This work introduces a non-linear Laplacian operator specific to signed and directed networks (NLSD) and proposes an efficient spectral GNN framework (NLSD-GNN), which not only integrates signed and directional data effectively but also achieves superior performance across diverse datasets.
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.
Learning on signed graphs poses unique challenges due to the presence of both positive and negative links, which represent complex social dynamics such as trust and conflict. While existing signed graph neural networks (SGNNs) have achieved promising results, most rely on deep, multi-hop propagation architectures that suffer from scalability issues. In this work, we revisit message passing from the perspective of opinion dynamics, and propose SigFJProp, a novel and lightweight SGNN framework inspired by the Friedkin–Johnsen model. SigFJProp models signed message propagation as a discrete-time opinion update process, whose equilibrium state admits a closed-form solution involving the signed forest matrix. To make this computation tractable on large-scale graphs, we introduce Expansion Forest Sampling, a linear-time approximation method tailored for signed networks. Our approach decouples neural representation learning from propagation dynamics, enabling efficient and interpretable learning. Experimental results on seven benchmark datasets, including one with over 750K nodes and 10M edges, demonstrate that SigFJProp achieves competitive or superior performance compared to state-of-the-art methods, while significantly reducing computational overhead. The code is available at https://github.com/SunYubo23/SigFJProp.
Yubo Sun, Haoxin Sun, Zhongzhi Zhang· Proceedings of the 32nd ACM...· 0 citations
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