This document discusses using a graph-based approach to analyze topological relationships in geospatial data. It involves constructing graphs of adjacencies and containments between polygons identified in a triangulated irregular network (TIN) of LiDAR points. Depth-first and breadth-first searches are used to analyze the graph of adjacencies. Further work includes constructing a graph of "touchings" between polygons and using the topological analysis to support applications like land-use mapping and image understanding.