SigFJProp: Lightweight and Scalable Signed Graph Learning via Opinion Dynamics

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.