Commute Graph Neural Networks

TL;DR

Commute Graph Neural Networks (CGNN) enhance directed graph learning by integrating commute time into message passing, effectively capturing asymmetric relationships and outperforming existing methods on multiple benchmarks.

Contribution

We introduce CGNN, a novel GNN variant that incorporates commute time via a new digraph Laplacian, addressing the challenge of modeling asymmetrical relations in digraphs.

Findings

CGNN outperforms 13 state-of-the-art methods on 8 datasets.

Efficient computation of commute time improves message passing.

CGNN effectively captures asymmetric relationships in directed graphs.

Abstract

Graph Neural Networks (GNNs) have shown remarkable success in learning from graph-structured data. However, their application to directed graphs (digraphs) presents unique challenges, primarily due to the inherent asymmetry in node relationships. Traditional GNNs are adept at capturing unidirectional relations but fall short in encoding the mutual path dependencies between nodes, such as asymmetrical shortest paths typically found in digraphs. Recognizing this gap, we introduce Commute Graph Neural Networks (CGNN), an approach that seamlessly integrates node-wise commute time into the message passing scheme. The cornerstone of CGNN is an efficient method for computing commute time using a newly formulated digraph Laplacian. Commute time is then integrated into the neighborhood aggregation process, with neighbor contributions weighted according to their respective commute time to the central node in each layer. It enables CGNN to directly capture the mutual, asymmetric relationships in digraphs. Extensive experiments on 8 benchmarking datasets confirm the superiority of CGNN against 13 state-of-the-art methods.