Papers › Edge Directionality Improves Learning on Heterophilic Graphs

Edge Directionality Improves Learning on Heterophilic Graphs

17 May 2023arXiv:2305.10498archive 2025-07-28

Emanuele Rossi, Bertrand Charpentier, Francesco Di Giovanni, Fabrizio Frasca, Stephan Günnemann, Michael Bronstein

Graph Neural Networks (GNNs) have become the de-facto standard tool for modeling relational data. However, while many real-world graphs are directed, the majority of today's GNN models discard this information altogether by simply making the graph undirected. The reasons for this are historical: 1) many early variants of spectral GNNs explicitly required undirected graphs, and 2) the first benchmarks on homophilic graphs did not find significant gain from using direction. In this paper, we show that in heterophilic settings, treating the graph as directed increases the effective homophily of the graph, suggesting a potential gain from the correct use of directionality information. To this end, we introduce Directed Graph Neural Network (Dir-GNN), a novel general framework for deep learning on directed graphs. Dir-GNN can be used to extend any Message Passing Neural Network (MPNN) to account for edge directionality information by performing separate aggregations of the incoming and outgoing edges. We prove that Dir-GNN matches the expressivity of the Directed Weisfeiler-Lehman test, exceeding that of conventional MPNNs. In extensive experiments, we validate that while our framework leaves performance unchanged on homophilic datasets, it leads to large gains over base models such as GCN, GAT and GraphSage on heterophilic benchmarks, outperforming much more complex methods and achieving new state-of-the-art results.

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Tasks

Graph Neural NetworkNode ClassificationNode Classification on Non-Homophilic (Heterophilic) Graphs

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Node Classification Chameleon Dir-GNN Accuracy 79.71±1.26 #3 of 61 Archive leaderboard report
Node Classification Squirrel Dir-GNN Accuracy 75.31±1.92 #3 of 59 Archive leaderboard report
Node Classification arXiv-year Dir-GNN Accuracy 64.08±0.26 #3 of 12 Archive leaderboard report
Node Classification on Non-Homophilic (Heterophilic) Graphs Chameleon (48%/32%/20% fixed splits) Dir-GNN 1:1 Accuracy 79.71±1.26 #2 of 29 Archive leaderboard report
Node Classification on Non-Homophilic (Heterophilic) Graphs Squirrel (48%/32%/20% fixed splits) Dir-GNN 1:1 Accuracy 75.31±1.92 #2 of 29 Archive leaderboard report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

Methods

GATGCNGraph Neural NetworkGraphSAGE

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