Correlation of Eigenvector Centrality to Other Centrality Measures: Random, Small-world and Real-world Networks

In this paper, we thoroughly investigate correlations of eigenvector centrality to five centrality measures, including degree centrality, betweenness centrality, clustering coefficient centrality, closeness centrality, and farness centrality, of various types of network (random network, smallworld network, and real-world network). For each network, we compute those six centrality measures, from which the correlation coefficient is determined. Our analysis suggests that the degree centrality and the eigenvector centrality are highly correlated, regardless of the type of network. Furthermore, the eigenvector centrality also highly correlates to betweenness on random and real-world networks. However, it is inconsistent on small-world network, probably owing to its power-law distribution. Finally, it is also revealed that eigenvector centrality is distinct from clustering coefficient centrality, closeness centrality and farness centrality in all tested occasions. The findings in this paper could lead us to further correlation analysis on multiple centrality measures in the near future.