A novel method to identify influential nodes in complex networks based on gravity centrality

Identifying influential nodes in complex networks is a significant issue in analyzing the spreading dynamics in networks. Many existing methods focus only on local or global information of nodes but neglect the interaction between nodes. Gravity centrality is a recently raised centrality method that combines a node’s local and global information to properly describe the interaction between nodes. However, node degree is the local information metric in gravity centrality, which omits the connection situation of its neighboring nodes. To overcome the drawbacks of node degree parameters used in gravity centrality, we introduced Laplacian centrality to optimize the initial gravity centrality and put up Laplacian gravity centrality. Regarding real networks from different fields, our method has the highest Kendall’s correlation coefficient to the result of node infection ability simulated by the susceptible-infected-recovered model than other methods in 7 out of 10 real networks. Furthermore, the proposed method's time complexity can be as low as linear time complexity in sparse networks. Results show that Laplacian gravity centrality is an effective method to identify influential nodes, especially in networks with smaller average node degrees and longer average path lengths.