Evaluating Group Degree Centrality and Centralization in Networks

Abstract

Given a network G, the importance of groups can be modeled by group centrality measures. Freeman's centralization is a way to normalize any given centrality or group centrality measure, which enables us to compare individuals or groups from different networks. We focus on a degree-based measure of group centrality and centralization, presented by Krnc and Škrekovski (2020). We describe its efficient implementation and study the behaviour of various real-world networks within this context. We conclude that very small groups, as well as very big ones, are not very central, i.e. as the group is growing, its value is increasing but, at some point it starts decreasing. Such unimodular behaviour is confirmed by our analysis of of group degree centralization of six real-world networks. At the end, we provide some challenges for future work.