The paper presents a scalable and generalized approach to social network analysis using fuzzy graph theory. In this, we propose an intelligent sociocentric approach that calculates the degree of potential relationship of a social network of finite size, by proposing a fuzzy graph social network model. It takes into account social entity functional and relational attributes simultaneously. In this, the degree of potential relationship of a social network is computed by using two steps. In the first step, the fuzzy pairwise relationship between all social entities is computed using the proposed fuzzy node activeness index parameter with their online and offline communication relationship parameters. In the second step, all fuzzy pairwise relationships that are calculated in the first step are further employed for the calculation of the degree of potential relationship of a social network using an astute function utilizing both weighted arithmetic and geometric means. Here two weights - betweenness and closeness centrality of an entity are assigned to the social entities. The paper performs the experimental work on a small size WhatsApp social network of undergraduate students in the university. The proposed degree of potential relationship can further be used as a global parameter to compare different social networks by incorporating both the functional as well as the relational attributes of social entities.