Modeling centrality measures in social network analysis using bi-criteria network flow optimization problems

Centrality measures play an important role in the field of network analysis. In the particular case of social networks, the flow represents the way in which information passes through the network nodes. Freeman et al. (1991) were the first authors to relate centrality measures to network flow optimization problems in terms of betweenness, closeness, and the influence of one node over another one. Such measures are single dimensional and, in general, they amalgamate several heterogeneous dimensions into a single one, which is not suitable for dealing with most real-world problems. In this paper we extend the betweenness centrality measure (or concept) to take into account explicitly several dimensions (criteria). A new closeness centrality measure is defined to deal not only with the maximum flow between every ordered pair of nodes, but also with the cost associated with communications. We shall show how the classical measures can be enhanced when the problem is modeled as a bi-criteria network flow optimization problem.