CSBA-Net: Learning Cross-Scale Structural Dependencies for Influential Node Identification in Complex Networks

Identifying influential nodes is a fundamental task in complex network analysis, with applications in epidemic control, information diffusion, and network robustness. Existing centrality-based and learning-based methods often provide limited integration of structural information across different network scales. To address this limitation, we propose CSBA-Net, for Cross-Scale Structural BiGRU Attention Network, a multi-scale structural representation learning framework that jointly captures local, community-level, and global structural patterns. The extracted representations are processed by CNNs and integrated through a BiGRU with multi-head self-attention to model dependencies across structural scales. Influential-node scores are learned through regression using SIR-based diffusion simulations as reference targets. We conduct experiments on 24 real-world and 12 synthetic networks from social, biological, technological, and knowledge domains, and show that CSBA-Net achieves Kendall's tau=0.802, Spearman's rho=0.943, NDCG10 =0.898, and NDCG20 =0.916, outperforming the considered centrality-, CNN-, and GNN-based baselines. The results demonstrate the effectiveness of combining complementary structural scales for accurate influential-node ranking across diverse network structures.