With ever growing competition in telecommunications markets, operators have to increasingly rely on business intelligence to offer the right incentives to their customers. Toward this end, existing approaches have almost solely focussed on the individual behaviour of customers. Call graphs, that is, graphs induced by people calling each other, can allow telecom operators to better understand the interaction behaviour of their customers, and potentially provide major insights for designing effective incentives.In this paper, we use the Call Detail Records of a mobile operator from four geographically disparate regions to construct call graphs, and analyse their structural properties. Our findings provide business insights and help devise strategies for Mobile Telecom operators. Another goal of this paper is to identify the shape of such graphs. In order to do so, we extend the well-known reachability analysis approach with some of our own techniques to reveal the shape of such massive graphs. Based on our analysis, we introduce the Treasure-Hunt model to describe the shape of mobile call graphs. The proposed techniques are general enough for analysing any large graph. Finally, how well the proposed model captures the shape of other mobile call graphs needs to be the subject of future studies.