Manifestation of Coupled Geometric Complexity in Urban Road Networks under Mono-Centric Assumption

TL;DR

This study investigates the geometric complexity of urban road networks using a ring-buffer approach, revealing coupled patterns of fractal and exponential behaviors, and introduces new indices to characterize urban evolution.

Contribution

It presents a novel ring-buffer method to analyze urban road network complexity and introduces density and decay indices for urban system insights.

Findings

Urban road networks exhibit coupled fractal and exponential patterns.

Two new indices effectively characterize urban system evolution.

Complexity patterns vary systematically with distance from city centers.

Abstract

This article analyzes the complex geometry of urban transportation networks as a gateway to understanding their encompassing urban systems. Using a proposed ring-buffer approach and applying it to 50 urban areas in the United States, we measure road lengths in concentric rings from carefully-selected urban centers and study how the trends evolve as we move away from these centers. Overall, we find that the complexity of urban transportation networks is naturally coupled, consisting of two distinct patterns: (1) a fractal component (i.e., power law) that represent a uniform grid, and (2) a second component that can be exponential, power law, or logarithmic that captures changes in road density. From this second component, we introduce two new indices, density index and decay index, which jointly capture essential characteristics of urban systems and therefore can help us gain new insights into how cities evolve.