  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 datasets 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 their phase. A "charge" parameter
attunes spectral information to variation among directed cycles. We apply our
network to a variety of directed graph node classification and link prediction
tasks showing that MagNet performs well on all tasks and that its performance
exceeds all other methods on a majority of such tasks. The underlying
principles of MagNet are such that it can be adapted to other spectral GNN
architectures.
