Journal of Geographical Sciences >
Spatial evolution and growth mechanism of urban networks in western China: A multiscale perspective
Yang Liangjie (1977), PhD and Associate Professor, specialized in urban ecology and city networks research. Email: yangljmnx@163.com 
Received date: 20210525
Accepted date: 20211117
Online published: 20220525
Supported by
National Natural Science Foundation of China(41501176)
National Natural Science Foundation of China(41961030)
Globalization and informatization promote the evolution of urban spatial organization from a hierarchical structure mode to a network structure mode, forming a complex network system. This study considers the coupling of “space of flows” and “spaces of places” as the core and “embeddedness” as the link and a relevant theoretical basis; then we construct a conceptual model of urban networks and explore the internal logic of enterprise networks and city networks. Using the interlockingaffiliate network model and data from China’s top 500 listed companies, this study constructs a directed multivalued relational matrix between cities in western China from 2005 to 2015. Using social network analysis and the multiple regression of quadratic assignment program model (MRQAP), this study adopts a “topdown” research perspective to analyze the spatiotemporal evolution and growth mechanism of the city network in western China from three nested spatial scales: large regions, intercity agglomerations, and intracity agglomerations. The results show the following: (1) Under the large regional scale, the city network has good symmetry, obvious characteristics of hierarchical diffusion, neighborhood diffusion, and crossadministrative regional connection, presenting the “coreperiphery” structural pattern. (2) The network of intercity agglomerations has the characteristics of centralization, stratification, and geographical proximity. (3) The internal network of each urban agglomeration presents a variety of network structure modes, such as dualcore, singlecore, and multicore modes. (4) Administrative subordination and economic system proximity have a significant positive impact on the city network in western China. The differences in internet convenience, investment in science and technology, average time distance, and economic development have negative effects on the growth and development of city networks. (5) The preferential attachment is the internal driving force of the city network development.
YANG Liangjie , WANG Jing , YANG Yongchun . Spatial evolution and growth mechanism of urban networks in western China: A multiscale perspective[J]. Journal of Geographical Sciences, 2022 , 32(3) : 517 536 . DOI: 10.1007/s1144202219598
Figure 1 Conceptual framework for city network research 
Figure 2 The multiscale based city network research framework 
Figure 3 Geographical location of western China 
Table 1 Calculation formula of the decomposition index of centrality 
Calculation formula  Remarks  

Degree centrality  ${{C}_{a}}=\underset{b=1}{\overset{M}{\mathop \sum }}\,{{C}_{ab}}$ (4) $C=\underset{a=1}{\overset{M}{\mathop \sum }}\,\underset{b=1}{\overset{M}{\mathop \sum }}\,{{C}_{ab}}$ (5) ${{\text{{C}'}}_{\text{a}}}=\frac{{{\text{C}}_{\text{a}}}}{\text{j}1}$ (6)  ${{C}_{a}}$ refers to the degree of node city a, ${{C}_{ab}}$ is the total connection intensity between city a and city b, $C$ is the total connection intensity of the whole network, and $M$is the number of cities. ${{{C}'}_{a}}$ is the relative centrality of node a, and $j1$ is the maximum possible link. 
Outdegree and indegree  $C_{a}^{out}=\underset{b=1}{\overset{M}{\mathop \sum }}\,~$ (7) $C_{a}^{in}=\underset{b=1}{\overset{M}{\mathop \sum }}\,~$ (8) $C_{a}^{O}=\frac{C_{a}^{out}}{j1}$ (9) $C_{a}^{I}=\frac{C_{a}^{in}}{j1}$ (10)  $C_{a}^{out}$ is the point outdegree of city a, $\text{ }\!\!~\!\!\text{ }C_{a}^{in}$ is the point indegree of city a, $C_{a}^{o}$ and $C_{a}^{I}$ are, respectively, the relative point outdegree and relative point indegree of city a. 
Betweenness centrality  ${{C}_{B}}\left( {{N}_{i}} \right)=\underset{j<k}{\overset{M}{\mathop \sum }}\,~\frac{{{g}_{jk}}\left( {{n}_{i}} \right)}{{{g}_{jk}}}$ (11)  The shortest path through point i that exists between points j and k is expressed in terms of g_{jk}(n_{i}). C_{B}(N_{i}) is the probability that i is in the shortest path between points j and k. 
Node symmetry  $S{{M}_{a}}=\text{C}_{\text{a}}^{\text{o}}\text{C}_{\text{a}}^{I}$(12) $SM=1\frac{1}{2}\underset{a}{\mathop \sum }\,\left C_{a}^{o}C_{a}^{I} \right$ (13)  SM_{a} represents node symmetry, SM represents overall network symmetry. 
Note: When SM_{a} is greater than 0, the city is defined as a dominant city; when SM_{a} is less than 0, it is a subordinate city; when SM_{a} is equal to 0, it is an equivalent city, the closer the SM is to 1, the higher the overall network symmetry. The closer the SM is to 0, the more asymmetrical the overall network node. 
Table 2 The influencing factors of city networks in western China and related theoretical hypotheses 
Target layer  Index layer  Index meaning  Theoretical hypothesis 

