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Urban Spatial Order: Street Network Orientation, Configuration, and Entropy
Geoff Boeing
TL;DR
Existing research has offered limited worldwide evidence on how street-network orientation, configuration, and entropy express urban spatial order. This study analyzes 100 cities using OpenStreetMap and OSMnx with multiple network indicators and a new single-grid orientation-order measure, finding regional and cross-indicator patterns that clarify the extent and nuance of griddedness.
Problem
Worldwide patterns of street-network orientation and entropy remain insufficiently documented because prior studies used small samples, limited geographies, and abstract indicators.
Method
The study analyzes 100 cities with OpenStreetMap and OSMnx, measuring orientation entropy, circuity, connectedness, grain, and a new indicator φ for alignment with a single grid.
Results
US/Canadian cities are more grid-like, with far less entropy and circuity than typical cities elsewhere, while φ significantly correlates with circuity and connectedness indicators.
Takeaways & Limitations
Considering φ, circuity, node degree, and segment length together reveals the extent and character of griddedness across cities.
Takeaways & Limitations
The study does not identify whether or how a city is planned, and future research should add controls and analyze regions or neighborhoods separately.
Abstract
from arXiv · showhide
Street networks may be planned according to clear organizing principles or they may evolve organically through accretion, but their configurations and orientations help define a city's spatial logic and order. Measures of entropy reveal a city's streets' order and disorder. Past studies have explored individual cases of orientation and entropy, but little is known about broader patterns and trends worldwide. This study examines street network orientation, configuration, and entropy in 100 cities around the world using OpenStreetMap data and OSMnx. It measures the entropy of street bearings in weighted and unweighted network models, along with each city's typical street segment length, average circuity, average node degree, and the network's proportions of four-way intersections and dead-ends. It also develops a new indicator of orientation-order that quantifies how a city's street network follows the geometric ordering logic of a single grid. A cluster analysis is performed to explore similarities and differences among these study sites in multiple dimensions. Significant statistical relationships exist between city orientation-order and other indicators of spatial order, including street circuity and measures of connectedness. On average, US/Canadian study sites are far more grid-like than those elsewhere, exhibiting less entropy and circuity. These indicators, taken in concert, help reveal the extent and nuance of the grid. These methods demonstrate automatic, scalable, reproducible tools to empirically measure and visualize city spatial order, illustrating complex urban transportation system patterns and configurations around the world.
Introduction
Street-network orientation and configuration help define urban spatial order, but broader evidence has been limited by small samples, restricted geographies, and abstract indicators. This study addresses that gap by examining multiple dimensions of street-network order across cities worldwide.
- Street networks organize and constrain urban transportation dynamics through planned or unplanned, ordered or disordered spatial logic.
- Past research has typically relied on small samples, limited geographies, and abstract indicators when studying street-network patterns and entropy.
- Measuring network patterns can help researchers, planners, and communities understand urban design histories, evaluate transportation configurations, and explore infrastructure alternatives.
- Jointly considered indicators reveal the extent and nuance of the urban grid around the world.
Background
Urban spatial order can arise from different geometric and developmental logics, and street networks provide a graph-based way to study those differences. Griddedness is useful but should not be equated with broader functional or social order.
- Orthogonal grids are common planned street patterns with documented examples in ancient settlements across regions and historical periods.
- Street networks may follow non-grid spatial logics while remaining well-structured in terms of human dynamics and land use.
- Specific visual or geometric order should not be confused with functional or social order.
- Cities often juxtapose or intermingle planned districts, organic cores, winding suburbs, and self-organized complexity as urban form evolves.
- Street-network graphs represent intersections and dead-ends as nodes and the linking street segments as edges.
Methods
The study analyzes geographically diverse city street networks using OpenStreetMap and OSMnx, then computes orientation, connectivity, grain, and circuity indicators. It also introduces φ to measure alignment with a single grid and uses statistical analysis and clustering to compare cities.
- Data: The sample includes 100 large cities across North America, South America, Europe, Africa, Asia, and Oceania selected for population, regional significance, and geographic diversity.
- Data: OSMnx automatically downloads OpenStreetMap boundaries and streets and constructs graph-theoretic objects for network analysis.
- Orientation entropy: Street bearings are calculated using simplified networks whose edges represent street segments while retaining full spatial geometry.
