MagNet: A Neural Network for Directed Graphs.

Journal: Advances in neural information processing systems
Published Date: Dec 1, 2021

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 , a 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 GNN architectures.

Authors

  • Xitong Zhang
    Michigan State University, Department of Computational Mathematics, Science & Engineering, East Lansing, Michigan, United States.
  • Yixuan He
    University of Oxford, Department of Statistics, Oxford, England, United Kingdom.
  • Nathan Brugnone
    Michigan State University, Department of Computational Mathematics, Science & Engineering, East Lansing, Michigan, United States.
  • Michael Perlmutter
    University of California, Los Angeles, Department of Mathematics, Los Angeles, California, United States.
  • Matthew Hirn
    Michigan State University, Department of Computational Mathematics, Science & Engineering, East Lansing, Michigan, United States.

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