Robustness and Closeness Centrality for Self-Organized and Planned Cities

Street networks are important infrastructural transportation systems that cover a great part of the planet. It is now widely accepted that transportation properties of street networks are better understood in the interplay between the street network itself and the so called $\mathit{\text{information}}$ or $\mathit{\text{dual}}\mathit{\text{network}}$, which embeds the topology of the street network navigation system. In this work, we present a novel robustness analysis, based on the interaction between the primal and the dual transportation layer for two large metropolis, London and Chicago, thus considering the structural differences to intentional attacks for $\mathit{\text{self-organized}}$ and planned cities. We elaborate the results through an accurate closeness centrality analysis in the Euclidean space and in the relationship between primal and dual space. Interestingly enough, we find that even if the considered planar graphs display very distinct properties, the information space induce them to converge toward systems which are similar in terms of transportation properties.