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Signed and directed networks are ubiquitous in real-world applications.However, there has been relatively little work proposing spectral graph neuralnetworks (GNNs) for such networks. Here we introduce a signed directedLaplacian matrix, which we call the magnetic signed Laplacian, as a naturalgeneralization of both the signed Laplacian on signed graphs and the magneticLaplacian on directed graphs. We then use this matrix to construct a novelefficient spectral GNN architecture and conduct extensive experiments on bothnode clustering and link prediction tasks. In these experiments, we considertasks related to signed information, tasks related to directional information,and tasks related to both signed and directional information. We demonstratethat our proposed spectral GNN is effective for incorporating both signed anddirectional information, and attains leading performance on a wide range ofdata sets. Additionally, we provide a novel synthetic network model, which werefer to as the Signed Directed Stochastic Block Model, and a number of novelreal-world data sets based on lead-lag relationships in financial time series.

MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplacian