Commute Graph Neural Networks

Wei Zhuo, Guang Tan

Keywords: Graph Neural Networks, Message Passing, Commute Time, Node Classification

TL;DR: We propose an approach to integrate commute time into graph neural networks to enhance the analysis of directed graphs, effectively addressing the asymmetry and complex path interactions inherent in these structures.

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 confirm the superior performance of CGNN. Source code of CGNN is anonymously available here.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 6734