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.

翻译：图神经网络（GNN）已成为建模关系数据的事实标准工具。然而，尽管许多真实世界的图是有向的，当前大多数GNN模型通过简单地将图视为无向图而完全丢弃了这一信息。造成这一现象的历史原因有二：1）谱域GNN的早期变体明确要求使用无向图；2）早期基于同配图的基准测试并未发现利用方向性带来的显著增益。本文证明，在异配图场景中，将图处理为有向图能提升其有效同配性，表明正确利用方向性信息可能带来增益。为此，我们提出有向图神经网络（Dir-GNN），一种用于有向图深度学习的新型通用框架。Dir-GNN可通过分别聚合入边和出边信息，将任意消息传递神经网络（MPNN）扩展为能利用边方向性信息的模型。我们证明Dir-GNN的表达能力与有向Weisfeiler-Lehman测试相匹配，超越了传统MPNN。大量实验验证，该框架在同配数据集上保持原有性能不变，而在异配基准测试中，其对GCN、GAT和GraphSage等基础模型带来显著增益，超越更复杂的方法并达到新的最优性能水平。