In this paper we address the question of the relationships between visualization challenges and the representation components that provide solutions to these challenges. Our approach involves extracting such relationships through an identification of the context and the components of a significant number of representations and a comparison of the result to existing theoretical studies. To make such an identification possible, we rely on a characterization of the representation context based on a thoughtful aggregation of existing characterizations of the data type, the tasks and the context of use of the representations. We illustrate our approach on a use-case with examples of a relationships extraction and of a comparison of that relationships to the theory. We believe that the establishment of such relationships makes it possible to understand the mechanisms behind the representations, in order to build a representation design recommendation tool. Such a tool will enable us to recommend the components to use in a representation, given a visualization challenge to address.