Fig. 2

Exploration of feasible space for correlations between urban morphology and network structure. (Top left) Statistical distribution of crossed-correlations between vectors \(\vec {M}\) of morphological indicators (in numbering order Moran index, mean distance, entropy, hierarchy) and \(\vec {N}\) of network measures (centrality, mean path length, speed, diameter). (Top right) Heatmaps for amplitude of correlations, defined as \(a_{ij}=\max _k{\rho _{ij}^{(k)}}-\min _k{\rho _{ij}^{(k)}}\) and maximal absolute correlation, defined as \(c_{ij}=\max _k\left| \rho _{ij}^{k} \right|\). (Bottom left) Projection of correlation matrices in a principal plan obtained by Principal Component Analysis on matrix population (cumulated variances: PC1 = 38%, PC2 = 68%). Error bars are initially computed as 95% confidence intervals on each matrix element (by standard Fisher asymptotic method), and boundaries of confidence intervals are transformed into the component space. Scale color gives mean absolute correlation on full matrices. Black dots and error bars correspond to the realizations of the null model. (Bottom right) Representation in the principal plan, scale color giving proximity to real data defined as \(1 - \min _r \Vert \vec {M}-\vec {M}_r \Vert\) where \(\vec {M}_r\) is the set of real morphological measures, point size giving mean absolute correlation. The points highlighted in blue correspond to the configurations shown in Fig. 1. Black dots correspond to the realizations of the null model