Shaping ideal cities: The graph representation of the urban utopia

The ideal Renaissance city is designed as a star-shaped fortress, where the streets and squares are organized to speed the movement of people and soldiers. Symmetry and accessibility represent the key features for the organization of the urban space. The resulting city is hierarchized and does not always guarantee an optimal degree of connectivity. Starting from the space syntax definition, we suggest a method to compute urban graphs from the Euclidean representation, the corresponding line graph and the contraction of nodes with the same urban function. We analyze the urban graphs of five historic cities and compare the analysis with the corresponding results from space syntax. Analysis of the spectral gap and the relative asymmetry distribution show a similar structure for these cities. The irregular or reticular housing structure seems to ensure connectivity and accessibility more than the regular grids. However, connectivity is ensured by the most peripheral streets, which in the space syntax representation play a marginal role.