MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplacian
This work addresses the lack of spectral GNNs for signed and directed networks, which are common in real-world applications like finance, but it is incremental as it builds on existing Laplacian generalizations.
The authors tackled the problem of modeling signed and directed networks by proposing MSGNN, a spectral graph neural network based on a novel magnetic signed Laplacian, which achieved leading performance on node clustering and link prediction tasks across various datasets.
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.