The relationship between Liaoning urban agglomeration based on Gravity Model

. This paper simulates the economic gravitation between 14 prefecture level cities of Liaoning province by gravity model, and achieves data visualization through ArcMap and Ucinet . It is concluded that the central city group of Liaoning is composed of Shenyang, Liaoyang, Benxi, Anshan, Fushun and Tieling.The southern city group of Liaoning is composed of Dalian, Yingkou, Panjin, Huludao and Jinzhou.


Introduction
Over the past decades, it has been manifested that urban agglomeration has become an important force in regional development. According to theoretical studies, the close economic links between urban agglomerations are the essential characteristics of urban agglomeration. Quantitative analysis of economic links is the basis for determining the scope of urban agglomerations.In this paper, a gravity model is established to reflect the spatial and economic interaction of cities based on the theory of city connection in regional economics. In the Chinese urban agglomerations, the central city group of Liaoning is a typical resource-based city group in Northeast China. Because Shenyang and Dalian are the leading cities in Liaoning, there is also a theory based on the dual core cities in central and southern Liaoning (the coastal area of southern Liaoning includes Dalian, Dandong, Yingkou and Panjin. The central Liaoning region includes Shenyang, Anshan, Fushun, Benxi and Liaoyang).Therefore, with the increasing role of the urban system in revitalizing the old industrial base in Northeast China, it is necessary to study the spatial economic structure and hierarchical structure of the city. We take Liaoning Province as an example to make an empirical analysis.

Related Work
Liaoning province, located in the south of northeast China, is the cradle of new China's industry. Liaoning province has 14 prefecture-level cities. There are two main views on the division of city clusters in Liaoning Province.The central city group of Liaoning refers to the central part of Liaoning, the core area of heavy industry in Northeast China, with Shenyang as the central city, including Anshan, Fushun, Benxi and Liaoyang, which are five large and medium-sized cities. It is also one of the most densely populated metropolitan groups in China( [1]).The second point is the dual core mode of Shenyang -Dalian, which was first proposed as a dual core system of regional tourism. Shenyang, one of the capital of Liaoning Province, and Dalian, one of the famous port cities located at the southern tip of Liaodong Peninsula, are interrelated and develop harmoniously, forming the backbone of Liaoning regional tourism system, and it is a typical "dual core" structural mode( [2]).
Existing studies on urban agglomeration in Liaoning Province mainly focus on the economic growth of urban agglomeration with Shenyang as the center. A variety of methods have been used in the literature for map comparison and model verification to evaluate the simulation performance of urban growth model of Shenyang metropolitan circle in China( [5]).Regarding the industrial structure of Liaoning urban agglomeration, the industrial structure and economic growth structure of the urban agglomeration are better than the contrast area when the cities outside the urban agglomeration are taken as the contrast area. Therefore, resource-based cities, such as Fushun and Fuxin, can make use of the advantages of industrial priority and urban system interaction to realize the strategy of urban economic transformation( [6]).When studying the coupling degree of spatial energy consumption and industrial structure, the coupling degree of energy efficiency and industrial structure in Liaoning is low except that of Shenyang and Dalian( [7]).The main research is based on the relationship between air pollution and the urban agglomeration in the central of Liaoning( [3]).With the development of social economy, environmental problems are becoming more and more serious, especially urban carbon dioxide emissions. In order to quantify the driving force of carbon dioxide emissions in China's cities, it is necessary to consider the comparative analysis between the level of the state and the urban agglomeration( [8]). The research mentioned above lacks the analysis and definition of the current urban agglomeration of Liaoning Province. Gravity model is a common tool to divide the economic attraction between cities [9]. It can be used to basically divide the level of urban agglomeration according to the strength of the level of economic attraction( [10]).Based on gravity model, the present situation of Liaoning urban agglomeration is analyzed by using ArcGIS and UCINET.

Data
The paper selects 14 cities in Liaoning Province, and the shortest distance between cities calculated and the coordinates of urban longitude and latitude data come from the Baidu map. The GDP and population data of each city were collected from the National Statistical Yearbook.Administrative divisions refer to the Bureau of Surveying, Mapping and Geographic Information.

