Fractal development and spatial synergy of urban road network: A case study of India

doi:10.3969/j.issn.1004-9479.2024.01.20222284

Abstract

Abstract:

The road network is a large-scale space transportation channel and a small-scale space social connection bridge, and its spatio-temporal complexity emerging mechanism has been a multi-disciplinary research hotspot. Fractal is one of the important tools to explore geographical complexity. This paper collects the road networks data of the top 200 districts in India's total population, excavates the geometric and structural fractal characteristics of the road networks in each district, and analyzes the statistical correlation and spatial similarities and differences of the geometric and structural fractal characteristics. The results show that:①The spatial distribution of the road network in the sample districts in India is uneven, maintaining the pattern of dense in the south and sparse in the north, with coastal density higher than inland. The difference between the north and the south is stronger than that between coastal and inland areas, which is consistent with the urban development pattern and the driving force of urban development in India;②The road network in all districts of India has significant geometric and structural fractal characteristics. The geometric fractal dimensions of the road networks box-covering [1.229,1.857], the structural fractal dimensions [1.623,3.179],and the fractal dimensions of the volume and degree volume structures [1.941,3.539] and [2.410,3.822], respectively, indicate that the road networks construction in most districts of India is dominated by spatial spread, thickening and densification, and three-dimensional development level needs to be strengthened, especially the cross grade and multi-layer roads are limited;③The regional linkage effect of high-grade traffic corridors is obvious, which is conducive to the coordinated development of space.Key words: road network; geometric fractal; structural fractal; coordinated development; India

摘要：

道路网是大尺度空间的交通渠道和小尺度空间的社会联系桥梁，其时空复杂性涌现机制一直是多学科研究热点。分形是探索地理复杂性的重要工具之一。收集印度总人口数排名前200的县的道路网数据，挖掘各县道路网的几何与结构分形特征，分析几何与结构分形特征的统计相关性及空间异同配性。结果表明：（1）印度样本县道路网空间分布不均衡，保持南密北疏、沿海密度高于内陆的格局。南北方差异强于沿海-内陆差异，这与印度城市发展格局与城镇发展驱动力一致；（2）印度样本县道路网均具有显著的几何与结构分形特征。道路网盒覆盖几何分形维取值［1.229，1.857］，结构分形维取值［1.623，3.179］，体积和度体积结构分形维分别取值［1.941，3.539］和［2.410，3.822］，表明印度大部分县道路网建设以空间蔓延和稠化加密为主，立体化发展水平有待加强，特别是跨等级、多层连接的道路较有限；（3）高等级交通廊道区域联动效应较明显，有利于区域协同发展。

关键词: 道路网, 几何分形, 结构分形, 协同发展, 印度

Caiwei LIU, Hong ZHANG, Shiyu TANG. Fractal development and spatial synergy of urban road network: A case study of India[J]. World Regional Studies, 2024, 33(1): 43-56.

刘采玮, 张红, 唐诗钰. 印度道路网的分形自组织与协同特征[J]. 世界地理研究, 2024, 33(1): 43-56.

