Towards a hierarchical approach and scalable semi-local centrality for key node identification in weighted complex networks.

The analysis of complex networks is crucial for understanding the structural and functional dynamics of real-world systems. Identifying key nodes in weighted complex networks represents a fundamental challenge in network science, as such nodes often play pivotal roles in information diffusion, resilience, and control processes. Traditional centrality metrics, which primarily rely on single-feature criteria, frequently suffer from limitations in scalability and sensitivity to network topology. These methods often overlook dynamic factors, unequal neighbor influence, and evolving structural risks, thereby reducing their ability to effectively distinguish key nodes in large, weighted, and heterogeneous systems. To address these limitations, this study proposes a Hierarchical and Scalable Semi-Local Centrality (HSSLC) framework designed to efficiently capture both local and semi-local structural influences in complex networks. We convert unweighted networks into weighted networks using their degree. HSSLC integrates multi-level entropy-based neighborhood information to balance local connectivity strength with the global propagation of influence. The proposed metric constructs weighted local subgraphs through multi-step connectivity to enhance computational efficiency when dealing with large-scale networks. Furthermore, a hierarchical key node identification algorithm is introduced, incorporating diverse node attributes across the entire network. Entropy-based evaluation that accounts for neighboring node contributions yields more reliable local influence assessment than degree-based indices. Experimental validation using real-world networks under the susceptible–infected–removed (SIR) diffusion model demonstrates that the proposed metric achieves up to a 2.8% improvement in Kendall’s rank correlation, while exhibiting superior scalability and computational efficiency compared to existing centrality metrics.