Weighted Signed Directed Graph Convolutional Network Based on Magnetic Signed Laplacian Matrix

Weighted signed directed graphs have attracted widespread attention for their ability to model interactions in complex systems via signed, directed and weighted edges. Applying Laplacian-based spectral graph convolution methods to such graphs is of great value, as these methods are both concise and interpretable. However, such applications face three major challenges: the Laplacian matrix tends to lose positive semi-definiteness, spectral decomposability and eigenvalue bounded‐ness, thus limiting its scope of application; model performance is sensitive to the number of edges and weight distribution of datasets, leading to poor stability; and the computational cost is high with limited efficiency. To address these issues, this paper proposes a novel magnetic signed Laplacian matrix and designs a Weighted Signed Directed Graph Convolutional Network (WSDGCN) based on this matrix. Theoretical derivation demonstrates that this matrix preserves the core superior properties of the Laplacian matrix when adapted to weighted signed directed graphs. While achieving differentiated topological characterization, it exhibits favorable robustness to edge weights. Experiments on node classification and link prediction tasks conducted on both synthetic and real-world datasets verify that the proposed method achieves superior performance compared with other competing methods.