The research investigates the application of some mathematical tools for the analysis and design of architectural paths and spaces. The aim is not to attribute the phenomenon of architectural space configuration to automatic mechanisms but rather to verify the effectiveness of systematic analysis to establish relationships between paths and built environments, particularly in the context of exhibition spaces. For this purpose, the concept of the graph is introduced, within its historical context, linked to its formulation for defining cyclical paths without repetition. Additionally, its role in Space Syntax studies is explored, where it serves as a tool for analysing spatial connections. The formulation of cyclical paths without repetition, and in its dimension, was developed in the Space Syntax studies to indicate spatial connections. A qualitative approach has also been explored. A development in the qualitative field has also been experimented with regard to the characteristics influencing orientation linked to simplifying the distributive graphs of the environments, which can also lead to the evaluation of alternative spatial geometries. This approach enables the assessment of alternative spatial geometries.