Towards identifying influential nodes in complex networks using semi-local centrality metrics

The influence of the node refers to the ability of the node to disseminate information. The faster and wider the node spreads, the greater its influence. There are many classical topological metrics that can be used to evaluate the influencing ability of nodes. Degree centrality, betweenness centrality, closeness centrality and local centrality are among the most common metrics for identifying influential nodes in complex networks. Degree centrality is very simple but not very effective. Global metrics such as betweenness centrality and closeness centrality can better identify influential nodes, but they are not compatible on large-scale networks due to their high complexity. In order to design a ranking method of influential nodes, in this paper a new semi-local centrality metric is proposed based on the relative change in the average shortest path of the entire network. Meanwhile, our metric provides a quantitative global importance model to measure the overall influence of each node. To evaluate the performance of the proposed centrality metric, we use the Susceptible-Infected-Recovered (SIR) epidemic model. Experimental results on several real-world networks show that the proposed metric has competitive performance in identifying influential nodes with existing equivalent centrality metrics and has high efficiency in dealing with large-scale networks. The effectiveness of the proposed metric has been proven with numerical examples and Kendall's coefficient.