Abstract
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.
Highlights
Centrality metrics have been compared in various networks, such as sampled networks, biological networks, food webs, and vocabulary networks in literature [4,15,16,17,18]
In this paper we have studied the correlation between widely studied and recently proposed centrality metrics in numerous real-world networks as well as in network models, i.e., as in Erdos-Renyi (ER) random networks and scale-free (SF) networks
We study the correlations between the centrality metrics using the Pearson correlation coefficient and the centrality similarity
Summary
Centrality metrics have been compared in various networks, such as sampled networks, biological networks, food webs, and vocabulary networks in literature [4,15,16,17,18]. To investigate the correlation between any two centrality metrics, we compute their Pearson correlation coefficient and their similarity in ranking nodes in both network models and real-world networks. We choose inflexible contrarians using all the centrality metrics we have considered in both modelled networks and real-world networks. We compare the efficiencies of these centrality metrics in reducing the size of the largest opinion A cluster and find that strongly correlated centrality metrics have approximately the same efficiency in both modelled networks and real-world networks.
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