Identifying influential nodes in weighted complex networks by considering the importance of shortest paths

Numerous real-world networks, including those in communication, transportation, and social systems, inherently possess weighted structures. While traditional centrality metrics like degree, betweenness, and closeness centrality offer useful insights, they often overlook key aspects such as the contribution of the number and importance of shortest paths across extended neighborhoods, particularly in weighted networks. Moreover, existing methods frequently face scalability challenges and struggle to accurately rank nodes in large-scale networks. To address these gaps, this study proposes Semi-local centrality based on the importance of Shortest Paths in Weighted complex networks (SSPW). SSPW employs a distributed approach to extract semi-local subgraphs, leveraging an extended neighborhood concept that incorporates multi-hop connections. This enables a more comprehensive representation of the network structure and the propagation potential of nodes. By integrating the theory of average shortest paths, SSPW ensures an efficient and precise identification process, even in large-scale networks with significant complexity. Additionally, the metric is extended to unweighted networks, further enhancing its applicability. The effectiveness of SSPW through susceptible–infected–recovered (SIR) information diffusion model has been carried out on real-world datasets. These findings indicate that SSPW outperforms the best available centrality in identifying influential nodes by an average of 4.6% in terms of Kendall’s $$\:\tau\:$$ coefficient.