In recent decades, a number of centrality metrics describing network properties of nodes have been proposed to rank the importance of nodes. In order to understand the correlations between centrality metrics and to approximate a high-complexity centrality metric by a strongly correlated low-complexity metric, we first study the correlation between centrality metrics in terms of their Pearson correlation coefficient and their similarity in ranking of nodes. In addition to considering the widely used centrality metrics, we introduce a new centrality measure, the degree mass. The mth-order degree mass of a node is the sum of the weighted degree of the node and its neighbors no further than m hops away. We find that the betweenness, the closeness, and the components of the principal eigenvector of the adjacency matrix are strongly correlated with the degree, the 1st-order degree mass and the 2nd-order degree mass, respectively, in both network models and real-world networks. We then theoretically prove that the Pearson correlation coefficient between the principal eigenvector and the 2nd-order degree mass is larger than that between the principal eigenvector and a lower order degree mass. Finally, we investigate the effect of the inflexible contrarians selected based on different centrality metrics in helping one opinion to compete with another in the inflexible contrarian opinion (ICO) model. Interestingly, we find that selecting the inflexible contrarians based on the leverage, the betweenness, or the degree is more effective in opinion-competition than using other centrality metrics in all types of networks. This observation is supported by our previous observations, i.e., that there is a strong linear correlation between the degree and the betweenness, as well as a high centrality similarity between the leverage and the degree.@en

Networks portray a multitude of interactions through which people meet, ideas are spread and infectious diseases propagate within a society ^1-5 . Identifying the most efficient 'spread-ers' in a network is an important step towards optimizing the use of available resources and ensuring the more efficient spread of information. Here we show that, in contrast to common belief, there are plausible circumstances where the best spreaders do not correspond to the most highly connected or the most central people ^6-10 . Instead, we find that the most efficient spreaders are those located within the core of the network as identified by the k-shell decomposition analysis ^11-13 , and that when multiple spreaders are considered simultaneously the distance between them becomes the crucial parameter that determines the extent of the spreading. Furthermore, we show that infections persist in the high-k shells of the network in the case where recovered individuals do not develop immunity. Our analysis should provide a route for an optimal design of efficient dissemination strategies.

@en