In this paper we are interested in the choice of a graph-based knowledge representation formalism that would allow for the representation, manipulation, query, and reasoning over linguistic knowledge of the Explanatory Combinatorial Dictionary of the Meaning-Text Theory (MTT). We show that neither the semantic web formalisms nor the Conceptual Graphs Formalism are suitable for this task, and we justify the introduction of the new Unit Graphs framework. We then detail the core of this formalism which is a hierarchy of unit types driven by their actantial structure. Finally we define the new deep semantic representation level for the MTT, where the specialization of actantial structures of deep semantic unit types may correspond to a specialization of conveyed meanings.