The application and development of graph theory through the space syntax method: The implementation of analytical practical model in architecture

Abstract Over the last few decades, different mathematical methods have been used to design and analyze architectural spaces. Meanwhile, the graph theory provides an abstract model to study the spatial configuration, so that a simple and flexible mathematical framework is obtained to analyze the spatial topological features and their relationship with social and functional concepts in architectural and urban spaces. In the eighteenth century, the Euler theorem was the basis of graph theory and later led to the formation of the syntactical model of form, shape grammar and space syntax. The main question of this research is how designers and researchers can choose the appropriate space syntax technique to achieve their goals? The research process uses a qualitative approach and a descriptive-analytical method. Adopting library research and documentary studies, this investigation reviews various theories and experiences regarding the applications of graph theory and space syntax in architecture. Furthermore, the latest achievements in space syntax techniques are expressed. Then, the unique strengths and weaknesses that each technique possesses is identified and analyzed in a deductive manner. The aim is to provide a model for its optimal application in the design and analysis of architectural works by studying the principles of graph theory and extending it to space syntax techniques. This approach helps designers and architects evaluate the effectiveness of proposed designs during the design process or to analyze the spatial structure features of existing buildings and to provide appropriate solutions to different problems in each situation. The findings of the research indicate that convex space, axial line and intersection point techniques provide the basis for examining the relationship between spatial structure and social concepts and functions, hierarchy of access, modeling of motion patterns and the study of spatial index points and isovist technique and graphs of vision consider visual and perceptual capabilities of space. Finally, a model for intelligent application of the space syntax method by designers and architects and to achieve more accurate and useful analytical results is presented.