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The angular nature of road networks.

Carlos Molinero¹, Roberto Murcio², Elsa Arcaute³

¹Centre for Advanced Spatial Analysis (CASA), UCL, 90 Tottenham Court Rd., London, W1T 4TJ, UK. c.molinero@ucl.ac.uk.

Scientific Reports

|June 29, 2017

Summary

This study applies percolation theory to the UK road network, using street segment angles to identify critical road structures. It reveals a hierarchical integration of roads, enabling a new index for classifying road importance that aligns with official designations.

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Area of Science:

Network Science
Urban Planning
Geographical Information Systems (GIS)

Background:

Road networks possess complex structural and geometrical properties influencing urban system behavior.
While topology offers insights, spatial constraints mean geometry critically shapes network dynamics and segment influence.

Purpose of the Study:

To apply percolation theory to the UK road network, using relative street segment angles as occupation probability.
To develop a hierarchical index for classifying road importance based on network integration.
To provide a framework for extracting and classifying the main skeleton of urban systems.

Main Methods:

Application of percolation theory to the UK's road network data.
Utilizing the relative angle between street segments as the occupation probability parameter.
Computation of Shannon's entropy for cluster sizes to analyze percolation stages.

Main Results:

The appearance of a spanning cluster signifies a phase transition, indicating critical system behavior.
Analysis of cluster sizes reveals a hierarchical integration of roads into the main cluster.
The developed hierarchical index shows strong correspondence with official road designations.

Conclusions:

Percolation theory effectively models road network criticality and hierarchy.
The new hierarchical index offers a consistent method for classifying road importance.
This framework aids in understanding and managing urban infrastructure skeletons.