In this paper we provide an introduction to a set of tools for syntactic analysis based on graph theory, and apply them to the study of some properties of English accusativus cum infinitivo constructions, more commonly known as raising to object or exceptional case marking structures. We focus on puzzling extraction asymmetries between base-generated objects and ‘raised’ objects and on the interaction between raising to object and Right Wrap. We argue that a lexicalised derivational grammar with grammatical functions as primitives delivers empirically adequate analyses.