Modeling Dynamic Network with Centrality-based Logistic Regression

Abstract

Statistical analysis of network data is an active field of study, in which researchers inves- tigate graph-theoretic concepts and various probability models that explain the behaviour of real networks. This thesis attempts to combine two of these concepts: an exponential random graph and a centrality index. Exponential random graphs comprise the most useful class of probability models for network data. These models often require the assumption of a complex dependence structure, which creates certain difficulties in the estimation of unknown model parameters. However, in the context of dynamic networks the exponential random graph model provides the opportunity to incorporate a complex network structure such as centrality without the usual drawbacks associated with parameter estimation. The thesis employs this idea by proposing probability models that are equivalent to the logistic regression models and that can be used to explain behaviour of both static and dynamic networks.