Edge Directionality Improves Learning on Heterophilic Graphs

TL;DR

This paper demonstrates that incorporating edge directionality in Graph Neural Networks significantly improves learning on heterophilic graphs, introducing a new framework that enhances expressivity and achieves state-of-the-art results.

Contribution

The paper introduces Dir-GNN, a general framework for directed graphs that extends message passing neural networks to utilize edge directionality, improving performance on heterophilic graphs.

Findings

Dir-GNN matches the expressivity of the Directed Weisfeiler-Lehman test.

Significant performance gains on heterophilic benchmarks.

Achieves new state-of-the-art results on heterophilic graph datasets.

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.