Two thirds of the people who have been infected by human immunodeficiency virus (HIV) in the world live in Sub-Saharan African countries. The results of a study measuring the degree distribution of the network of sexual contacts in Burkina Faso are described. Such a network is responsible for the spread of sexually transmitted diseases, and in particular of HIV. It has been found that the number of different sexual partners reported by males is a power law distribution with an exponent gamma = 2.9 (0.1). This is consistent with the degree distribution of scale-free networks. On the other hand, the females can be divided into two groups: the prostitutes with an average of 400 different partners per year, and females with a stable partner, having a rapidly decreasing degree distribution. Such a result may have important implications on the control of sexually transmitted diseases and in particular of HIV. Since scale-free networks have no epidemic threshold, a campaign based on prevention and anti-viral treatment of few highly connected nodes can be more successful than any policy based on enlarged but random distribution of the available anti-viral treatments.