  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.
