Agglomeration centrality to examine spatial scaling law in cities

Abstract

Cities grow with processes resulting in the agglomeration of population and socioeconomic activities. At any stage of urban development, a city possesses a spatial structure of urban fabric to facilitate its functions. In this study, we find that the agglomeration characteristics of a city are significant for the identification and understanding of urban spatial structure. We propose a new centrality measure, termed agglomeration centrality, to examine the centrality of a node based on its relative level of clumpiness in an urban road network. We show a simple method to computationally define the agglomeration centrality based on Voronoi tessellations of all nodes in the network. On this basis, we investigate the spatial distribution of agglomeration centrality of urban road networks. Experiments on a set of randomly selected cities show that the agglomeration distributions of all these urban street networks present a remarkable double-power-law phenomenon. The distribution of the agglomeration centrality measures shows an invariant spatial scaling rule for cities. The regions with the highest centralities are always found to be urban centers. In comparison, this cannot be achieved by any current centrality measures. Finally, in an effort to explore the potential additional applicability of the new centrality measure to aid our understanding of spatial structures of other urban demographic or socioeconomic attributes, the agglomeration centrality was combined with the population data to create a population agglomeration index. The distribution of this index indicates a single-power-law property. In summary, this study develops a new centrality measure and demonstrates its effectiveness for understanding the spatial structures and spatial evolution of cities.