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

Machine Learning;Artificial Intelligence;Machine Learning;Social and Information Networks