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In recent decades, a number of centrality metrics describing networkproperties of nodes have been proposed to rank the importance of nodes. Inorder to understand the correlations between centrality metrics and toapproximate a high-complexity centrality metric by a strongly correlatedlow-complexity metric, we first study the correlation between centralitymetrics in terms of their Pearson correlation coefficient and their similarityin ranking of nodes. In addition to considering the widely used centralitymetrics, we introduce a new centrality measure, the degree mass. The m orderdegree mass of a node is the sum of the weighted degree of the node and itsneighbors no further than m hops away. We find that the B_{n}, the closeness,and the components of x_{1} are strongly correlated with the degree, the1st-order degree mass and the 2nd-order degree mass, respectively, in bothnetwork models and real-world networks. We then theoretically prove that thePearson correlation coefficient between x_{1} and the 2nd-order degree mass islarger than that between x_{1} and a lower order degree mass. Finally, weinvestigate the effect of the inflexible antagonists selected based ondifferent centrality metrics in helping one opinion to compete with another inthe inflexible antagonists opinion model. Interestingly, we find that selectingthe inflexible antagonists based on the leverage, the B_{n}, or the degree ismore effective in opinion-competition than using other centrality metrics inall types of networks. This observation is supported by our previousobservations, i.e., that there is a strong linear correlation between thedegree and the B_{n}, as well as a high centrality similarity between theleverage and the degree.

Correlation between centrality metrics and their application to the opinion model