A novel gravity model for influential node identification in complex networks based on multiple paths and personalized influence radius

Identifying influential nodes is a central problem in complex networks. Many methods have been proposed, among which the gravity model is an effective one. Many gravity models assume that the interaction between nodes only happens on the shortest path, or the influence radius of all nodes is identical and determined by the diameter of networks. However, empirical analysis shows that there are numerous paths except for the shortest path, especially as the path length is large. Although the shortest path is effective, other paths also provide complementary communications for nodes, and therefore multiple paths should be included. Moreover, the path analysis shows a different maximum shortest path length for nodes, suggesting a heterogeneous nodes’ influence range. Henceforth, in this paper, we propose an improved gravity model by considering an interaction distance of multiple paths with a path-length constraint and a personalized influence radius. A comprehensive information of the local, position and global information is also considered in the node mass. Experiments are conducted on nine real-world networks and three artificial networks. By comparing the proposed method with seven high-performance algorithms, we demonstrate the advantage of the proposed method.