Bicriteria shortest path centrality based on information entropy for multidimensional network analysis

Identifying influential nodes in complex networks is a fundamental problem in network analysis, with wide-ranging applications in epidemic control and information diffusion. Shortest path-based centrality metrics play a crucial role in analyzing such networks. Although these metrics provide valuable insights, they are often limited to single-dimensional representations and are not capable of capturing the complexity of real-world networks characterized by multicriteria features. In addition, many existing approaches rely on fixed weighting schemes to represent multidimensional aspects, which do not necessarily reflect the true importance of different features. In this study, we propose the Bicriteria Entropy-based Shortest Path Centrality (BESP-C) to identify influential nodes for the analysis of multidimensional networks. BESP-C integrates multiple shortest path-based features, including the number of shortest paths, and average shortest paths, within a bicriteria framework in which each edge is associated with two distinct attributes. To effectively balance these heterogeneous features, information entropy is employed to adaptively determine their weights, resulting in a more accurate and data-driven evaluation of node importance. Furthermore, BESP-C adopts a semi-local perspective, enabling it to simultaneously capture both local and nonlocal interactions while maintaining computational efficiency. The effectiveness of the proposed metric is evaluated on a set of real-world networks using the susceptible–infected–recovered model and Kendall’s tau correlation coefficient. The results demonstrate that BESP-C outperforms existing advanced centrality metrics in terms of both performance and scalability in identifying influential nodes.