Ranking the spreading influence of nodes in complex networks: An extended weighted degree centrality based on a remaining minimum degree decomposition

Ranking the spreading influence of nodes is crucial for developing strategies to control the spreading process on complex networks. In this letter, we define, for the first time, a remaining minimum degree (RMD) decomposition by removing the node(s) with the minimum degree iteratively. Based on the RMD decomposition, a weighted degree (WD) is presented by utilizing the RMD indices of the nearest neighbors of a node. WD assigns a weight to each degree of this node, which can distinguish the contribution of each degree to the spreading influence. Further, an extended weighted degree (EWD) centrality is proposed by extending the WD of the nearest neighbors of a node. Assuming that the spreading process on networks follows the Susceptible-Infectious-Recovered (SIR) model, we perform extensive experiments on a series of synthetic and real networks to comprehensively evaluate the performance of EWD and other eleven representative measures. The experimental results show that EWD is a relatively efficient measure in running efficiency, it exposes an advantage in accuracy in the networks with a relatively small degree heterogeneity, as well as exposes a competitive performance in resolution.