Description-based approaches towards reasoning about and processing natural language stress the distinction between linguistic structures themselves (such as parse trees, lambda terms, or discourse structures), and languages to talk about these structures.  In this presentation, I will use hybrid logic to talk about a bunch of linguistic structures that can be modelled as graphs.  I will show how three rather different tasks in Natural Language Processing (assembling underspecified semantic descriptions, surface realisation in NLG, and dependency parsing) can be cast as configuration problems on graphs, and why this perspective is interesting.  In the second half of my talk, I will discuss three open questions that I have chosen as the starting points for my next phase of research on graph configuration problems.