This study was aimed at measuring the degree distribution of the network of sexual contacts in Burkina Faso, in order to gain a better understanding of the sexual risk behaviours for HIV and other sexually transmitted diseases. It was found that the number of different sexual partners reported by males is distributed as a power law, with an exponent γ=2.9 (0.1). This is consistent with the degree distribution of a scale-free network. On the other hand, the females can be divided into two groups: the prostitutes with an average of 400 different partners per year (highly connected nodes), and females with a stable partner, having a rapidly decreasing degree distribution. Such a result may have important implications on the strategies to control sexually transmitted diseases (STD) and in particular HIV. Since scale-free networks exibit no epidemic threshold, a campaign based on the identification of infected individuals and the use of antiviral treatment of few highly connected nodes, associated to effective programs of sexual and sanitary education, can be more successful than any policy based on enlarged but random distribution of the available antiviral or barrier treatments, whose current result in term of sexual transmitted diseases has been a full failure.