This paper explores some of the dimensions related to poverty and exclusion, by defining a Relational Capability Index (RCI) which focuses on the quality of relationships among people and on their level of relational empowerment. This index is rooted in a relational anthropology; it insists on the quality of the social fabric and of interpersonal relations as a key aspect of human development. As a multidimensional index, the RCI includes integration into networks, private relations and civic commitments. We provide an axiomatization of a family of multidimensional indexes. This axiomatic viewpoint fills the gap between theories of justice and poverty measurements. By means of illustration, we apply three different versions of the RCI, which are elements of this family, to the measurement of the impact of oil companies on local communities in the Niger Delta (Nigeria) and to national surveys (Afrobarometer).