Vital nodes identification method integrating degree centrality and cycle ratio

Identifying vital nodes is one of the core issues of network science, and is crucial for epidemic prevention and control, network security maintenance, and biomedical research and development. In this paper, a new vital nodes identification method, named degree and cycle ratio (DC), is proposed by integrating degree centrality (weight α) and cycle ratio (weight 1 − α). The results show that the dynamic observations and weight α are nonlinear and non-monotonicity (i.e., there exists an optimal value α* for α), and that DC performs better than a single index in most networks. According to the value of α*, networks are classified into degree-dominant networks (α* > 0.5) and cycle-dominant networks (α* < 0.5). Specifically, in most degree-dominant networks (such as Chengdu-BUS, Chongqing-BUS and Beijing-BUS), degree is dominant in the identification of vital nodes, but the identification effect can be improved by adding cycle structure information to the nodes. In most cycle-dominant networks (such as Email, Wiki and Hamsterster), the cycle ratio is dominant in the identification of vital nodes, but the effect can be notably enhanced by additional node degree information. Finally, interestingly, in Lancichinetti–Fortunato–Radicchi (LFR) synthesis networks, the cycle-dominant network is observed.