Fast algorithm for successive computation of group betweenness centrality

In this paper, we propose a method for rapid computation of group betweenness centrality whose running time (after preprocessing) does not depend on network size. The calculation of group betweenness centrality is computationally demanding and, therefore, it is not suitable for applications that compute the centrality of many groups in order to identify new properties. Our method is based on the concept of path betweenness centrality defined in this paper. We demonstrate how the method can be used to find the most prominent group. Then, we apply the method for epidemic control in communication networks. We also show how the method can be used to evaluate distributions of group betweenness centrality and its correlation with group degree. The method may assist in finding further properties of complex networks and may open a wide range of research opportunities.