Attributed graphs can be described using two dimensions: first a structural dimension that contains the social graph, e.g. the actors and the relationships between them, and second a compositional dimension describing the actors, e.g. their profile, their textual publications, the metadata of the videos they share, etc. Each of these dimensions can be used to explain different phenomena occurring on the social network, whether from a connectivity or an thematic perspective. This paper claims that the integration of both dimensions would allow researchers to analyze real social networks from different perspectives. We present here a novel approach to the community detection problem with the integration of the two dimensions composing an attributed graph. We show how to integrate but also how to control the integration of two different partitions, one based on the links, the other one based on the attributes. The resulting partition exhibits interesting properties, such as dense and homogeneous groups of actors, revealing new types of communities to the analyst. Because we use a contingency matrix, and because the analyst may invent new ways of combining rows and columns, we open new perspectives for the exploration of attributed social networks.