Xiaojia He¹ and Natarajan Meghanathan², ¹University of Georgia, USA and ²Jackson State University, USA

In this paper, we measure and analyze the correlation of betweenness centrality (BWC) to five centrality measures, including eigenvector centrality (EVC), degree centrality (DEG), clustering coefficient centrality (CCC), farness centrality (FRC), and closeness centrality (CLC). We simulate the evolution of random networks and small-world networks to test the correlation between BWC and the five measures. Additionally, nine real-world networks are also involved in our present study to further examine the correlation. We find that DEG is highly correlated to BWC on most cases and can serve as alternative to computationallyexpensive BWC. Moreover, EVC, CLC and FRC are also good candidates to replace BWC on random networks. Although it is not a perfect correlation for all the real-world networks, there still exists a relatively good correlation between BWC and other three measures (CLC, FRC and EVC) on some networks. Our findings in this paper can help us understand how BWC correlates to other centrality measures and when to decide a good alternative to BWC.

Betweenness Centrality, Random Networks, Small-World Networks, Real-World Networks, Correlation Coefficient