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arXiv · 2610.04657

Path Laplacian Encodings for Directed Graphs

Lydia Mezrag·Semih Cantürk·Michael Perlmutter·Bastian Rieck·Guy Wolf
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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.

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Lydia Mezrag, Semih Cantürk, Michael Perlmutter, Bastian Rieck, Guy Wolf. 2026-10-03. Path Laplacian Encodings for Directed Graphs. https://arxiv.org/abs/2610.04657

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