武汉城市圈城乡道路网的空间结构复杂性

doi:10.13249/j.cnki.sgs.2012.04.426

摘要/Abstract

摘要：

以武汉城市圈为研究区,借助ArcGIS9.3、Pajek2.7和SPSS16.0等软件,从节点重要性、可达性、集聚性3个方面定量揭示了复杂城乡道路网的空间异质性：① 高度节点重要性呈幂律分布,表现出无标度性,低度节点重要性则基本呈钟型泊松分布,呈现一定的随机性,导致整个圈域节点的重要性分布曲线既不遵循钟型泊松分布也不遵循幂律分布,出现“涌现”性;节点度值空间分布较均匀,呈现点状特征和弱集聚性,具有明显间断性和跳跃性,表现出一定的“中心–边缘”和“等级圈层”的复合结构;② 节点的可达性主要由网络平均路径长度、紧密度和介数指标表达,其中道路网平均路径长度较大,节点交通联系呈线状组织,遵循距离衰减律,成等级圈层分异,但受快速干道影响明显,空间收敛减慢,发生“摄动”变形,形成两条以南北京珠高速和东西宜黄高速为轴的城市交通走廊;节点的紧密度系数较随机网络小,但高紧密度节点在空间分布上较为集中,呈现出一定的“中心–边缘”空间格局;节点的介数指标相对较高,呈现指数分布,空间分布较均匀,但仍呈现出一定的“等级圈层”分异;③ 网络的集聚性空间差异显著,形成多个大型网络社团,网络的聚类系数近似为零,局部呈现耦合性质,高聚类系数节点集聚成“半月形”展布,低聚类系数节点分布较为离散。

关键词: 空间复杂性, 复杂网络模型, 城乡道路网, 武汉城市圈

Abstract:

Studies on the complexity and non-linearity of the spatial structure of road networks have attracted increasing attention during the past several years. However, few efforts have been devoted to the spatial and structural properties of large-scale road networks. In addition, most of current studies focused on either spatial morphology of road networks or structural pattern of road structure, while a comprehensive analysis on the spatial restriction of road network structures is ignored. To fill in the knowledge gap, this article introduces a series of approaches to uncover the spatial influences on the structural characteristics of general road networks. The road network of Wuhan Metropolitan Area (RNWMA) is taken as a case study and the spatial heterogeneity of the structure of RNWMA is analyzed from three aspects with the help of software including ArcGIS9.3, Pajek2.7 and SPSS16.0. Three aspects of spatial heterogeneity of the RNWMA are studied, which are importance of road intersections, accessibility of road intersections and clustering of road intersections. For each property, both statistic analysis and spatial distribution analysis are carried out. Results are visualized by map or chart. Possible explanations are also given. It is found that in the RNWMA: 1) the importance values of roads with high accessibilities in RNWMA follows a power-law distribution, which may indicate that the RNWMA is a scale-free network. While the importance values of roads with low accessibilities follow a Poisson distribution. The co-existence of scale-free and random properties for roads with different accessibility makes the entire road network a complex system with some “emergent” properties; 2) the average length of the shortest path between two roads is relatively large. While the traffic links between two roads in terms of topological distance follow the law distance decay and obvious hierarchy circles can be observed. The spatial convergence of the shortest path length is significantly influenced by roads with high hierarchy (e.g. expressway) and shows perturbation deformation. Two urban transportation corridors, i.e., the Beijing-Zhuhai (north-south) and Yichang-Huangshi (west-east) are observed. Besides, statistically the values of the betweenness of road intersections show exponential distribution although spatially they are relatively even; 3) The clustering coefficient for the RNWMA approaches zero, while several network communities are observed. The spatial distribution for the road intersections with large value of clustering coefficient are “crescent” like, and road intersections with low clustering coefficient values are sparsely distribution in the region. Attempt made in this study will not only help to interpret the structural organization and growth in a limited geographical space, but also shed light on visual analytic means for geographic environments. It is our hope if the findings of this article can provide any alternatives for current road network study, and give practical supports for the construction of urban-rural road network.

Key words: spatial complexity, Complex Network Model, urban-rural road network, Wuhan Metropolitan Area

中图分类号:

F294.3

刘承良, 余瑞林, 曾菊新, 王家琦. 武汉城市圈城乡道路网的空间结构复杂性[J]. 地理科学, 2012, 32(4): 426-433.

Cheng-liang LIU, Rui-lin YU, Ju-xin ZENG, Jia-qi Wang. Complexity of Spatial Structure on the Urban-rural Road Network in Wuhan Metropolitan Area[J]. SCIENTIA GEOGRAPHICA SINICA, 2012, 32(4): 426-433.

