Edge Directionality Improves Learning on Heterophilic Graphs

Emanuele Rossi, Bertrand Charpentier, Francesco Di Giovanni, Fabrizio Frasca, Stephan Günnemann, Michael M. Bronstein
Proceedings of the Second Learning on Graphs Conference, PMLR 231:25:1-25:27, 2024.

Abstract

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. The code for the paper can be found at https://github.com/emalgorithm/directed-graph-neural-network.

Cite this Paper

BibTeX
@InProceedings{pmlr-v231-rossi24a, title = {Edge Directionality Improves Learning on Heterophilic Graphs}, author = {Rossi, Emanuele and Charpentier, Bertrand and Giovanni, Francesco Di and Frasca, Fabrizio and G{\"u}nnemann, Stephan and Bronstein, Michael M.}, booktitle = {Proceedings of the Second Learning on Graphs Conference}, pages = {25:1--25:27}, year = {2024}, editor = {Villar, Soledad and Chamberlain, Benjamin}, volume = {231}, series = {Proceedings of Machine Learning Research}, month = {27--30 Nov}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v231/rossi24a/rossi24a.pdf}, url = {https://proceedings.mlr.press/v231/rossi24a.html}, abstract = {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. The code for the paper can be found at https://github.com/emalgorithm/directed-graph-neural-network.} }
Endnote
%0 Conference Paper %T Edge Directionality Improves Learning on Heterophilic Graphs %A Emanuele Rossi %A Bertrand Charpentier %A Francesco Di Giovanni %A Fabrizio Frasca %A Stephan Günnemann %A Michael M. Bronstein %B Proceedings of the Second Learning on Graphs Conference %C Proceedings of Machine Learning Research %D 2024 %E Soledad Villar %E Benjamin Chamberlain %F pmlr-v231-rossi24a %I PMLR %P 25:1--25:27 %U https://proceedings.mlr.press/v231/rossi24a.html %V 231 %X 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. The code for the paper can be found at https://github.com/emalgorithm/directed-graph-neural-network.
APA
Rossi, E., Charpentier, B., Giovanni, F.D., Frasca, F., Günnemann, S. & Bronstein, M.M.. (2024). Edge Directionality Improves Learning on Heterophilic Graphs. Proceedings of the Second Learning on Graphs Conference, in Proceedings of Machine Learning Research 231:25:1-25:27 Available from https://proceedings.mlr.press/v231/rossi24a.html.

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