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.

本文提出了 Directed Graph Neural Network (Dir-GNN) 模型，用于在定向图上进行深度学习，将 incoming 和 outgoing edges 进行独立聚合，以利用方向性信息来增强图的同质性。比较了多种模型并在异质性数据集上进行了广泛实验，结果证明 Dir-GNN 可以在异质性图上取得最好的表现。