Figures/Tables 12

Fig.1 Distribution of administrative divisions and road networks in India

Tab.1 Analysis index and meaning of road network topology

指标名称		计算公式	变量含义	指标含义
中心性	度中心性	$k i = ∑ j = 1, i ≠ j n L i j$	$n$ ：节点总数； $L i j$ ：节点 $i$ 与节点 $j$ 之间的连边数量	路划的直接连通性
	中介中心性	$B i = ∑ s, t ∈ V, s, t ≠ i o (s, t i) o (s, t)$	$o (s, t i)$ ：节点 $s$ 和节点 $t$ 之间的最短路径经过节点 $i$ 的次数； $o s, t$ ：节点 $s$ 和节点 $t$ 之间的最短路径数	路划在网络中的桥介作用
	邻近中心性	$C i = n - 1 ∑ j = 1, i ≠ i n d i j$	$d i j$ ：节点 $i$ 到节点 $j$ 的最短路径； $n - 1$ ：节点 $i$ 的最大邻接数	路划的平均可达性
结构分形维	盒覆盖结构分形维	$D S = - l i m l B → 0 l n N (l) l n l$	$l$ ：网络直径； $N (l)$ ：覆盖网络所需的最少盒子数； $D S$ ：盒覆盖结构分形维	路划交叉连通方式的多样性
	体积结构分形维	$D V = - l i m r → 0 l n ∑ i n V i (r) n l n r$	$r$ ：拓扑半径；n：节点数； $V i (r)$ ：节点 $i$ 在拓扑距离内的节点个；数，即体积； $D V$ ：体积分形维	路划网络互通衔接能力
	度体积结构分形维	$D D = - l i m r → 0 l n ∑ i n V i D (r) n l n r$	$r$ ：拓扑半径； $n$ ：节点数； $V i D (r)$ ：节点 $i$ 拓扑距离内节点度值，即度体积； $D D$ ：度体积分形维	路划跨等级连接能力

Tab.1 Analysis index and meaning of road network topology

指标名称		计算公式	变量含义	指标含义
中心性	度中心性	$k i = ∑ j = 1, i ≠ j n L i j$	$n$ ：节点总数； $L i j$ ：节点 $i$ 与节点 $j$ 之间的连边数量	路划的直接连通性
	中介中心性	$B i = ∑ s, t ∈ V, s, t ≠ i o (s, t i) o (s, t)$	$o (s, t i)$ ：节点 $s$ 和节点 $t$ 之间的最短路径经过节点 $i$ 的次数； $o s, t$ ：节点 $s$ 和节点 $t$ 之间的最短路径数	路划在网络中的桥介作用
	邻近中心性	$C i = n - 1 ∑ j = 1, i ≠ i n d i j$	$d i j$ ：节点 $i$ 到节点 $j$ 的最短路径； $n - 1$ ：节点 $i$ 的最大邻接数	路划的平均可达性
结构分形维	盒覆盖结构分形维	$D S = - l i m l B → 0 l n N (l) l n l$	$l$ ：网络直径； $N (l)$ ：覆盖网络所需的最少盒子数； $D S$ ：盒覆盖结构分形维	路划交叉连通方式的多样性
	体积结构分形维	$D V = - l i m r → 0 l n ∑ i n V i (r) n l n r$	$r$ ：拓扑半径；n：节点数； $V i (r)$ ：节点 $i$ 在拓扑距离内的节点个；数，即体积； $D V$ ：体积分形维	路划网络互通衔接能力
	度体积结构分形维	$D D = - l i m r → 0 l n ∑ i n V i D (r) n l n r$	$r$ ：拓扑半径； $n$ ：节点数； $V i D (r)$ ：节点 $i$ 拓扑距离内节点度值，即度体积； $D D$ ：度体积分形维	路划跨等级连接能力

Fig.2 Numerical and spatial distribution of road networks density

Fig.3 Frequency and spatial distribution of geometric fractal dimension of road networks

Fig.4 Road networks and topological connectivity graphs of the top five districts in terms of box-counting geometric fractal dimension

Fig.5 Centrality value distribution of road networks

Fig.6 Frequency distribution and spatial distribution of the structural fractality of road networks

Fig.7 Road networks and topological connectivity graphs of the top five districts in terms of structural fractal dimension

Fig.8 Bivariate map of geometric fractal dimension and structural fractal dimension

Tab.2 Global Moran's I calculation results of fractal dimension

分形维	莫兰指数	预期指数	Z得分
盒覆盖几何分形维	0.427	－0.005	18.479
体积结构分形维	0.240	－0.005	10.469
度体积结构分形维	0.208	－0.005	9.104
盒覆盖结构分形维	0.092	－0.005	4.135

Fig.9 Clustering and outlier analysis

Fig.10 Spatial coupling between geometric fractal dimension and structural fractal dimension of road networks

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