Correlation among network centrality metrics in complex networks

Abstract

Complex networks represent one of the corner stones and play a central role in several Computer Science domains. Research in these networks represents a multidisciplinary approach due to the requirements to implement the statistical mechanics with graph theory and other techniques. The key property in the complex networks are their centrality measures. Network centrality is having a high impact on the network behaviors, dynamicity, and information spreading can deliver significant information about its organizations. Several metrics are developed to estimate the node centrality in complex networks. Each node centrality measure reflects its topological importance in the network among others. Adjacency matrix is used to derive and perform all the centrality measures based on several mathematical computations. Most of these measures may behave similarly in their statistical analyses. So some of these measures can be considered as redundant due to these and their complexity. This study tries to investigate the correlation between any pair of six selected centrality measures. This approach may advise to use the strongly correlated low-complexity metric as an approximation instead of the high complexity one. To perform this study a correlation analysis study is implemented on 6 estimated centrality measures for three different datasets. The alternate measures are selected according to their correlation coefficients strengths.