Identifying influential nodes in social networks: Centripetal centrality and seed exclusion approach

Identifying influential nodes in a network is vital for the study of social network structure and to facilitate the dissemination of requisite information. The challenge we address is that, given a complex network, which nodes are more important? How can a group of disseminators be identified and selected to maximize any given field of influence? A series of centrality measures are proposed from different perspectives based on the topology of nodes. However existing methods suffer from problems that are intrinsic to singular consideration of node topology information, and they neglect the connection relationship between nodes when filtering the spreaders, resulting in imprecise evaluation results and limited spread scale. To solve this issue, this paper proposes a new centrality, inspired by the centripetal force formula. Centripetal centrality combines global, and local, as well as semi-local topological information about the nodes resulting in a more comprehensive evaluation. For the problems related to influence maximization, we propose a heuristic algorithm called seed exclusion (SE) that filters propagators. To demonstrate the performance of the proposed measures, we conducted experiments on both real-world and synthetic networks by comparing distinct metrics, improvements in network efficiency, the propagation of nodes under the SIR model and the average shortest distance between spreaders. The experimental results show that the proposed centripetal centrality is more accurate and effective than similar measures, while comparison with baselines the SE algorithm significantly improves spread speed and infection scale.