HIV has been introduced in Cuban in 1986. From the beginning of the epidemics, contact-tracing is used, in the purpose of detecting more HIV-positive individuals and of controlling the spread of the disease. The data generated from this contact-tracing program provide some partial information on the social networks underlying the propagation of HIV. In this talk, we present this big network (5389 nodes, with a giant component of 2386 nodes) together with some possible modelling of the phenomenon.