Commute Graph Neural Networks

Wei Zhuo, Han Yu, Guang Tan, Xiaoxiao Li
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:80612-80628, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-zhuo25a, title = {Commute Graph Neural Networks}, author = {Zhuo, Wei and Yu, Han and Tan, Guang and Li, Xiaoxiao}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {80612--80628}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/zhuo25a/zhuo25a.pdf}, url = {https://proceedings.mlr.press/v267/zhuo25a.html}, 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.} }
Endnote
%0 Conference Paper %T Commute Graph Neural Networks %A Wei Zhuo %A Han Yu %A Guang Tan %A Xiaoxiao Li %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-zhuo25a %I PMLR %P 80612--80628 %U https://proceedings.mlr.press/v267/zhuo25a.html %V 267 %X 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.
APA
Zhuo, W., Yu, H., Tan, G. & Li, X.. (2025). Commute Graph Neural Networks. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:80612-80628 Available from https://proceedings.mlr.press/v267/zhuo25a.html.

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