Towards a scalable semi-local centrality for weighted complex networks using information entropy and shortest path analysis

Identifying influential nodes in weighted complex networks remains a significant challenge, particularly due to the trade-off between accuracy and computational scalability. Existing centrality metrics often overlook the heterogeneous influence of neighboring nodes and the structural nuances embedded in multi-hop connectivity and fail to incorporate the varying strength of node relationships. Moreover, previous studies indicate that considering shortest paths can be effectively used to evaluate the influence abilities of nodes. To address these limitations, this study proposes a scalable semi-local centrality metric for weighted complex networks that leverages both shortest paths and information entropy to enhance node ranking precision. The metric constructs distributed weighted semi-local subgraphs by incorporating multi-hop connections and employs the average shortest paths to preserve computational efficiency while capturing essential topological attributes. Additionally, the proposed metric integrates node information entropy derived from node degree, neighborhood degree, and neighborhood overlap to enhance influence estimation. Unlike traditional centrality metrics that often assume uniform neighbor impact, proposed metric differentiates relationship strength through entropy-based combination. Experimental results on real-world networks using the susceptible–infected–recovered (SIR) diffusion model demonstrate that our metric outperforms existing approaches in terms of accuracy, scalability, and adaptability. Quantitatively, proposed metric improves influential node identification by up to 1.8 % over the best-performing existing method based on Kendall's coefficient.