In this paper, we address the characterization task and we present a general framework for the characterization of a target set of objects by means of their own properties, but also the properties of objects linked to them. According to the kinds of objects, various links can be considered. For instance, in the case of relational databases, associations are the straightforward links between pairs of tables. We propose \mathfrakCaracteriX\mathfrak{CaracteriX}, a new algorithm for mining characterization rules and we show how it can be used on multi-relational and spatial databases.