Whether engineering designers aim to be creative or simply to meet the design requirements their design processes often produce creative solutions. We view creativity in engineering design as a title given after the design product is evaluated in the context of its requirements and historical setting. The potential for creative design is increased as more of a solution space can be explored and as new problem formulations are utilized. In this light, we discuss a representation that allows both a reformulation of our design problem and an expanded search space. The graph-based representation, adjacency structures, is presented along with recent work on its use within particular design methods. The representation integrates a geometric model with functional information as a means of expressing a more complete formulation of the design problem. A systematic approach is discussed as a search method increasing the potential for creative design by exploring larger regions of a solution space. In this paper we focus on the use of adjacency structures within the domain of architectural and structural design.