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.

翻译：图神经网络（GNNs）在图结构数据学习方面已展现出显著的成功。然而，将其应用于有向图时，由于节点关系固有的不对称性，带来了独特的挑战。传统的GNNs擅长捕捉单向关系，但在编码节点间的相互路径依赖性（例如有向图中常见的非对称最短路径）方面存在不足。认识到这一差距，我们引入了通勤图神经网络（CGNN），该方法将节点间的通勤时间无缝集成到消息传递机制中。CGNN的核心是使用新提出的有向图拉普拉斯算子高效计算通勤时间的方法。随后，通勤时间被整合到邻域聚合过程中，每一层中邻居节点的贡献根据其与中心节点的通勤时间进行加权。这使得CGNN能够直接捕捉有向图中相互的、非对称的关系。大量实验证实了CGNN的卓越性能。