Transportation networks serve as windows into the complex world of urban systems. By properly characterizing a road network, we can therefore better understand its encompassing urban system. This study offers a geometrical approach towards capturing
inherent properties of urban road networks. It offers a robust and efficient methodology towards defining and extracting three relevant indicators of road networks: area, line, and point thresholds, through measures of their grid equivalents. By applying the methodology to 50 U.S. urban systems, we successfully observe differences between eastern versus western, coastal versus inland, and old versus young, cities. Moreover, we show that many socio-economic characteristics as well as travel patterns within urban systems are directly correlated with their corresponding area, line, and point thresholds.
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.
