# Urban Design Sustainability

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<summary>Definition</summary>

Urban Design Sustainability evaluates how efficiently urban spaces utilize resources such as land, materials, and infrastructure. It considers the geometric efficiency of a district’s layout—using diameter periphery as a proxy—to understand how much spatial coverage and connectivity are achieved per cubic meter of built material (e.g., concrete, steel, glass). High scores indicate a morphologically optimized urban form that minimizes waste and maximizes performance, balancing compactness, accessibility, and infrastructure deployment.

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<summary>Navigation</summary>

Urban Design Sustainability is presented as a heatmap that visualizes levels of morphological efficiency across the city.

* Blue areas reflect high sustainability, where urban form achieves optimal spatial coverage and connectivity with minimal material input. These areas are compact, well-connected, and geometrically efficient.
* Red areas indicate low sustainability, where urban layout is fragmented, overextended, or spatially inefficient—requiring more infrastructure and materials to achieve similar levels of performance.
* Users can click on any urban unit to view its Urban Sustainability Score.
* Sidebar visualizations provide comparative insights across the city.

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<summary>Methodology</summary>

Urban Sustainability is derived from morphological eccentricity, which evaluates the structural efficiency of a city’s physical network—such as streets, pathways, or other connective infrastructure.

For each urban unit:

* The method computes the eccentricity of each node in the spatial network.
* Eccentricity is defined as the maximum distance between a node and all other nodes within the same network.
* The average of these maximum distances is used to reflect how efficiently space is organized.
* The lower the average maximum distance, the more compact and resource-efficient the area is.
* High scores indicate areas where infrastructure connects spaces with minimal spatial redundancy or waste.

This indicator estimates how efficient the urban network is in deploying physical infrastructure to achieve spatial coverage and accessibility. Higher scores indicate shorter average maximum distances, meaning better performance.

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<summary>Calculation</summary>

Urban Design Sustainability is defined as:

$$\Omega\_i=max(\epsilon\_i)=e(v)=max(u\in G)d(v,u)$$

Where:

* $$e(v)$$ = Eccentricity of node
* $$d(v,u)$$ = Euclidean distance between nodes v and u
* $$G$$ = Set of all nodes in the network (urban unit)

The final score is the average of maximum distances from each node to all others in the urban network

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<summary>Interpretation</summary>

* High Urban Design Sustainability Scores reflect compact, well-connected layouts where the average maximum distance between nodes is low. These areas achieve full internal connectivity using minimal spatial extension, indicating efficient land use and reduced infrastructure demand.
* Moderate scores suggest irregular or partially stretched configurations, where connectivity is still feasible but requires more infrastructure to support.
* Low scores point to fragmented, spatially inefficient areas, where large distances between key points lead to redundant resource use and reduced accessibility.

Urban Design Sustainability helps identify:

* Areas where urban form is spatially efficient versus overextended
* Opportunities for infill, reconfiguration, or network optimization
* Zones where transit, housing, or services are misaligned with for

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