Commute Graph Neural Networks

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.

Many GNNs treat directed graphs (digraphs) as collections of one-way edges, so they fail to capture the asymmetric round-trip connectivity that actually determines how strongly two nodes interact. This limitation is evident in social media, where a fan can instantly reach a celebrity, yet the return interaction rarely occurs.We introduce Commute Graph Neural Networks (CGNN) to explicitly model this asymmetry. CGNN leverages a novel digraph Laplacian (DiLap) coupled with lightweight, feature-based graph rewiring. This ensures sparsity and irreducibility, facilitating efficient computation of deterministic commute times, defined as the expected number of steps for a random walk from one node to another and back again. These commute times serve as weights for neighbor messages, allowing mutually reachable nodes to exert greater influence during aggregation.Commute time naturally captures realistic mutual interactions, such as follower-celebrity dynamics in social media or bidirectional web traffic, therefore, CGNN provides a more accurate, interpretable, and broadly applicable framework for learning from directed networks.