Correlations among centrality measures in complex networks

TL;DR

This paper empirically analyzes correlations among four centrality measures in complex networks, revealing a strong correlation between degree and betweenness, with betweenness following a power-law distribution independent of network type.

Contribution

It uncovers the power-law distribution of betweenness centrality and its relation to degree, providing insights into the structure of complex networks.

Findings

Degree and betweenness are highly correlated.

Betweenness follows a power-law distribution across networks.

Random networks do not exhibit these characteristics.

Abstract

In this paper, we empirically investigate correlations among four centrality measures, originated from the social science, of various complex networks. For each network, we compute the centrality measures, from which the partial correlation as well as the correlation coefficient among measures is estimated. We uncover that the degree and the betweenness centrality are highly correlated; furthermore, the betweenness follows a power-law distribution irrespective of the type of networks. This characteristic is further examined in terms of the conditional probability distribution of the betweenness, given the degree. The conditional distribution also exhibits a power-law behavior independent of the degree which explains partially, if not whole, the origin of the power-law distribution of the betweenness. A similar analysis on the random network reveals that these characteristics are not found in the random network.