关键词: 乡镇公路网, 节点度, 无尺度结构, 苏南

Abstract: Understood from the viewpoint of Graph Theory, free-scale structure essentially is the exponential function of vertex degree, D, in network graphy. The paper proposes rank vertex degree (D_r) and population size vertex degree (D_p) on the basis of the numeral vertex degree (D) of regional town road networks. Firstly, town road networks are discribed based on mathematics method, which aims to reveal the heterogeneity structure of three kinds of vertex degrees from the math background. The results show that the characteristic of free-scale structure is relative, and changes with the analysis objects and their attribute and scale; vertex degree D does not exhibit free-scale property, while D_r and D_p form free-scale structure; and the exponential function of town poulation sizes of a region corresponds with Rank-Size Rule of urban system. Then, town road networks are analysized on relational analysis of SPSS and spatial analysis of GIS, which aims to find the relationship between town vertex degrees D, D_r and D_p. The results show that the correlation coefficient between D_p and D is 0.569 while the correlationship and spatial contacts on town road networks graphy between D_p and D_r are all very evident. The numbers of roads linked by each town are limited and cannot be changed into free-scale structure because of two-dimensional spatial distribution on earth surface and costly construction expense of these roads. The Poisson distribution of D is affected not only by population size of towns but also town location and others factors. High ranked roads are contact bridges of production and communication among cities whose spatial pattern influences these roads assign and pattern. Accordingly these high ranked roads and "spill-over effect" of urban change road linkage priority mechanism of towns, which results in D_r upgrade of some towns in some specific area. Town population sizes increase with their vertex degree D_r upgrade. D_r and D_p of town road network shows exponential function distributions structure in the end. The above inherently mutual mechanism between town population size and its road linkage rank spatially shows the "Core-Belt" model of town development in the rigion, where the "Core" corresponds to the area around cities, and the "Belt" corresponds to the area around high ranked roads. The open town clusters model benefits both economic development and eco-environmental convocation.Finally the paper suggests that the area of Suzhou city, Wuxi city, Changzhou council area and Wujin city need controlling towns high-dense pattern model, where town centralization and consolidation policies should be conducted, and the development and pattern of high ranked roads need proper control and scientific planning; the area of Nanjing city, Zhenjiang city, Jintan city and Liyang city need to strengthen developing towns around high ranked roads, but avoid the overspread pattern of towns.

Key words: town road networks, vertex degree, free-scale structure, southern Jiangsu Province