MagNet: A Neural Network for Directed Graphs

TL;DR

MagNet introduces a spectral graph neural network for directed graphs using a complex Hermitian matrix called the magnetic Laplacian, effectively capturing directionality and outperforming existing methods on classification and link prediction tasks.

Contribution

It presents MagNet, a novel spectral GNN for directed graphs leveraging the magnetic Laplacian, which encodes directionality and improves performance over prior models.

Findings

MagNet outperforms existing methods on most directed graph tasks.

The magnetic Laplacian effectively encodes directional information.

MagNet can be adapted to other spectral GNN architectures.

Abstract

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.