Exploiting total unimodularity for classes of random network problems

Abstract

Network analysis is of great interest for the study of social , biological and technolog- ical networks, with applications, among others, in busines s, marketing, epidemiology and telecommunications. Researchers are often interested in a ssessing whether an observed fea- ture in some particular network is expected to be found withi n families of networks under some hypothesis (named conditional random networks, i.e., networks satisfying some linear constraints). This work presents procedures to generate ne tworks with specified structural properties which rely on the solution of classes of integer o ptimization problems. We show that, for many of them, the constraints matrices are totally unimodular, allowing the efficient generation of conditional random networks by polynomial ti me interior-point methods. The computational results suggest that the proposed methods ca n represent a general framework for the efficient generation of random networks even beyond the models analyzed in this pa- per. This work also opens the possibility for other applicat ions of mathematical programming in the analysis of complex networks.