Braess交通网络模型是经典的图论模型,但该模型同时具有很强的地理学色彩。Braess借助一个简单的网络揭示了出人意料的地理现象:增加交通路线有时反而降低运输效率。从理论地理学的角度对Braess网络进行了数学抽象,然后利用规划理论、图论和微分方程解析等方法揭示出区域-城市地理系统的空间复杂化两个重要动因:空间相互作用和宏观对称破坏。

One of the important projects of spatial complexity science is spatial complication, which needs concrete and substaintial researches by means of effective methods. The paradox of traffic assignment problems is taken as an example to show how a system of cities and towns become complicate with the passage of time. Planning theory, graph theory, and differential dynamics, and so on, are employed to analyze the Braess’s paradox of traffic network, and new mathematical models are built in the process of geographical analyses based on the Braess’s network that is symmetric in macro-level. After new expressway is added in the network, two changes appear: one is macro-symmetry breaking of Braess’s network, and the other is spatial interaction between vehicle flows of different communication lines. Spatial interaction is associated with time lag and feedback what always give rise to non-linearity, while symmetry breaking implies spatial order breaking and reconstruction. A conclusion is drawn that spatial interaction and macro symmetry breaking are two dynamic factors activating spatial complication of self-organizing network of cities and towns.