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This research introduces PathLapPE, a spectral positional encoding designed to better capture directional structures in directed graphs like citation networks and web graphs. By leveraging the path Laplacian, the method offers consistent performance gains over existing symmetrized approaches without requiring additional hyperparameter tuning for directionality. The work advances graph learning architectures by providing node- and edge-level features that more effectively exploit asymmetric interactions inherent in real-world systems.
Path Laplacian Encodings for Directed Graphs
arXiv:2610.04657v1 Announce Type: new Abstract: Directed graphs naturally model many real-world systems in which interactions are asymmetric, such as citation networks, web graphs, and information-flow networks. However, graph learning methods commonly rely on message passing with symmetrized graph representations or positional encodings that only partially exploit edge directionality. We introduce PathLapPE, a novel spectral positional encoding (PE) derived from the path Laplacian on directed graphs. PathLapPE provides node- and edge-level features that encode directional higher-order structure and can be incorporated into standard graph learning architectures. Empirical results on node- and graph-level benchmark tasks show that PathLapPE yields consistent improvements across several architectures, especially when combined with direction-aware message passing. Compared with magnetic Laplacian positional encodings, a widely studied spectral positional encoding for directed graphs, PathLapPE does not require additional fine-tuning of directionality hyperparameters while offering competitive runtime and performance.
Abstract:Directed graphs naturally model many real-world systems in which interactions are asymmetric, such as citation networks, web graphs, and information-flow networks. However, graph learning methods commonly rely on message passing with symmetrized graph representations or positional encodings that only partially exploit edge directionality. We introduce PathLapPE, a novel spectral positional encoding (PE) derived from the path Laplacian on directed graphs. PathLapPE provides node- and edge-level features that encode directional higher-order structure and can be incorporated into standard graph learning architectures. Empirical results on node- and graph-level benchmark tasks show that PathLapPE yields consistent improvements across several architectures, especially when combined with direction-aware message passing. Compared with magnetic Laplacian positional encodings, a widely studied spectral positional encoding for directed graphs, PathLapPE does not require additional fine-tuning of directionality hyperparameters while offering competitive runtime and performance.
Machine Learning (cs.LG)
arXiv:2610.04657 [cs.LG]
(or arXiv:2610.04657v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.04657 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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