Betweenness Centrality and Vertex Relative Position in Subnetworks

In this work, we address the problem of assessing the node position related to centrality of the other nodes, for both the whole network as well as an identified attribute-based subnetwork. To this end, a methodology is proposed, consisting in computing a relative betweenness measure rather than measuring the node position by means of the betweenness centrality. Our indicator is the ratio of the betweenness value to a power of the total betweenness measure, referred to the subnetwork. A suitable positive parameter alpha adjusts the intensity of the subgraph betweenness in computing the relative betweenness. Our methodology make it possible the possibility of characterizing the different nodes based on their position not only as regards the entire network, but also considering their subnetworks identified by a relevant attribute. In order to test our measure we provide examples obtained by the simulation of various network structures. In order to show the effectiveness of our methodology, we propose two possible real applications, in two different fields. The algorithm of this method is provided, in order to allow the replication of the computations.