V-E Algorithm: A New Vital Vertex Identifying Algorithm Based on Vertex-Edge Interaction

Finding vital vertices is an important issue in complex network analysis, which has wide applications in disease control, information diffusion, etc. This topic has attracted increasing attention from various disciplines. In this paper, we propose a new algorithm called Vertex–Edge algorithm to find vital vertices. This algorithm takes both the incident edges and also its neighbors into consideration when evaluating a vertex’s importance, and the importance of vertices and edges construct a mutually updated iterative framework. We also give convergence conditions for the iterative framework. Besides, we verify the stability, effectiveness, accuracy, and superiority of this new Vertex–Edge algorithm by applying it on lots of networks (unweighted or weighted) and comparing the results with other 10 more existing methods. This new method is expected to have promising applications in the future.