Correlation Coefficient Analysis of Centrality Metrics for Complex Network Graphs

The high-level contribution of this paper is a correlation coefficient analysis of the well-known centrality metrics (degree centrality, eigenvector centrality, betweenness centrality, closeness centrality, farness centrality and eccentricity) for network analysis studies on real-world network graphs representing diverse domains (ranging from 34 nodes to 332 nodes). We observe the two degree-based centrality metrics (degree and eigenvector centrality) to be highly correlated across all the networks studied. There is predominantly a moderate level of correlation between any two of the shortest paths-based centrality metrics (betweenness, closeness, farness and eccentricity) and such a correlation is consistently observed across all the networks. Though we observe a poor correlation between a degree-based centrality metric and a shortest-path based centrality metric for regular random networks, as the variation in the degree distribution of the vertices increases (i.e., as the network gets increasingly scale-free), the correlation coefficient between the two classes of centrality metrics increases.t