| To date, Physics has nearly covered the whole spectrum of scales. From the size of smallest particles to the diameter of the universe, theories and models are built for objects of all possible orders of magnitude. As a result, social networks, which are built on relationships between people, as an abstract and complicated object at a social scale, interest physicists as well. Although several models have been proposed to study social networks, the experimental results indicate that improvement are needed in order to better describe social networks.;Consequently, this dissertation is guided by two tasks; 1) Building theorems and models on social networks with realistic assumptions, 2) verifying the theorems and models by experiments with published real social network data.;This dissertation starts with reviewing existing models and theorems for social networks. By examining the assumptions and experimental results of these models and theorems, we concluded that the assumptions of existing models are too simple to capture the intrinsic properties of social networks. Consequently, model with better assumptions is needed.;We then introduce the generalized Markov Graph model, which is based on more realistic assumptions, provides more crucial features, as well as more accurate statistical description of social networks. The advantage of this new model is then verified by classification experiments for additional features provided by the model, and information flow experiments for the statistical characteristics. We end up the dissertation by showing a variation of the Generalized Markov model and its impact on Laplacian operators. |
