Betweenness centrality correlation in social networks

TL;DR

This paper investigates how betweenness centrality correlates among nodes in different types of scale-free social networks, revealing unique patterns especially in assortative networks where influence environments are uniform.

Contribution

It provides a detailed analysis of betweenness centrality correlations in various scale-free networks, highlighting the nontrivial behavior in assortative social networks.

Findings

BC-BC correlation similar to degree-degree in dissortative and neutral networks

In assortative networks, a node's neighbors have similar influence levels regardless of the node's own influence

Mean BC of neighbors is nearly independent of the node's BC in assortative networks

Abstract

Scale-free (SF) networks exhibiting a power-law degree distribution can be grouped into the assortative, dissortative and neutral networks according to the behavior of the degree-degree correlation coefficient. Here we investigate the betweenness centrality (BC) correlation for each type of SF networks. While the BC-BC correlation coefficients behave similarly to the degree-degree correlation coefficients for the dissortative and neutral networks, the BC correlation is nontrivial for the assortative ones found mainly in social networks. The mean BC of neighbors of a vertex with BC $g_i$ is almost independent of $g_i$, implying that each person is surrounded by almost the same influential environments of people no matter how influential the person is.