Discrete Dynamics in Nature and Society

Volume 2018, Article ID 3698071, 11 pages

https://doi.org/10.1155/2018/3698071

## Spatial Pattern and Evolution of Urban System Based on Gravity Model and Whole Network Analysis in the Huaihe River Basin of China

^{1}Research Institute for Smart Cities and Shenzhen Key Laboratory of Spatial Information Smart Sensing and Services, School of Architecture and Urban Planning, Shenzhen University, Shenzhen, China^{2}College of Geographic Sciences, Xinyang Normal University, Xinyang, China^{3}Garmin, Shanghai, China^{4}School of Resource and Environmental Sciences, Wuhan University, Wuhan, China^{5}Center for Assessment and Development of Real Estate, Shenzhen, China

Correspondence should be addressed to Biao He; moc.liamtoh@oaibeh_uhw

Received 14 January 2018; Revised 9 May 2018; Accepted 28 May 2018; Published 27 June 2018

Academic Editor: Leonid Shaikhet

Copyright © 2018 Yong Fan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The spatial pattern and evolution of urban system have been hot research issues in the field of urban research. In this paper, the network analysis method based on the gravity model and the related measurements were used to reveal the properties of the spatial pattern and evolution of the urban system in the HRB (Huaihe River Basin) of China. The findings of this study are as follows: During the period from 2006 to 2014, the economic contact between the HRB cities has been strengthened, but the differences between cities have been expanding. In general, the HRB cities have not yet formed a close network structure, and a trend of economic integration has not been found. This paper expresses the spatial pattern and evolution of urban system in an intuitive way and helps to explain the evolution mechanism of urban system. The method was confirmed by empirical research. Because of the operational and visual expression, this method has broad application prospects in the urban system research.

#### 1. Introduction

The spatial pattern and evolution of urban system are important manifestations of the human social development process on a spatial level [1], which reflects the change in the human social spatial structure and reveals the spatial patterns of the overall behavior of human society. These changes and their patterns are the foundations for the research of the sustainable development of human society [2].

Six super-large urban agglomerations have been formed in mainland China: Shanghai-Nanjing-Hangzhou, Beijing-Tianjin-Tangshan, Pearl River Delta, the central and southern Liaoning Province, Sichuan Basin, and Shandong Peninsula. Six city-and-town-concentrated areas (approximate to urban agglomeration) have also been formed: Central Shanxi Province, Central Hunan Province, Central Plains, Fuzhou-Xiamen, Harbin-Daqing-Qiqihar, and Wuhan area [3, 4]. If the geographical positions of urban agglomerations are compared with several main rivers in China (the Changjiang River, the Huanghe River, the Liaohe River, the Huaihe River, the Songhuajiang River, the Pearl River, the Haihe River, and the Minjiang River), it can be found that they mostly have corresponding relations. Only the HRB (Huaihe River Basin) has not formed large scale urban agglomeration [5]. Therefore, this paper wishes to determine the relationship between the HRB cities and puts forward feasible suggestions to promote contact between cities [6].

Population and economic growth are the main driving forces for the growth of urban system [7]. The cellular automata model [8], support vector machine [9], self-organizing structure model [10], gravity model [11], and systematic dynamics [12] have been used to describe spatial expansion of cities. The growth of urban systems is also influenced by the scale of urban space, traffic network, and complexity of the terrain [13–15]. A mechanism for the growth of the city has been proposed [16] but modeling the spatial and temporal dynamics of urban formation and evolution remains difficult [17]. Urban systems evolution mainly includes changes in two aspects: land use pattern and system structure [18]. The gravity model has been widely applied in this field. Based on graph theory, large scale analysis has demonstrated that the spatial structure of urban system becomes increasingly effective and stable with increased complexity and more favorable to the sustainable development of the urban system [19].

The formation of urban agglomeration is not only connected with geographical location and distribution of the city but also relevant to the economy and social culture [20]; the cross-border movement of capital, information, products, talented people, and technology is the notable feature of regional economic development [21, 22].

From previous literature, we know that network analysis can be used to analyze resource exchange and relation between actors (i.e., individuals, groups, cities, etc.) [23]. Because of this characteristic, network analysis has a great contribution in the field of information exchange [24], group behavior research, and other fields [25, 26]. However, although network analysis has received great concern in regional economics since the last century [27], only in recent years whole network analysis has been used to study regional economic network structures [28–30]. The method of whole network analysis could be used to study the relationship, especially economic contact, among cities.

Currently, the main focus of whole network urban system is on explicit urban networks (i.e., traffic networks [14, 19]) or the ranking of urban system centers, but there is a lack of dynamic and visual expression on internal membership in urban system [31]. The distinction between an urban system, as a specific geographical cluster, and a city is its complex interactions and connections among network members. Therefore, the internal connection of urban system should be multilateral, interactive, and networked [32].

