Mathematical modeling and analysis of social networks

With the rapid development of internet technologies, social networks have also become widespread, and their usage rate has increased. For this reason, many studies have been started on the analysis of social networks. In these studies, text-based analyzes were generally made, and graph structures were used to model the network structure. Since graphs are static structures, they are insufficient to model the dynamic behavior of social networks. Within the scope of this thesis study, Petri nets, a dynamic structure, were used to model user behaviors in the social network. Petri nets are a graphical and mathematical modeling tool and are used to model dynamic structures. For this reason, the use of Petri nets has been proposed, and a new model called Marked Social Networks is presented. Also, this model is divided into two different groups, Concurrent Marked Social Networks, and Parallel Marked Social Networks. Mathematical analysis was made on the obtained models and the structural and behavioral properties of the models were examined. At the same time, matrix operations and reachability tree methods have been examined to analyze the reachability cases between users on the models. Within the scope of the experimental results, social network groups consisting of different numbers of users were modeled and analyzed and it was revealed that the proposed model could be used to model dynamic behaviors in social networks.