This paper shows how the Rao-Stirling diversity index may be extensively used for positioning and comparing institutions interdisciplinary practices. Two decompositions of this index make it possible to explore different components of the diversity of the cited references in a corpus of publications. The paper aims at demonstrating how these bibliometric tools can be used for comparing institutions in a research field by highlighting collaboration orientations and institutions strategies. To make the method available and easy to use for indicator users, this paper first recalls a previous result on the decomposition of the Rao-Stirling index into multidisciplinarity and interdisciplinarity components, then proposes a new decomposition to further explore the profile of research collaborations and finally presents an application to Neuroscience research in French universities.