Capturing the Signature of Topological Evolution from the Snapshots of Road Networks

Road networks serve as the backbone of cities, shaping urban structure as well as providing the critical function of transport for people, goods, and services. The design and management of resilient road infrastructure, therefore, is essential for building a sustainable city. Road networks grow and evolve over time, such that their topology shifts from an initially planned state to the one that emerges from self-organization and urban growth. In this work, we use a dual mapping approach to compare the topological features of road networks in 25 districts in Seoul, South Korea. By using average node degree as an indicator of the level of self-organization, we present that multiple topological variables including power-law exponent gradually shift as a network grows. By testing static error and attack tolerance of these networks, we also show that the gradual shift in topology also has an important implication in network resilience. We suggest a new method, inspired by Lorenz curve, for quantifying network vulnerability. This modified Lorenz curve enables calculating the relative impact of intensive attacks to random failures and shows that a more self-organized road network tends to become more vulnerable to selective attacks.