Identifying vital nodes in complex networks by node comprehensive influence

Vital nodes play a pivotal role in spreading on complex networks. Various node centrality methods can quantify each node's importance to find important nodes. This paper proposed a comprehensive node influence method, which considers both node self-influence factors and total influence received from other nodes. Six real networks are employed to validate the proposed method's effectiveness. Node spreading ability in Susceptible-Infected-Recovered simulation is used as a benchmark of node importance by comparing Kendall's correlation coefficient between node centrality value and spreading ability in Susceptible-Infected-Recovered simulation to evaluate the performance of different centrality methods on finding essential nodes. In the simulation, the proposed method has the highest Kendall's correlation coefficient in all networks, and comprehensive node influence is closer to revealing the relative size of node spreading ability than existing centrality methods. The proposed method's general applicability and ability to find important nodes under different infection probabilities in the Susceptible-Infected- Recovered model are also discussed by comparing it with other centrality methods. The result shows that Kendall's correlation between comprehensive node influence and spreading ability is still advantageous over other centrality methods. Formed by node degree, K-Shell value, and topological distance between nodes, comprehensive node influence is a simple and effective way to identify vital nodes in complex networks.