (GNNs) and Graph Transformers by modifying the graph topology to improve information flow. While effective, rewiring inherently alters the graph's structure, raising the risk of distorting important topology-dependent signals. Yet, despite the growing use of rewiring, little is known about which structural properties must be preserved to ensure both performance gains and structural fidelity. In this work, we provide the first systematic analysis of how rewiring affects a range of graph structural metrics, and how these changes relate to downstream task performance. We study seven diverse rewiring strategies and correlate changes in local and global graph properties with node classification accuracy. Our results reveal a consistent pattern: successful rewiring methods tend to preserve local structure while allowing for flexibility in global connectivity. These findings offer new insights into the design of effective rewiring strategies, bridging the gap between graph theory and practical GNN optimization.