The “Program of Food Access” (PFA) is one of most important policies implemented in Brasil at the framework of “Fome Zero” program. The two goals of this PFA are, on the one hand, to support family farmers’ incomes (state institutions sell food production provided by them) and, on the other hand, to fight against the hanger and malnutrition of people (state insitutions distribute those foods to the poorest population). The success of the PFA depends on the existence of a good governance between the different players participating in the implementation of the Program (family farmers and consumers, and public agencies). In this article, their authors analyse how the PFA is implemented in Boa Vista (a municipality placed in the North-western state of Roraima), and they pay a special attention on the effects of the Program in the land reform settlement called “Nova Amazonia” (composed of family farmers). Based on both the theoretical approach of social capital and the methodological tool of social networks, they analyse the kind of social relationships existing within the “Nova Amazonia” settlement, as well as the institutional network developping between family farmers and state agencies in order to implement the PFA. The data show that the PFA is implemented on the base of a strong institutional network of state agencies, but a weak social network. They debate about the sustainability of social policies such as the PFA in contexts where the level of social cohession is slow and where the logic of implementation of the Program is more top-down than bottom-up.