Y: city network  X_{1}: Industrial structure similarity  Using the industrial structure similarity model to describe the economic industrial relations based on data of secondary and tertiary industries  A negative influence on city networks 
X_{2}: Economic development gap relationship  Using the per capita GDP difference to construct the economic development gap  A positive influence on city networks  
X_{3}: Administrative relationship  According to the national standard of city administrative grade classification to divide the grades of cities  A positive influence on city networks  
X_{4}: Economic system proximity  According to industrial parks above the provincial level to calculate the intercity economic proximity  A positive influence on city networks  
X_{5}: Average time distance relationship  By the average time distance between highway and railway to construct the distance relation between two cities  A negative influence on city networks  
X_{6}: Internet gap  Taking the difference in the number of Internet users per 10,000 people between two cities to build the difference in Internet convenience  A negative influence on city networks  
X_{7}: Science and technology gap  Taking the difference of expenditure on scientific undertakings between two cities to construct the differential relationship of scientific and technological innovation  A negative influence on city networks 
Figure 4 Spatial and temporal distribution of city networks in western China 
Table 3 Urban node symmetry in western China (top 10) 
 2005  2010  2015  

City  C^{o}C^{i}  City  C^{o}C^{i}  City  C^{o}C^{i}  
Dominant city  Chongqing  0.1983  Chongqing  0.1402  Chongqing  0.0563 
Xi’an  0.0776  Aksu  0.0898  Liuzhou  0.0101  
Chengdu  0.0485  Xi’an  0.0481  Chengdu  0.0096  
Wuhai  0.0267  Chengdu  0.0376  Hohhot  0.0071  
Kunming  0.0087  Yibin  0.0213  Deyang  0.0068  
Nanning  0.004  Kunming  0.0136  Xi’an  0.006  
Hohhot  0.0033  Nanning  0.0092  Guilin  0.005  
Bayingolin  0.0007  Urumqi  0.0081  Xianyang  0.0047  
Yinchuan  0.0002  Ordos  0.0036  Mianyang  0.0044  
Gannan  0.0002  Liuzhou  0.0012  Kunming  0.0044  
┋  ┋  ┋  ┋  ┋  ┋  
Equivalent city  Huangnan  0  Huangnan  0  Huangnan  0 
Golog  0  Golog  0  Ngari  0  
Ganzi  0  Yushu  0  Beihai  0  
Changdu  0  Kizilsu  0  
Nyingchi  0  Changdu  0  
Shannan  0  Shannan  0  
Nagqu  0  Nagqu  0  
Ngari  0  Ngari  0  
Bijie  0  Liupanshui  0  
Bijie  0  
┋  ┋  
Subordinate city  Xianyang  0.0184  Hechi  0.018  Weinan  0.0154 
Tongliao  0.0181  Guang’an  0.0171  Urumqi  0.013  
Urumqi  0.0132  Hezhou  0.0116  Zhangye  0.0096  
Guiyang  0.0121  Yuxi  0.0097  Laibin  0.0065  
Lanzhou  0.0101  Nanchong  0.0083  Wuwei  0.0064  
Nanchong  0.01  Wuhai  0.0081  Jiuquan  0.0062  
Yuxi  0.0096  Tianshui  0.0078  Zunyi  0.0058  
Deyang  0.009  Suining  0.0078  Qujing  0.0049  
Qujing  0.0071  Guiyang  0.0075  Xining  0.0049  
Xining  0.0071  Qujing  0.0072  Lanzhou  0.0044  
┋  ┋  ┋  ┋  ┋  ┋  
Symmetry  0.63  0.63  0.75 
Figure 5 Symmetry diagram of city networks in western China 
Table 4 Network contact among urban agglomerations in western China 
Urban agglomerations 1  Urban agglomerations 2  2005  2010  2015 

LanzhouXining  ChengduChongqing  33728  27610  210694 
LanzhouXining  Guanzhong Plain  8272  8629  67382 
LanzhouXining  Beibu Gulf  1937  4271  35036 
ChengduChongqing  Guanzhong Plain  79017  59175  428342 
ChengduChongqing  Beibu Gulf  28025  27852  212851 
Guanzhong Plain  Beibu Gulf  5909  7711  67043 
Figure 6 Spatial and temporal distribution of the network among urban agglomerations in western China 
Figure 7 Spatial and temporal distribution of the inner network of city agglomerations in western China 
Table 5 Regression results of influencing factors of the city network in western China 
Influencing factor  Regression coefficient  

2010  2015  
Industrial structure similarity Economic development gap relationship  0.0003 0.0254*  0.0101 0.0230* 
Administrative relation  0.6998***  0.6709*** 
Economic systems proximity  0.0850*  0.0908** 
Average time distance relationship  0.0499**  0.0333* 
Internet gap relationship  0.1394***  0.1649*** 
Science and technology gap relationship  0.0812***  0.0740*** 
R^{2}  0.37  0.48 
Note: * p < 0.1; ** p < 0.05; *** p < 0.01 
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