Collective Betweenness Centrality in Networks

Abstract

The shortest path betweenness value of a node quantifies the amount of information passing through the node when all the pairs of nodes in the network exchange information in full capacity measured by the number of the shortest paths between the pairs assuming that the information travels in the shortest paths. It is calculated as the cumulative of the fractions of the number of shortest paths between the node pairs over how many of them actually pass through the node of interest. It's possible for a node to have zero or underrated betweenness value while sitting just next to the giant flow of information. These nodes may have a significant influence on the network when the normal flow of information is disrupted. We propose a betweenness centrality measure called collective betweenness that takes into account the surroundings of a node. We will compare our measure with other centrality metrics and show some applications of it.