Commute-Time-Optimised Graphs for GNNs

TL;DR

This paper introduces graph rewiring techniques optimized for commute time that incorporate prior knowledge to improve GNN performance on synthetic and real-world datasets.

Contribution

It presents two novel rewiring methods that leverage prior information to enhance commute-time optimization in graphs for GNNs.

Findings

Rewiring improves test performance on synthetic datasets with known priors.

Incorporating prior knowledge enhances the effectiveness of commute-time optimization.

Case study shows practical benefits on a real-world citation graph.

Abstract

We explore graph rewiring methods that optimise commute time. Recent graph rewiring approaches facilitate long-range interactions in sparse graphs, making such rewirings commute-time-optimal on average. However, when an expert prior exists on which node pairs should or should not interact, a superior rewiring would favour short commute times between these privileged node pairs. We construct two synthetic datasets with known priors reflecting realistic settings, and use these to motivate two bespoke rewiring methods that incorporate the known prior. We investigate the regimes where our rewiring improves test performance on the synthetic datasets. Finally, we perform a case study on a real-world citation graph to investigate the practical implications of our work.