The Evolving Model Of Urban Road Network Topology

Urban road network system is comprehensive, dynamic and open, its complexityreflects in many aspects. More and more attention are paid to the studies on evolution ofurban road network topology, which is the key and theoretical basis of the research ofurban road network complexity. Based on the complex network theory, some related issuesof the evolving model of urban road topology are studied in this paper.Urban road network topology is constructed with the dual method. According to thestudy on the composition of urban evolution system, we propose the self-organized effectand planning effect of urban road network topology. Self-organized effect is the essentiallaw and plays a major role in urban road network evolution, while planning effect onlyplays a minor role.According to the both evolving effects, the preferential attachmentmechanism and modular growth mechanism are introduced into the BA model. Then wepropose an evolving network model growing fast in units of module, each module is asmall-world network containing several interconnected nodes, and the nodes between themodules are linked by preferential attachment on degree of nodes. The preferentialattachment mechanism reflects the self-organized effect of urban road network topologyevolution, while the modular growth mechanism reflects the combination ofself-organized effect and planning effect.It is derived that the modularity measure formula of this proposed model, which canbe adjusted by changing ratio of the number of inner-module edges and the number ofinter-module edges. Based on the mean field theory, we develop an analytical function ofthe degree distribution, which is verified by a numerical example and indicates that thedegree distribution shows characteristics of the small-world network and the scale-freenetwork distinctly at different segments.By numerical simulation, the changes of modular structure property, small-worldproperty, and scale-free property, the comparative analysis of which is made with differentpreferential attachment, size of the module and network morphology of the module. Then the impact of self-organized effect and planning effect in the evolving progress of urbanroad network topology, can be reflected clearly.