The regional economic spatial pattern of Northeast China and its economic integration trend based on network perspective

Based on the modified gravity model and social network analysis method, the paper constructed the economic linkage intensity matrix of 34 prefecture-level cities of Northeast China and analyzed the density and structure of urban linkage networks. The results show that at present, the urban linkage network in the Northeast region is getting closer, and the radiation role of core cities is gradually increasing. However, the degree of regional integration in Northeast China is not high, and some remote cities are still semi-isolated from the network.


Introduction
Urban network refers to a networked group of cities of different scales and functions that are closely connected in terms of resources, industries, information, and transportation. The closeness degree and spatial structure of urban networks have become important indicators in measuring the social and economic development of a region.
The central place theory proposed by Christal laid the foundation for the study on spatial linkages of urban agglomerations [1] . After World War II, a large scale of urban group emerged, which lead to the formation of foreign scholars' ideas on the study of urban systems. In the 1990s, with the increasing development of transportation and communication, the relationship between cities became more complex. Scholars began to further explore inter-city economic linkage networks from new perspectives, such as transportation networks [2] , air flows [3] , and logistics [4] .
In recent years, domestic scholars have mainly focused on provincial areas and more developed city clusters. They implemented their research based on gravity models [5] , affiliation models [6] , and urban flow intensity models [7] to analyze urban accessibility and urban cluster economic linkage patterns.
At present, some developed city clusters in coastal areas have formed a relatively mature city network system, while the economic development of northeast China still faces many problems. The paper takes into account various transportation modes, time cost, and monetary cost between the two cities to modify the traditional gravitational model and constructs a matrix of economic linkage intensity of northeast China. Subsequently, the paper analyzes the density and structure of economic linkage network based on social network analysis. On this basis, policy recommendations are proposed to strengthen the spatial linkages of Northeast cities.

Modified gravitational model
The gravitation model is a common measure of economic link intensity between cities, The strength of economic ties between cities is calculated as follows F �� � k �� �M � M � /D �� � � k �� � M � /�M � � M � � (1) Where F �� is the gravitational force of city a on city b, k �� is the gravitational coefficient of city a on city b, M � and M � are the combined masses of city a and city b, respectively, and D �� is the distance from city a to city b.
In measuring the comprehensive quality of cities, We select 18 indicators from four aspects to construct a comprehensive quality evaluation system f based on the principal component analysis.
In terms of measuring the distance between two cities, we refer to Sun Jing's viewpoint [8] , combining time distance and monetary distance to calculate economic distance. The "time distance" refers to the actual time required to travel between cities by various modes of transportation; the "monetary distance" refers to the actual price required to travel between cities by various modes of transportation. Subsequently, we assign different weights to various modes of transportation, which can help enhance fitting degree between distance variable and reality.
where D is the economic distance between two cities, w is the weight of the ith transportation mode, T is the time distance from the city a to city b for the ith transportation mode, and R the monetary distance from the city a to city b for the ith transportation mode.

Social network analysis
The social network analysis method is the mainstream method for analyzing interactions among nodes. Based on the economic linkage values calculated by the modified gravity model mentioned above, we construct the urban spatial linkage matrix, import it into UCINET to analyze the network density, network centrality, and network cohesion subgroups.

Network density analysis
Importing the calculated spatial linkage matrix into NetDraw to draw the linkage network structure (Figure 1), we can find that the city linkage network is gradually dense, which indicates the increasing economic linkage among cities in Northeast China.
According to in-degree centrality, we can conclude that among the three provincial capitals, The centrality of Shenyang is relatively low. Dalian has a high economic comprehensive quality, but its centrality is in the middle, which is not quite consistent with reality, probably because we regarded the Northeast as a relatively closed region, while Dalian is geographically located at the edge of the Northeast and has a long economic distance from other cities.

Block model analysis
In order to further analyze the network structure, the overall network can be divided into several subgroups. We choose the CONCOR clustering method to analyze the city clusters with relatively close economic relations and explore the structure of economic integration of the three eastern provinces. It can be seen that the 34 prefecturelevel cities in the eastern provinces can be divided into four cohesive subgroups. (Table 2) It can be seen that the members of agglomerate subgroups have not changed from 2010 to 2014. The first cohesive subgroup is formed around Changchun and Harbin, including two important urban agglomerations: Changji Economic Belt and the Hadazhi Industrial Corridor, which is the hub of economic development in the eastern provinces; the second cohesive subgroup consists of Tonghua, Baishan, and eastern cities of Heilongjiang Province. This subgroup contains several cities with less convenient transportation and weaker economic strength, which are less connected to other cities; the third subgroup is centered on Shenyang of Liaoning Province, and also contains Siping and Liaoyuan of Jilin Province, which is another pillar of the economic development of the eastern provinces; The fourth cohesive subgroup contains coastal cities such as Dalian and Huludao, which have convenient foreign trade, excellent industrial structure, and str ong comprehensive economic strength. Although Chaoyang should belong to the fourth subgroup from a geographical point of view, it is actually more closely connected with Shenyang, which may be related to the convenience of railroad transportation. In 2018, the members of each agglomerative subgroup changed significantly. Liaoyuan City and Baishan City join in the first cohesive subgroup, indicating that the radiation effect of the city network centered around Changchun and Harbin has increased; the second cohesive subgroup is still a less economically developed area in Heilongjiang Province; The members in the third cohesive subgroup have not changed, but it can be concluded that Siping City has established close ties with Liaoning Province; Tonghua joined in the fourth cohesive subgroup, which indicates that the completion of Tonghua International Inland Port in 2016 has greatly enhanced the degree of opening up of Jilin Province.

Conclusion
Based on the above analysis, the following conclusions can be drawn: The relatively weak economic strength of many cities and the unbalanced development of each region is one of the main obstacles to the integration of Northeast China. At present, Liaoning Province has has formed a certain close economic linkage network. Siping City is adjacent to Liaoning Province and has established close ties with it. There is still room to improve the radiation effect of the city cluster around Changchun and Harbin. Some remote cities of Heilongjiang Province are economically weak and are almost separated from the linkage network. the linkage network radiation with Harbin, Qiqihar, and Daqing as the core is not enough to drive some cities with backward economic development.

Policy recommendations
Firstly, it can be concluded that it is far from enough for the three eastern provinces to rely only on the three provincial capitals to support and drive the economic development of other cities. Therefore we should focus on giving full play to the advantages of the location, developing special industries and improving the quality of the city's economy. Secondly, It is urgent to improve the transportation networks of cities with more remote geographical locations, which can Reduce transportation costs and narrow the economic distance between cities.In addition, We should improve the radiation capacity of central cities and enhance the absorption capacity of small and medium-sized cities. It is suggested to create multilevel and multi-center city clusters and try to establish secondary economic centers.