These studies provide a method foundation for understanding the urban systems evolution. Our goal was to explain the urban system structure based on temporal and spatial evolution and use this to reconstruct the timelines of spatial patterns of regional urban system. Accordingly, in this paper, a modified gravity model is used to construct the network with the location, scale, and economic level data of the HRB cities, and the method of whole network analysis is used to study the urban network structure and the relationships among cities.

#### 2. Theories and Methods

##### 2.1. Gravity Model

The gravity model is based on the formula of universal gravitation:

which describes the interaction between the two masses* M*_{1} and* M*_{2} of objects, where d is the distance between the two objects and* G* is the universal gravitation constant.

Similar to the interaction between objects, there is also a relationship between cities in a certain area; in economics, this is called economic gravity theory [33, 34].

Because of this similarity, many scholars have attempted to apply the formula of universal gravitation to the measurement of a city’s gravity:

where denotes the quantity of spatial flows. and are the GDP (Gross Domestic Product) of a city; is the distance between two cities; , , , are constants.

To describe the scale and development degree of a city more scientifically, some scholars have also considered the population and area of a city when constructing the model [35, 36].

However, cities are not the same as ordinary objects. The economic impact of city* i* on city* j* is not equal to the economic impact of city* j* on city* i*, and the contributions of the two cities to the economic gravity are also different. Consequently, we defined the constant as the ratio of GDP in city* i* to the GDP in city* i* and city* j*, and the modified gravity model is thus obtained:

where and are the registered population in city* i* and city* j*; and are the GDP in city* i* and city* j*; is the distance between city* i* and city* j*; is the contribution rate from city* i* to city* j*. If the city is at a prefecture level or above, the statistical data do not include the counties under the jurisdiction of that city.

First, We calculated the of all the cities in the HRB based on (3) and showed the result as a matrix. Then, urban system network structure of the HRB was calculated and analyzed using Ucinet Platform.

##### 2.2. Whole Network Analysis

###### 2.2.1. Density

Network Density refers to the closeness degree among the network members: the closer the members, the higher the density of the network. For a binary network, its density is the ratio of the number of actual relationships in the network to the theoretical maximum number of relationships, whereas for a multivalued network, such as the network analyzed in this paper, its density is the average of all contact values except self-contact:

where is the economic impact of city* i* on city* j*;* n* is the number of cities in the urban network.

###### 2.2.2. Degree Centrality and Centralization Measurement

Degree centrality analysis is used to explore how central the members are in the network: the higher the degree centrality, the more important the member in the network [37]. Generally, degree centrality includes the absolute value and the standard value, the latter of which is used to compare between different network; thus, we use the absolute value of degree centrality in this analysis [38, 39].

Because what we construct is a directed network, each node has an out-degree and an in-degree, which represent the extent of a city’s influence on other cities and the extent to which a city is affected by other cities, respectively:

where* C*_{ADi} is the degree centrality of city* i* and is the economic impact of city* i* on city* j*.

Centralization is used to describe the overall centrality of a network; namely, it compares the highest degree of centrality in the network with the other members’ centrality:

where* C*_{max} is the highest degree of centrality of all cities in the agglomeration and* C*_{ADi} is the degree centrality of city* i* [40].

###### 2.2.3. Measurement of Subgroups

A subgroup refers to a number of closely related members in a network. This analysis is usually used to study the number of subgroups in the network, the relation of the internal members of a subgroup, and the relation among the subgroups. It is not conducive to the network development if there are many distantly related subgroups [41].

In this paper, we used the CONvergence of iterated CORrelations (CONCOR) algorithm to analyze the network:

where is the value in row* i (j)* of the matrix and is the value in column* i (j) *of the matrix. At the initial level of analysis, CONCOR calculates using the above equation until all values converge to either 1 or −1, resulting in all nodes being grouped into one of two categories [33].

###### 2.2.4. Structural Equivalence Measurement

Structural equivalence means that if two members in a network swap their positions, the network structure will not change:

Certainly, it is very difficult to find fully structural equivalence between two members in a network. This measurement can be used to develop a general analysis of the network structure to better understand the similarities among the members.

#### 3. Data Source and Processing

##### 3.1. Study Area

Historically, the HRB has experienced several changes, and this has led to a variety of versions of HRB cities. In this paper, to make the study area more scientific and standard, we use the “HRB and Shandong Peninsula map” provided by the Huaihe River Water Resource Network, and the research area is defined according to the basin boundary.

According to the latest administrative plan in 2016, the HRB covers 1 provincial city, 27 prefecture-level cities, and 139 county-level cities (Figure 1).