Applications of graph theory in architectural analysis: past, present and future research.

In the 1970s architectural scholars adopted graph theory to support several major analytical approaches to interior and urban design. While the basis for graph theory in architecture is identical to that in mathematics, architects developed several discipline-specific methods for mapping nodes and edges to various spatial and formal features, and then set out to interpret these maps through a combination of mathematical analysis and observations of human behaviour, social structures and building types. This chapter undertakes a review of architectural applications of graph theory, spanning from its initial use for solving pedestrian circulation problems, through to more recent applications providing insights into access planning, design psychology and way-finding. Through this critical review, three mapping or abstraction techniques, which are a precursor to graph theory analysis, are described and demonstrated. Finally, the chapter identifies three areas that could be the subject of future applications of graph theory in design.