MagNet: A Neural Network for Directed Graphs
This addresses a gap in graph neural network research for directed graphs, which is important for domains like social networks and transportation, but it is incremental as it builds on existing spectral GNN architectures.
The paper tackles the problem of applying graph neural networks to directed graphs, which are common in datasets like citation and traffic networks, by proposing MagNet, a spectral GNN based on the magnetic Laplacian, and shows that it performs well on node classification and link prediction tasks, exceeding other methods on most tasks.
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.