- Orientation entropy: Bearings are divided into 36 bins of 10° each, with a -5° shift placing common values such as 0° and 90° at bin centers.
- Orientation entropy: Orientation entropy uses the Shannon formula over the proportions of orientations in each bearing bin, with weighted and unweighted variants.
- Orientation entropy: The maximum entropy is 3.584 nats for a uniform distribution across bins, while entropy reaches 0 when all bearings occupy one bin.
- Orientation-order: The orientation-order indicator φ ranges from 0 for maximum disorder to 1 for a single idealized four-way grid.
- Network indicators: Average circuity measures how much more circuitous the network is than straight-line paths between adjacent nodes.
Results
Across 100 cities, street orientation, entropy, circuity, connectedness, and regional patterns reveal multiple forms and degrees of spatial order. US/Canadian cities are generally the most grid-like, while city-specific cases show that a single-grid measure can miss competing or offset grids.
- Chicago, Miami, and Minneapolis have the lowest orientation entropies, making them the most ordered networks in the study.
- US/Canadian cities have the lowest average entropy, circuity, and dead-end proportions, alongside the highest grid orientation-order and connectedness measures.Regional sample sizes are relatively small, so regional aggregation warrants the authors’ stated caveat.
- 49% of cities show an approximate north-south-east-west orientation trend, while other cities exhibit competing or more evenly distributed orientations.Polar histograms display street-bearing frequencies across 36 bins and expose differences in orientation concentration.
- Chicago most closely approximates a single perfect grid, with φ = 0.90 and most streets concentrated in four orthogonal bearing bins.Its dominant bins are centered on 0°, 90°, 180°, and 270°.
- φ correlates negatively with circuity and dead-end proportions but positively with average node degree and four-way intersections.The reported correlations are r(φ, ς) = -0.432, r(φ, Pde) = -0.376, r(φ, k̅) = 0.518, and r(φ, P4w) = 0.634, all statistically significant.
- Hierarchical clustering identifies three broad superclusters and eight intermediate clusters, with most North American cities grouped among relatively grid-like sites.The analysis uses standardized features and visualizes the clusters with a dendrogram and t-SNE.
Discussion
The indicators jointly distinguish different forms and degrees of griddedness, while revealing relationships between orientation-order, connectedness, and circuity. Regional heterogeneity and the inability to identify planning intent constrain interpretation and motivate more localized models and controls.
- Interpretive boundary: The study does not identify whether or how a city is planned, because specific spatial logics cannot be conflated with planning itself.Centrally planned and self-organized patterns may coexist as urban form evolves or accretes heterogeneous forms.
- Interpreting griddedness: Buenos Aires combines φ suggesting 15% adherence to a single grid with low circuity and high average node degree, indicating multiple competing grids.The indicators together distinguish heterogeneous, multi-grid griddedness from a single monolithic grid.
- Spatial-order relationships: Higher φ values coincide with higher node degrees, more four-way intersections, fewer dead-ends, and less-winding street patterns.Networks more consistently organized around a grid tend to be more connected and less circuitous.
- Regional differences: US/Canadian cities average nearly thirteen-times greater φ than European cities, with nearly double the proportion of four-way intersections.European streets are on average 42% more circuitous than US/Canadian streets.
- Future research: Future research should add regional or neighborhood-scale models and controls to clarify relationships and make the findings more actionable.Suggested controls include topography, development era, design paradigm, city size, and transportation planning objectives.
Conclusion
The study scales measurement of street-network orientation, configuration, and entropy to 100 cities worldwide. Its indicators reveal significant relationships among orientation-order, circuity, and connectedness, while showing that US/Canadian cities are generally more grid-like than cities elsewhere.
- Study scope: Past research faced small samples, limited geographies, and abstract entropy indicators; this study examines configuration and entropy across 100 cities worldwide.It measures orientation entropy, circuity, connectedness, and grain, and develops the orientation-order indicator φ for adherence to a single grid.
- Main findings: Significant correlations link φ with street circuity and connectedness measures.The study uses these relationships to compare spatial order across cities.
- Main findings: US/Canadian cities are more grid-like on average, exhibiting less entropy and circuity than cities elsewhere.The indicators together reveal the extent and nuance of the grid.