Nonlinear Laplacians Improve Signed-Directed Graph Learning

2026-08-01

AI Summary

Existing graph neural networks (GNNs) for signed directed graphs rely on linear Laplacian operators, which struggle to effectively integrate sign and directional information. This work proposes the first nonlinear Laplacian operator for signed directed graphs (NLSD), which enables direction-aware message passing by aligning edge directions with node potential differences. Building upon this operator, we develop NLSD-GNN, a spectral-domain GNN framework that jointly models the unique characteristics of both signs and directions. The proposed method consistently outperforms current state-of-the-art models in node classification and link prediction tasks, achieving superior performance across multiple benchmark datasets containing signed edges, directional edges, or both.

Abstract

While signed-directed graphs have been studied using linear Laplacians in the design of graph neural networks, relatively little research has focused on developing non-linear Laplacian operators for such networks. We introduce a non-linear Laplacian operator specific to signed and directed networks (NLSD). This non-linear operator extends the concepts of the signed Laplacian for signed graphs and the Laplacian for directed graphs. The NLSD calculates node-specific potentials based on features More precisely, if the potential discrepancy is not aligned with the edge direction, we ignore it (and vice versa) leveraging message-passing techniques only across edges where potential discrepancies align with the edge's direction. Utilizing this novel operator, we propose an efficient spectral GNN framework (NLSD-GNN). We conducted comprehensive evaluations focusing on node classification and link prediction, examining scenarios involving signed, directional, or both types of information. Our findings reveal that this spectral GNN framework not only integrates signed and directional data effectively but also achieves superior performance across diverse datasets.

Problem

• signed-directed graphs
• nonlinear Laplacian
• graph neural networks
• spectral GNN

Innovation

• non-linear Laplacian
• signed-directed graph
• spectral GNN
• message passing
• graph neural networks