Community detection in online social networks is a difficult but important phenomenon in term of revealing hidden relationships patterns among people so that we can understand human behaviors in term of social-economics perspectives. Community detection algorithms allow us to discover these types of patterns in online social networks. Identifying and detecting communities are not only of particular importance but also have immediate applications. For this reason, researchers have been intensively investigated to implement efficient algorithms to detect community in recent years. In this paper, we introduce set theory to address the community detection problem considering node attributes and network structural patterns. We also formulate probability theory to detect the overlapping community in online social network. Furthermore, we extend our focus on the comparative analysis on some existing community detection methods, which basically consider node attributes and edge contents for detecting community. We conduct comprehensive analysis on our framework so that we justify the performance of our proposed model. The experimental results show the effectiveness of the proposed approach.