This paper presents a novel method for qualitative mapping of large scale spaces. The proposed framework makes use of a graphical representation of the world in order to build a map consisting of qualitative constraints on the geometric relationships between landmark triplets. A novel measurement method based on camera imagery is presented which extends previous work from the field of Qualitative Spatial Reasoning. Measurements are fused into the map using a deterministic, iterative graph update. A Branch-and-Bound approach is taken to solve a set of non-convex feasibility problems required for generating on-line measurements and off-line operator lookup tables. A navigation approach for travel between distant landmarks is developed, using estimates of the Relative Neighborhood Graph extracted from the qualitative map in order to generate a sequence of landmark objectives based on proximity. Average and asymptotic performance of the mapping algorithm is evaluated using Monte Carlo tests on randomly generated maps, and data-driven simulation results are presented for a robot traversing the Jet Propulsion Laboratory Mars Yard while building a relational map. Simulation results demonstrate an initial rapid convergence of qualitative state estimates for visible landmarks, followed by a slow tapering as the remaining ambiguous states are removed from the map.