Urban road networks -- Spatial networks with universal geometric features? A case study on Germany's largest cities

TL;DR

This study analyzes the geometric properties of urban road networks in Germany's largest cities, revealing universal features like heavy-tailed distributions and rectangularity, driven by cost-efficiency constraints.

Contribution

It provides a comprehensive statistical analysis of urban road network geometry, highlighting universal patterns across different cities and linking them to underlying cost-efficiency factors.

Findings

All examined cities show similar small-scale geometric properties.

Road segment and cellular structure distributions have heavy tails.

A high degree of rectangularity is observed across networks.

Abstract

Urban road networks have distinct geometric properties that are partially determined by their (quasi-) two-dimensional structure. In this work, we study these properties for 20 of the largest German cities. We find that the small-scale geometry of all examined road networks is extremely similar. The object-size distributions of road segments and the resulting cellular structures are characterised by heavy tails. As a specific feature, a large degree of rectangularity is observed in all networks, with link angle distributions approximately described by stretched exponential functions. We present a rigorous statistical analysis of the main geometric characteristics and discuss their mutual interrelationships. Our results demonstrate the fundamental importance of cost-efficiency constraints for in time evolution of urban road networks.