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In this paper, we analyze patterns in the Short Message Service (SMS) behavior of customers in a large telecom service provider network. Toward this, we construct SMS Graphs, which are graphs induced by people exchanging SMSs, from the SMS Call Detail Records of the concerned service provider. These patterns are modeled by a weighted graph G(V, E, W), in which the vertices represent the customers, and the edges and weights characterize the SMS transactions. We analyze properties of this graph, such as the distribution of component sizes, cliques, and vertex degrees. It is our belief that this study should enable the telecom operators to utilize the social behavior of their customers to design better service plans, and generate optimum incentives.