Gravity model
Gravity Therefore, Newton's theory can be used to explain the patterns of certain human activities between physically separated entities in space. In the mid 1850s, this theory was first applied to the overall structure of movement and communication generated by behavioral decision making processes for linkage, demand / supply decisions or site selection. In brief, it was used to analyze spatial interaction( [11]). In these pioneering applications, gravity is replaced by the strength of the interaction between two regions, expressed in terms of the distance or number of moves between the two regions, and the mass needs to be defined according to the type of activity being modeled. Until Stewart's work (1941), quality is defined as the origin and destination of the floating population( [12]). Based on the above, we can establish an inter city gravity model: ij T is the attraction of I city and J City, i P and j P are the staff members of the non-agricultural sector of i city and j City.K is the coefficient. ij R shows the distance between cities and β shows the friction paramete. It can be applied to the urban agglomerations, then we can get urban gravitational matrix T. T indicate the economic attractiveness of cities in the urban agglomeration, that is, the flow of social or economic factors. Therefore, we can obtain the representation of the connection level between city i and other cities: i L indicates the intensity of economic ties between urban i and urban j. It is an indicator of the degree of economic dependence of cities in a city group or the trend of developing into a strong city.

Gravitational matrix
Population, GDP and distance between cities in Liaoning province are shown in table 1. Define i k here only expresses the gravitational coefficient of a large GDP city to a small GDP city. From table 1 and formula 2, we can get the gravitational matrix between different cities in Liaoning province, as shown in Table 2.
From the gravitational matrix of Table 2, we can see that there are significant differences in the economic links between cities. The visualization of ArcMap data is shown in figure 1.
According to the formula (3), we can get the link rank relationship between other cities and Dalian Shenyang, which is supposed to be the core city, as shown in Table 3 and Table 4.

Urban agglomeration Division
Redefine i k as new bidirectional matrix that is calculated by combining Table 1 with the gravitational coefficient of all cities, as shown in Table 5.  I import table3 data into UCINET to realize data visualization and get figure 2.
The degree of line thickness indicates the strength of economic attraction between cities. The size of the urban punctuation indicates the strength of the other cities and their economic gravity. The red point indicates that the city group with the strongest intercity economic ties, the blue city group is the next, while the gray represents the marginal city group.
From the diagram, we can see the following points: firstly, the strongest economic gravitational relationship is around the core city of Shenyang. The core city group consists of Shenyang, Liaoyang, Benxi, Anshan, Fushun and Tieling. Unlike the mentioned theory about five cities in the central city group of Liaoning, the study also finds that Tieling has strong economic attraction with Shenyang, which should be attributed to the central cities of Liaoning. In these six cities, Anshan and Liaoyang have strong economic attraction lines except Shenyang and other cities.
Secondly, Dalian, Yingkou, Panjin, Huludao and Jinzhou constitute an urban agglomeration with the second strongest gravity links.It can be seen from the graph that Huludao and Jinzhou have stronger economic attraction than Dandong and other three cities.
Finally, Dandong, Fuxin and Chaoyang are marginal cities. Apart from forming a certain economic gravitational strength with Shenyang, they have weak gravitational relations with other cities.

Conclusion
This paper simulates the economic gravitation between cities in 14 prefecture level cities in Liaoning province by gravity model, and realizes data visualization through ArcMap and Ucinet software. Compared with the Liaoning central city group and the southern Liaoning city group mentioned above, this paper gives different views. It is concluded that the central city group of Liaoning is composed of Shenyang, Liaoyang, Benxi, Anshan, Fushun and Tieling, and the southern city group of Liaoning is composed of Dalian, Yingkou, Panjin, Huludao and Jinzhou.
There are still many deficiencies in this paper. The conclusion of the model still lacks other ways of testing. We hope to include other refined data in subsequent research and further verify the validity of the establishment of urban agglomeration.