Applications in molecular biology more and more require geometric data management along with physicochemical data handling. Thus, 3D structures and surfaces of molecules become basic objects in molecular databases. We propose the neighborhood query on graphs such as molecular surfaces as a fundamental query class concerning topological information on patch adjacency. Furthermore, we suggest a patch-based data structure, called the TriEdge structure, first, to efficiently support neighborhood query processing, and second, to save space in comparison to common 2D subdivision data structures such as the quad-edge structure or the doubly-connected edge list. In analogy to the quad-edge structure, the TriEdge structure has an algebraic interface and is implemented via complex pointers. However, we achieve a reduction of the space requirement by a factor of four. Finally, we investigate the time performance of our prototype which is based on an object-oriented database management system.