Identifying influential spreaders in complex networks based on gravity formula

•Each node’s k-shell value is considered as its mass and the shortest path distance between two nodes is viewed as their distance.•A new method based on gravity formula is proposed to identify the influential nodes in complex networks.•Our method yields better performance of identifying the influential nodes than many previous methods.•The method can be further generalized.

How to identify the influential spreaders in social networks is crucial for accelerating/hindering information diffusion, increasing product exposure, controlling diseases and rumors, and so on. In this paper, by viewing the k-shell value of each node as its mass and the shortest path distance between two nodes as their distance, then inspired by the idea of the gravity formula, we propose a gravity centrality index to identify the influential spreaders in complex networks. The comparison between the gravity centrality index and some well-known centralities, such as degree centrality, betweenness centrality, closeness centrality, and k-shell centrality, and so forth, indicates that our method can effectively identify the influential spreaders in real networks as well as synthetic networks. We also use the classical Susceptible–Infected–Recovered (SIR) epidemic model to verify the good performance of our method.