In this paper we investigate a pure form of the topological mapping problem in mobile robotics. We consider the mapping ability of a robot navigating a graph-like world in which it is able to assign a relative ordering to the edges leaving a vertex with reference to the edge by which it arrived, but is unable to associate a unique label with any vertex or edge. Our work extends and builds upon earlier approaches in this problem domain, which are based on constructing an exploration tree of plausible world-models. The main contributions of the paper are: improved exploration strategies that reduce model ambiguity; a new method of searching through consistent models in the exploration tree that maintains a bounded set of likely hypotheses based on the principle of Occam's Razor; the incorporation of arbitrary feature vectors into the problem formulation; and an investigation of various aspects of this problem through numerical simulations.