Betweenness Centrality for Networks with Non-Overlapping Community Structure

Evaluating the centrality of nodes in complex networks is one of the major research topics being explored due to its wide range of applications. Among the various measures that have been developed over the years, Betweenness centrality is one of the most popular. Indeed, it has proved to be efficient in many real-world situations. In this paper, we propose an extension of the Betweenness centrality designed for networks with non-overlapping community structure. It is a linear combination of the so-called ``local'' and ``global'' Betweenness measures. The Local measure takes into account the influence of a node at the community level while the global measure depends only on the interactions between the communities. Depending of the community structure strength, more or less importance is given to each of these two elements. By using the Susceptible-Infected-Recovered (SIR) model in epidemic spreading simulations, we show that the ``Weighted Community Betweenness'' centrality is more efficient than the traditional Betweenness which is agnostic of the community structure. The proposed measure stands out also the traditional measure by its low complexity, allowing its use in very large scale networks.