Fast exact computation of betweenness centrality in social networks

Abstract-Social networks have demonstrated in the last few years to be a powerful and flexible concept useful to represent and analyze data. They borrow some basic concepts from sociology in order to model how people (or data items) establish relationships with each other. The study of these relationships can provide a deeper understanding of many emergent global phenomena. The amount of data available in the form of social networks data is growing by the day, and this poses many computational challenging problems for their analysis. In fact many analysis tools suitable to analyze small to medium sized networks are inefficient for large social networks. In this paper we present a novel approach for the computation of the betweenness centrality, which speeds up considerably Brandes' algorithm, in the context of social networking. Our algorithm exploits the natural sparsity of the data to algebraically (and efficiently) determine the betweenness of those nodes organized as trees embedded in the social network. Moreover, for the residual network, which is often of much smaller size we modify the Brandes' algorithm so that we can remove the nodes already processed and perform the computation of the shortest paths only for the remaining nodes. We tested our algorithm using a set of 18 real sparse large social networks provided by Sistemi Territoriali which is an Italian ICT company specialized in Business Intelligence. Our tests show that our algorithm consistently runs more than an order of magnitude faster than the Brandes' procedure on such sparse networks.