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Social networks refer to structures made of nodes that represent people or other entities embedded in a social context, and whose edges represent interaction between entities. Typical examples of social networks are collaboration networks in a research community, networks arising out of interaction between colleagues of large organization etc. Social networks are highly dynamic objects that evolve quickly over time with addition and deletion of nodes and edges. Understanding the evolution of a social network is helpful in inferring trends and patterns of social contacts in a particular social context. In this paper, we consider social networks that are derived from telephone call records, i.e, graphs in which the individual phone numbers (and hence its users) are the nodes and the edges correspond to a telephonic contact between the two nodes they connect. We study the problem of extracting dense communities from such telecom call graphs. The problem studied here is set in the context of a larger project. We motivate the problem studied by describing the context in which it is set. Our analysis is based on suitable algorithmic engineering of an approximation algorithm for the densest subgraph problem by Charikar. We present empirical results on massive graphs with millions of nodes and edges. We also discuss many open problems that are important in the context of analyzing telecom call graphs.