Development of a multidimensional centrality metric for ranking nodes in complex networks

Ranking nodes in complex networks is a fundamental task in network science, with significant applications in fields like social networks, bioinformatics, and information dissemination. Many existing methods struggle to efficiently capture the multifaceted relationships between nodes, particularly in large-scale networks. However, they often ignore the semantic relationships between nodes when gathering information. To address these challenges, this paper introduces SAASP, a Semi-local centrality measure that combines an Augmented graph with Average Shortest Path theory to efficiently identify influential nodes in complex networks. In SAASP, the augmented graph can represent global relationships between nodes as semantic similarities, allowing distant relationships to be considered in node ranking. Additionally, it incorporates an enhanced version of average shortest path theory to handle the computational complexity associated with large networks. By extracting local subgraphs for each node and considering the extended neighborhood concept, SAASP ensures scalability while preserving key structural properties. The integration of the augmented graph and average shortest path theory enables SAASP to accurately and efficiently identify influential nodes in large-scale complex networks with lower complexity. The effectiveness of the proposed metric is demonstrated through extensive experiments using the SIR (Susceptible-Infected-Removed) model and Kendall's coefficient, where it outperforms existing centrality measures on real-world datasets.