Uncovering road network structure through complex network analysis

Abstract

Studies on road networks have received intensive interdisciplinary attention during latest several years for two reasons. The first is that the road network is a common and easily accessible spatial complex system. The second is that a road network has a close relationship with human life and city evolution. Current studies cover almost every aspect of a road network, for instance, road feature extraction from image data, road map generalization and schematization, road selection and optimization, traffic simulation and statistical analysis of road networks. However, little attention has been devoted to structure of a road network. This project attempts to study the properties of the structure of road networks in various aspects, i.e. scale-free, mixing patterns, small-world, hierarchy and structural fractal. By "scale-free" it is meant that the distribution of the node connectivities in a network follows a power law. In study of the scale-free, the revised Kolmogorov-Smirnov statistics was adopted to replace conventional least square method as it provides more reliable and robust result for a power law distribution. In the study of mixing patterns of road connectivities, the profile of connectivity correlation probability was firstly employed to visualize the results. By "small-world" it is meant that any two nodes in a network can be connected by a relatively short chain. In examination of the small-world structure, two measures, i.e., clustering coefficient and characteristic path length were introduced. In study of hierarchical structure, the ego network analysis rooted in social science was introduced to define the order of each road so as to construct the hierarchical structure of a road network. The ego network was then improved to become weighted ego network by assigning a weight to each link in the network. By "structural fractal" it is meant that the structures of an object at different scales look self-similar. To examine this structure, the Maximum Excluded Mass Burning (MEMB) algorithm was employed. Traffic and other socio-economic data were collected to explore their relationships with these structural properties. Through these studies, it has been found that (1) road networks are scale-free and the estimated exponents of power law distributions of their road connectivities range from 2.11 to 3.50 with an average of 2.69; (2) shortcuts that make a road network easily accessible are created by mixing pattern in a scale-free road networks, and the profile of connectivity correlation probability is valid to visualize the mixing pattern of road connectivities; (3) road networks are small-world with an average length of the shortest paths (between any two roads) of eight. Results also indicate that a more developed region has a more mature road network to meet its transportation demands; (4) road networks are hierarchical in terms of the opportunities and constrains of each road in flow transmission. Ego network analysis is effective in formation of the hierarchical structure of a road network, and the weighted ego network analysis improves the performance; (5) road networks are structural fractals with fractal dimensions ranged from 2.94 to 4.90. Results indicate that the more complex the structure of the road network is, the more developed the region will be. The findings shed new light on the organizational principles and dynamical mechanisms of road networks. They reveal that, like other complex adaptive systems, a road network develops in a self-organized way by maximizing its ability of flow transmission in a limited geographical space. In addition, this study help investigate the socio-economic meanings of an urban structure. It provides empirical guides for future planning and policymaking for regional development and transportation design.