A Sparse Transformer-Enhanced Graph Convolutional Model for Robust Node Importance Ranking in Complex Networks

Identifying and ranking influential nodes in complex networks is critical for broad applications in social, biological, transportation, and other infrastructure systems. Traditional centrality-based and heuristic methods often struggle to balance computational efficiency with accuracy and fail to capture long-range dependencies, limiting their effectiveness in large-scale and heterogeneous networks. To address these limitations, we propose a novel Sparse Transformer-based Graph Convolutional Network (STGCN) for robust and efficient node importance ranking. The STGCN integrates a hybrid architecture that combines Sparse Transformer layers and Graph Convolutional Networks (GCNs) to jointly model local topological features and global structural dependencies. Specifically, the Sparse Transformer layers employ a stochastic anchor mechanism and masked attention to reduce computational complexity while preserving critical long-range interactions. Additionally, a transfer learning strategy is introduced, where the model is pre-trained on synthetic Barabási-Albert networks and then transferred to real-world graphs, enhancing generalization across diverse network topologies. Extensive experiments conducted on 15 real-world datasets demonstrate that STGCN significantly outperforms state-of-the-art methods in ranking consistency, achieving an average Kendall's Tau correlation coefficient of 0.7832, near-perfect monotonicity index scores, and superior top-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> node identification accuracy. The proposed framework provides a scalable and generalizable solution for identifying key nodes in complex networks, enhancing network resilience and optimizing information dissemination.