Identifying the influential nodes via eigen-centrality from the differences and similarities of structure

One of the most important problems in complex network is the identification of the influential nodes. For this purpose, the use of differences and similarities of structure to enrich the centrality method in complex networks is proposed. The centrality method called ECDS centrality used is the eigen-centrality which is based on the Jaccard similarities between the two random nodes. This can be described by an eigenvalues problem. Here, we use a tunable parameter α to adjust the influence of the differences and similarities. Comparing with the results of the Susceptible Infected Recovered (SIR) model for four real networks, the ECDS centrality could identify influential nodes more accurately than the tradition centralities such as the k-shell, degree and closeness centralities. Especially, in the Erdös network, the Kendall's tau could be reached to 0.93 when the spreading rate is 0.12. In the US airline network, the Kendall's tau could be reached to 0.95 when the spreading rate is 0.06.