Correlation and Regression Analysis for Node Betweenness Centrality

In this paper, we seek to find a computationally light centrality metric that could serve as an alternate for the computationally heavy betweenness centrality (BWC) metric. In this pursuit, in the first half of the paper, we evaluate the correlation coefficient between BWC and the other commonly used centrality metrics such as Degree Centrality (DEG), Closeness Centrality (CLC), Farness Centrality (FRC), Clustering Coefficient Centrality (CCC) and Eigenvector Centrality (EVC). We observe BWC to be highly correlated with DEG for synthetic networks generated based on the Erdos-Renyi model (for random networks) and Watts-Strogatz model (for small-world networks). In the second half of the paper, we conduct a regression analysis for BWC with that of a recently proposed centrality metric called the localized clustering coefficient complement-based degree centrality (LCC'DC) for a suite of 47 real-world networks. The R-Squared metric and Correlation coefficient for the LCC'DC-BWC regression has been observed to be appreciably greater than those observed for the DEG-BWC regression. We also observe the LCC'DC-BWC regression to incur relatively a lower value for the standard error of residuals for a majority of the real-world networks.