Multi-dimensional geometric complexity in urban transportation systems

Transportation networks serve as windows into the complex world of urban systems. By properly characterizing a road network, one can better understand its encompassing urban system. This study offers a geometrical approach toward capturing inherent properties of urban road networks. It offers a robust and efficient methodology toward 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, one can successfully observe differences between eastern versus western, coastal versus inland, and old versus young cities. Moreover, we show that many socioeconomic characteristics, as well as travel patterns, within urban systems are directly correlated with their corresponding area, line, and point thresholds.