Nonlinear Laplacians Enhance Signed-Directed Graph Neural Networks

A new nonlinear Laplacian operator, termed NLSD (Nonlinear Laplacian for Signed and Directed networks), has been developed to advance graph neural network (GNN) learning on complex signed-directed graphs. Traditional approaches often rely on linear Laplacians, which may not fully capture the intricate relationships in such networks. The NLSD operator extends the principles of signed and directed Laplacians by calculating node-specific potentials based on features. Crucially, the NLSD facilitates message-passing techniques only across edges where potential discrepancies align with the edge's direction, effectively ignoring misaligned discrepancies. This selective message passing allows for a more nuanced understanding of network dynamics. Utilizing this novel operator, the researchers proposed an efficient spectral GNN framework called NLSD-GNN. Comprehensive evaluations were conducted on tasks such as node classification and link prediction, covering scenarios with signed, directional, or both types of information. The findings consistently demonstrated that the NLSD-GNN framework not only effectively integrates signed and directional data but also achieves superior performance across various datasets.