图/表 9

表1

复杂网络相关指标[23]"

研究内容	研究指标	公式	涵义	地理意义
网络节点重要性	度	（1）C_d(x)=d(x)	节点i的度k_i定义为与该节点连接的其他节点的数目	节点对外联系程度
网络节点重要性	度分布	（2） $Pk = ∑ k' = k ∞ P (k'$	P(k)表示的是一个随机选定的节点的度恰好为k的概率	节点度值的统计性质
网络节点可达性	平均路径长度	（3） $L = 1 N (N - 1) ∑ d ij$	N为网络节点数,d_ij定义为网络中两个节点i和j之间的距离即连接两个节点的最短路径的边数	网络的通达效率
	紧密度指标	（4） $Cc (i) = 1 / ∑ j = 1 n d ij$	d_ij定义为网络中两个节点i和j之间的距离,该节点到达其它节点的距离之和的倒数	网络通达的难易程度
	介数指标	（5） $Cb (i) = ∑ gjk (i) gjk$	g_jk节点j和k之间的最短路径数,g_jk(x)表示节点j和节点k之间经过节点i的最短路径数	节点的交通流负载
	可达性系数	（6） A_i=[1/L_i+C_c(i)+C_b(i)]/3	L_i为节点i平均路径长度,C_c(i)为节点i紧密度指标,C_b(i)为节点i介数指标	节点的可达性
网络节点集聚性	聚类系数	（7） C_i=E_i/[k_i(k_i-1)/2]	节点i有n个近邻点,那么这n个节点之间最多有k_i(k_i-1)/2条连线,以这n个点之间的实际连线数目E_i除以k_i(k_i-1)得出的值定义为i点的聚集系数	节点与相邻节点连接的集聚性

表1

图1

图2

图3

图4

图5

图6

图7

图8

参考文献 24

[1]	Barabasi A L,Albert R.Emergence of scaling in random networks[J]. Science, 1999, 286(5439):509-512.
[2]	Kansky K J.Structure of Transport Networks: Relationships Between Network Geometry and Regional Characteristics[D]. Chicago: University of Chicago Research papers,1963: 84-155.
[3]	Hillier B.Configurational modeling of urban movement networks[J].Environment and Planning B:Planning and Design, 1998,25:59-84.
[4]	Helbing D, Keltsch J, Molnar P.Modelling the evolution of human trail systems[J]. Nature, 1997, 388:47-50.
[5]	刘妙龙,黄佩蓓.分形理论在城市交通网络时空演变特征研究中的应用——以上海市为例[J].武汉大学学报·信息科学版,2003,28(6):749~753.
[6]	曹小曙,薛德升,阎小培.中国干线公路网络联结的城市通达性[J].地理学报,2005,60(6):903~910.
[7]	杨荫凯,金凤君.交通技术创新与城市空间形态的相应演变[J].地理学与国土研究,1999,15(1):44~47.
[8]	Schaeffer K H, Elliott S.Access for all: Transportation and Urban Growth[M].Baltimore Md.: Penguin, 1975.
[9]	Kim K S, Bengguigui L, Marinov M.The fractal structure of Seoul’s public transportation system[J]. Cities, 2003, 20(1):31-39.
[10]	胡一竑. 基于复杂网络的交通网络复杂性研究[D].上海:复旦大学,2008.
[11]	Lämmer Stefan, Gehlsen Björn, Helbing Dirk.Scaling laws in the spatial structure of urban road networks[J]. Physica A, 2006, 363:89-95.
	[12] Jiang B, Claramunt C. Topological analysis of urban street networks[J]. Environment and Planning B, Planning and Design 2004,31: 151-162.
[13]	Latora V, Marchiori M.Is the Boston subway a small-world network?[J]. Physica A, 2002,314:109-113.
[14]	姜克锦. 城市用地——交通综合系统演化机理与优化研究[D].成都:西南交通大学,2009.
[15]	Bossomaier T, Green D.Patterns in the Sand: Computers, Complexity and Life[M]. Reading, Massachusetts: Perseus Books, 1998.
[16]	Guimerá R, Mossa S, Turtschi A, et al.The worldwide air transportation network anomalous centrality, community structure, and cities global roles[J].PNAS, 2005, 102(22): 7794-7799.
[17]	Michael T. Gastner, Newman M.E.J. The spatial structure of networks[J].European Physical Journal B,2006,49:247-252.
[18]	王姣娥,莫辉辉,金凤君.中国航空网络空间结构的复杂性[J].地理学报, 2009, 64(8):899~910.
[19]	莫辉辉,王姣娥,金凤君.交通运输网络的复杂性研究[J].地理科学进展, 2008, 27(6):112~120.
[20]	Reggian A, Lampugnan G.Towards a typology of European inter-urban transport corridors for advanced transport telematics applications[J].Journal of Transport Geography,1996,3(1):53-67.
[21]	宗跃光,陈眉舞,杨伟,等.基于复杂网络理论的城市交通网络结构特征[J].吉林大学学报(工学版),2009,39(4):910~915.
[22]	苏伟忠,杨桂山,甄峰.基于无尺度结构的苏南乡镇公路网分析[J].地理研究, 2007, 26(5):1005~1002.
[23]	汪小帆,李翔,陈关荣.复杂网络理论及其应用[M].北京:清华大学出版社,2006:9~11.
[24]	刘力,之江仁,夏生魁,等.中国高速公路及城乡公路网地图集(超大详查版)[M].济南:山东省地图出版社,2010.