  In this paper, we analyze statistical properties of a communication network
constructed from the records of a mobile phone company. The network consists of
2.5 million customers that have placed 810 millions of communications (phone
calls and text messages) over a period of 6 months and for whom we have
geographical home localization information. It is shown that the degree
distribution in this network has a power-law degree distribution $k^{-5}$ and
that the probability that two customers are connected by a link follows a
gravity model, i.e. decreases like $d^{-2}$, where $d$ is the distance between
the customers. We also consider the geographical extension of communication
triangles and we show that communication triangles are not only composed of
geographically adjacent nodes but that they may extend over large distances.
This last property is not captured by the existing models of geographical
networks and in a last section we propose a new model that reproduces the
observed property. Our model, which is based on the migration and on the local
adaptation of agents, is then studied analytically and the resulting
predictions are confirmed by computer simulations.
