We study the structure of the social graph of mobile phone users in the country of Mexico, with a focus on demographic attributes of the users (more specifically the users' age). We examine assortativity patterns in the graph, and observe a strong age homophily in the communications preferences. We propose a graph based algorithm for the prediction of the age of mobile phone users. The algorithm exploits the topology of the mobile phone network, together with a subset of known users ages (seeds), to infer the age of remaining users. We provide the details of the methodology, and show experimental results on a network GT with more than 70 million users. By carefully examining the topological relations of the seeds to the rest of the nodes in GT, we find topological metrics which have a direct influence on the performance of the algorithm. In particular we characterize subsets of users for which the accuracy of the algorithm is 62% when predicting between 4 age categories (whereas a pure random guess would yield an accuracy of 25%). We also show that we can use the probabilistic information computed by the algorithm to further increase its inference power to 72% on a significant subset of users.