Commute Graph Neural Networks

2024-06-30

arXiv.org

AI Summary

Traditional GNNs struggle to model asymmetric path dependencies—such as asymmetric shortest paths—between nodes in directed graphs. To address this, we propose Commute Graph Neural Networks (CGNN), the first method to formulate the *commute time* on directed graphs as a differentiable quantity derived from a novel directed graph Laplacian operator. CGNN explicitly encodes pairwise node reciprocity and asymmetry by integrating commute-time-based dynamic weights into a multi-layer message-passing framework. The architecture supports end-to-end training while preserving theoretical interpretability and computational efficiency. Evaluated on eight standard directed graph benchmarks, CGNN consistently outperforms 13 state-of-the-art methods on both node classification and link prediction tasks, achieving statistically significant average performance gains.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Social Networks and Social Media: Computational social science

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.

Problem

• Challenges in applying GNNs to directed graphs due to asymmetry
• Traditional GNNs fail to capture mutual path dependencies in digraphs
• CGNN integrates commute time to model asymmetric node relationships

Innovation

• Integrates node-wise commute time into message passing
• Uses a newly formulated digraph Laplacian for computation
• Weights neighbor contributions by commute time