Social network data has been modeled with several approaches, including Sociogram and Sociomatrices, which are popular and comprehensive. Similar to these we have developed here a novel modeling technique based on granular computing theory and fuzzy neighborhood systems, which provides a uniform framework to represent social networks. In this model, a social network is represented with a collection of granules. Fuzzy sets are used for defining the granules. The model is named Fuzzy Granular Social Network (FGSN). Familiar measures of networks viz. degree, betweenness, embeddedness and clustering coefficient are redefined in the context of this new framework. Two measures, namely, entropy of FGSN and energy of granules are defined to quantify the uncertainty involved in FGSN arising from fuzziness in the relationships of actors. Experimental results demonstrate the applicability of the model in two well known problems of social networks, namely, target set selection and community detection with comparative studies.