Geometry of Urban Order
Abstract
Urban street networks are modeled as spatial graphs whose geometry reflects planning, history, and physical constraints. Global orientation measures describe the overall order of a city but do not reveal how street directions form coherent neighborhoods. Here we introduce bearings communities---spatially connected domains whose streets share a common orientation---and analyze them using concepts from the physics of polycrystalline materials. Across $1025$ large cities worldwide, these domains are almost perfectly ordered: their mean coherence is $0.964$ and varies by only 1.4% from one city to the next, far above the value expected for randomly oriented streets. Every city is therefore a mosaic of well-ordered orientational grains, differing only in their number, size, and mutual alignment. Because the grains are equally regular everywhere, a city's global order is set mainly by how many of them it averages over: a city appears ordered because it is built from a few large grains, not because its fabric is locally more regular. A null model in which grain orientations are randomized confirms this grain-counting mechanism. Finally, the interface fraction γ measures how strongly domains interlock, yielding a morphology diagram that organizes cities continuously between grid-like, polycrystalline, and fragmented limits.
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BibTeX
@misc{barthelemy2026geometry,
title = {{Geometry of Urban Order}},
author = {Marc Barthelemy and Geoff Boeing},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13029},
eprint = {2609.13029},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13029},
}
RIS
TY - UNPB
TI - Geometry of Urban Order
AU - Marc Barthelemy
AU - Geoff Boeing
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13029
UR - https://arxiv.org/abs/2609.13029
AB - Urban street networks are modeled as spatial graphs whose geometry reflects planning, history, and physical constraints. Global orientation measures describe the overall order of a city but do not reveal how street directions form coherent neighborhoods. Here we introduce bearings communities---spatially connected domains whose streets share a common orientation---and analyze them using concepts from the physics of polycrystalline materials. Across $1025$ large cities worldwide, these domains are almost perfectly ordered: their mean coherence is $0.964$ and varies by only 1.4% from one city to the next, far above the value expected for randomly oriented streets. Every city is therefore a mosaic of well-ordered orientational grains, differing only in their number, size, and mutual alignment. Because the grains are equally regular everywhere, a city's global order is set mainly by how many of them it averages over: a city appears ordered because it is built from a few large grains, not because its fabric is locally more regular. A null model in which grain orientations are randomized confirms this grain-counting mechanism. Finally, the interface fraction γ measures how strongly domains interlock, yielding a morphology diagram that organizes cities continuously between grid-like, polycrystalline, and fragmented limits.
ER -