Entropy-based semi-local centrality for identifying key nodes in weighted complex networks

In complex networks, identifying key nodes has attracted significant attention from researchers in areas such as information diffusion, network attacks, and epidemic spreading. In recent years, most studies have focused on identifying influential nodes in unweighted and undirected networks. However, many existing methods are not directly applicable to weighted and directed complex networks, as they typically consider only the immediate neighbors of a node without accounting for the interactions and structural information among them. Furthermore, traditional centrality measures for node ranking are often limited to single-feature factors and suffer from issues such as poor scalability, unequal neighbor contributions, and sensitivity to network topology. Incorporating multidimensional factors and edge weights into node importance evaluation can significantly enhance the identification of key nodes in large-scale and heterogeneous networks. To address these limitations, this article introduces a Multidimensional Entropy-based Weighted Semi-Local (MEWSL) centrality for identifying key nodes in weighted complex networks. To better capture semi-local neighbor influence and improve scalability, MEWSL constructs weighted semi-local subgraphs for each node in a distributed manner. It integrates multiple factors—such as the degree of neighboring nodes, the number of shortest paths, and the average shortest path—to quantify node importance within weighted semi-local subgraphs. Information entropy is employed to assign weights to different contributing factors, and MEWSL computes the final node ranking by aggregating these factors through a weighted sum. The proposed metric considers not only the relationship between a node and its neighbors but also the interactions among neighboring nodes by incorporating edge weights. MEWSL is evaluated on real-world networks using the susceptible–infected–removed (SIR) model and Kendall’s correlation, demonstrating more effective node ranking with lower computational complexity than existing methods.