Social networks are becoming an integral part of the modern society. Popular social network applications like Facebook, Twitter produces data in huge scale. These data shows all the characteristic of Big data. Accordingly, it leads to a deep change in the way social networks were being analyzed. The chapter describes a model of social network and its applications within the purview of information diffusion and community structure in network analysis.Here fuzzy granulation theory is used to model uncertainties in social networks. This provides a new knowledge representation scheme of relational data by taking care of the indiscernibility among the actors as well as the fuzziness in their relations. Various measures of network are defined on this new model. Within the context of this knowledge framework of social network, algorithms for target set selection and community detection are developed. Here the target sets are determined using the newmeasure granular degree, whereas it is granular embeddedness, together with granular degree, which is used for detecting various overlapping communities. The resulting community structures have a fuzzy-rough set theoretic description which allows a node to be a member of multiple communities with different memberships of association only if it falls in the (rough upper - rough lower) approximate region. A new index, called normalized fuzzy mutual information is introduced which can be used to quantify the similarity between two fuzzy partition matrices, and hence the quality of the communities detected. Comparative studies demonstrating the superiority of the model over graph theoretic model is shown through extensive experimental results. © Springer International Publishing AG 2017. All rights reserved.