Measuring urban forms from inter-building distances: combining MST graphs with a local index of spatial association

A new method is proposed for characterising local urban patterns at the scale of a large urban region. The approach overcomes the difficulties of surface-based representations of built-up morphologies and provides an efficient way to account for the proximity of built and non-built land. The strength of the approach resides in the direct use of the coordinates of each building, a very parsimonious input of external parameters, and a local spatial statistical perspective. The method consists in, first, constructing and clumping the Minimum Spanning Tree (MST) that links each building to its neighbours in order to obtain connected urban and suburban graph subsets, and second, measuring a Local Index of Spatial Association (LISA) on inter-building distances in order to characterise patterns. The method differentiates heterogeneous settlements from statistically significant homogeneous clusters with either long or short connections between buildings. The method is applied to the Southern periphery of Brussels (Belgium)