关键词: 城市体系, 交通网络, 分形城市, 空间复杂性, 无标度网络, 对称破缺

Abstract: An exclusively mathematical approach is proposed to address the scale-free property of selforganized networks of cities. Defining a spatial correlation function based on the triangular lattice model of cities stemming from central place networks, a scaling relationship is established between yardstick (r) and city-city correlation density (C(r)) such as C(r)∝r^D, where D is the scaling factor. The scaling factor is in fact the spatial correlation dimension if only 1≤D≤2. A self-organized network of cities is regarded as scale-free system provided there exists a linear range on the logr-logC(r) plot. The Henan cities of China are taken as an example to show how to fit the observed data to the correlation function for calculating the scaling factor, and to illustrate the process of spatial complication of urban evolution. The results indicate that urban systems and the traffic networks based on urban systems are scale-free networks, and the network of cities can be characterized with the power-law of yardstick and correlation density relation.

Key words: urban system, transport network, fractal cities, spatial complexity, scale-free network, symmetry breaking