Abstract: This report attempts to provide a descriptive analysis of online social media networks of Facebook, Twitter and LinkedIn based on graph theory concepts. The first part of the study focuses on identifying various activities of the above networks and constructing a suitable graph model for each social media to represent respective activities. The next part of this study addresses the evaluation of the constructed models of each social media separately in order to identify the applicability of them to analyze behavioral patterns and characteristics of the users. Final part of this study focuses on proposing a method to provide relevant information on online social networks to outsiders, which will be helpful for competent decision making without violating the user privacy.