The prevalence of graph-based data has spurred the rapid development of graph neural networks (GNNs) and related machine learning algorithms. Yet, despite the many data sets naturally modeled as directed graphs, including citation, website, and traffic networks, the vast majority of this research focuses on undirected graphs. In this paper, we propose MagNet, a spectral GNN for directed graphs based on a complex Hermitian matrix known as the magnetic Laplacian. This matrix encodes undirected geometric structure in the magnitude of its entries and directional information in the phase of its entries. A "charge" parameter attunes spectral information to variation among directed cycles. We show that MagNet's performance exceeds other spectral GNNs on directed graph node classification and link prediction tasks for a variety of datasets and exceeds commonly used spatial GNNs on a majority of such. The underlying principles of MagNet are such that it can be adapted to other spectral GNN architectures.

中文翻译：

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MagNet：有向图的磁性神经网络

基于图的数据的普及刺激了图神经网络（GNN）和相关机器学习算法的快速发展。然而，尽管自然地将许多数据集建模为有向图，包括引文，网站和交通网络，但本研究的绝大部分集中于无向图。在本文中，我们提出了MagNet，一种基于有向Hermitian矩阵（称为磁性Laplacian）的有向图的频谱GNN。该矩阵以其条目的大小编码无向的几何结构，并在其条目的相位中编码方向信息。“充电”参数将频谱信息调整为有向循环之间的变化。我们展示了MagNet' 其性能超过了针对各种数据集的有向图节点分类和链接预测任务上的其他频谱GNN，并且超过了大多数此类空间GNN。MagNet的基本原理可以使其适用于其他频谱GNN架构。