# Urban Connectivity

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<summary>Definition</summary>

Urban Connectivity measures how key locations, like intersections or public spaces, connect different parts of a neighborhood and the wider city. High connectivity values highlight neighborhoods with well-connected networks that make it easier for people, goods, and services to move efficiently. Urban Connectivity is a strong predictor of social interaction.

This metric is based on Betweenness Centrality, a network analysis measure (Freeman, 1977) that quantifies how often a node appears in the shortest paths between all other nodes in a network. In an urban context, it approximates pedestrian or vehicular flow through the built environment.

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<summary>Navigation</summary>

Urban Connectivity is presented as a heatmap across the city.

* Red areas indicate low connectivity, typically due to fragmented or inefficient street layouts.
* Blue areas highlight highly connected zones, where movement is easier and more fluid.
* Users can click on any location to view its Urban Connectivity Score, calculated based on shortest paths through the network.
* Sidebar visualizations show comparative scores across the city at street, block, or neighborhood scale.

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<summary>Methodology</summary>

The Urban Connectivity score is calculated using a network-based model of the urban area, analyzing how frequently locations appear in shortest paths across the network.

1. Network Model Creation – Represent the urban area as a graph, with intersections as nodes and streets as edges.
2. Shortest Path Computation – Compute all shortest paths between node pairs within a defined search radius.
3. Path Distribution Analysis – If multiple shortest paths exist, distribute weights evenly so they sum to one.
4. Connectivity Calculation – Count how often each node appears in these shortest paths and normalize the result.
5. Weighting Adjustments – Apply context-specific weighting (e.g., to prioritize pedestrian or vehicular flows).
6. Spatial Aggregation & Visualization – Aggregate values to street segments or blocks for intuitive visualization.

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<summary>Calculation</summary>

$$f(x) = x \* e^{2 pi i \xi x}$$$$Betweenness\[i]^r = \sum\_{j,k \in G - {i},\ d\[i,j] \leq r} \frac{n\_{jk}{\[i]}}{n\_{jk}} \cdot W\[j]$$$$Betweenness\[i]^r = \sum\_{j,k \in G - {i},\ d\[i,j] \leq r} \frac{n\_{jk}{\[i]}}{n\_{jk}} \cdot W\[j]$$

Where:

* $$Betweenness\[i]^r$$ = Connectivity score for location i within search radius r
* $$n\_{jk}\[i]$$ = Number of shortest paths from origin j to destination k that pass through i
* $$n\_{jk}$$ = Total number of shortest paths from j to k
* $$W\[j]$$ = Weighting factor for origin j

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<summary>Interpretation</summary>

* High Urban Connectivity indicates strategic importance in the urban flow, where a location supports many routes between other places. Often correlates with walkability, social activity, and efficient mobility.
* Moderate Connectivity suggests functional but not central positioning within the network.
* Low Connectivity reflects areas that are spatially isolated or structurally disconnected from surrounding infrastructure.

The Urban Connectivity KPI supports:

* Identification of mobility bottlenecks or redundancies
* Planning for public space or transit interventions
* Strengthening of economic and social integration in neighborhoods
* Evaluation of social interaction potential, as well-connected areas tend to support more vibrant public life and community engagement

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