Relationship between Urban Economic Connections and Geoeconomic Relations in Northeast China

Using Northeast China as the research area and three time nodes (2007, 2012, and 2017), the gravitational model and Euclidean distance method were used to measure the spatial economic connections and geoeconomic relations between four regional central cities and other smallandmedium-sized cities..e complexity of urban economic relations was systematically analyzed based on matching urban economic connections and geoeconomic relations. .is paper provides suggestions on how to strengthen and build a benign and sustainable urban economic relations system in Northeast China..e results of the study show that, from 2007 to 2017, the economic links between the four central cities and other cities continued to strengthen. Shenyang had the highest total of economic links, and Changchun, the fastest growth rate. From 2007 to 2017, the geoeconomic relations between the four central and other cities generally improved, shifting from competitiveness to complementarity. Competition intensified for Shenyang and Dalian with cities in Liaoning province, and their complementarity strengthened with cities outside the province..e relationship between the four central cities with other cities is to strengthen cooperation and complementarity. .erefore, the cities in Northeast China need to strengthen economic ties and the complementarity of geoeconomic relations and optimize the matching relationship..ey should focus on the role of regional central cities in promoting the economic integration of the entire Northeast China and jointly promote the orderly urban niche system and full coordination. .e formation and stability of the developing regional cooperative community are discussed.


Introduction
Cities, as places of interaction and association, are defined as connections with other cities [1]. e study of the spatial interaction between cities has attracted scholarly attention from the perspectives of regional economics, urban geography, and regional geography [2,3]. e urban economic relationship refers to the exchange of commodities, labor services, capital, technology, and information between cities, as well as the relatedness and participatory economic behaviors that occur on this basis [4]. Relevance focuses on the importance of economic ties between cities, reflecting the necessity that cities strengthen exchanges and cooperation, indicating whether the economic ties between them are frequent or occasional, and the quantitative stipulations of the ties. A participatory focus is on the closeness of economic ties between cities, reflecting the potential of cities to strengthen exchanges and cooperation, indicating whether the economic ties between them are competitive or cooperative, and the qualitative stipulations of the ties. As the center of a region, the city maintains economic, political, and cultural ties with surrounding areas and, to a certain extent, promotes or influences the development of these surrounding areas. As such, an urban economic connection is an important indicator of regional development and maturity [5]. Against the background of the continuous deepening of China's market economic system reform and regional open cooperation, the development trend of regional economic integration centered on large cities is becoming increasingly obvious. To enhance the momentum of urban economic growth and optimize the spatial pattern of regional development, the relationship between the central city of the urban agglomeration and peripheral cities [6] as well as the policy cooperation network between different levels of government must be strengthened [7]. Furthermore, the economic competition of urban interests has led to an increasing number of urban economic disputes, and conflicts in the economic field have become a major obstacle to the development of regional integration. e urban economic relationship has always been a hot issue in the study of urban and regional development. e spatial connection of the urban system can be delineated as the network connection, which focuses on large-scale and long-distance connection, and regional connection, which focuses on the connection between neighboring cities. ese indicate the regional global combination state and local cohesion state, respectively [8]. In Mainland China, research on economic links between cities began in the 1990s. e direction theory highlights the impact of economic links on the development of urban space and lays the theoretical foundation for the study of spatial economic links in China [9]. Research on the economic connection between cities is based on the gravitational model and uses traffic flow and product flow data [10]. Furthermore, the gravitational model is based on the analysis of regional influence, and the main direction and degree of intercity connections are determined by this influence [11,12], which reflects a close degree of spatial economic connection between cities [13]. erefore, many scholars have used the gravitational model and its extended models (e.g., economic membership model, urban potential model, urban flow strength model, and break point model) to measure urban economic relationships. Applied to Mainland China, based on the urban flow and urban interaction intensity models, the radiating driving intensity of the three central cities in the middle reaches of the Yangtze River is generally weak [13]. Using the gravity model, based on the strength of the spatial correlation within the nine major urban agglomerations in China, it is believed that it is more difficult for core cities to radiate to the peripheral cities [14]. Finally, the intercity economic connections in China's urban system, urban connections in the Northeast region, and Kunming and its surrounding areas were analyzed based on the gravitational model and urban flow intensity model [15][16][17].
Although the strength of economic ties can explain the frequent state of urban exchanges, it does not reflect whether the economic relationship between cities tends to be competition or cooperation. Geoeconomics refers to the interaction between core and peripheral areas and the impact of the flow of relevant factors on the regional economy [18]. Edward [19] proposed the concept of "geoeconomics" to represent the economic situation and economic relations gradually replacing military confrontation and political relations. For him, geoeconomics is a basic principle and "zero sum" that emphasizes the maximization of business interests. e best description of the basic logic of the "zero sum competitive game" conflict is mixed. Furthermore, geoeconomics refers to a focus on achieving the optimal allocation of personnel and other resources in a larger range.
Geoeconomic relations are mostly used in economic battles between countries [20][21][22][23]. With the deepening of economic globalization and regionalization, geoeconomics has been given a new connotation and significance, and competition between countries is becoming increasingly important [24][25][26][27]. Currently, to reflect the direction of urban economic relations or competition or cooperation, research on the geoeconomic relations of ethnic countries based on territorial boundaries has taken a microturn, providing a new perspective for urban development research [28,29]. Geoeconomic relations are delineated as complementary and competitive. Similarity leads to competition to restrain the economic development of the two places, and complementarity leads to cooperation to promote their economic development [30]. e urban geoeconomic relationship has a significant impact on the amount of urban economic links. Under the same external conditions, the amount of economic links between complementary cities is usually greater than the amount of economic links between competitive cities [31]. Based on an urban geoeconomic relations perspective, the intercity relations between Ningbo and many prefecture-level cities in the Yangtze River Economic Belt, the intergroup relations between the Pearl River Delta urban agglomeration and other urban agglomerations, and the interpersonal relations between the three provinces and two cities in the Bohai Rim region have received much scholarly attention [32][33][34].
Although previous studies had diverse search purposes, methods, and viewpoints, they generally contend that strengthening urban economic ties is important in promoting the economic development and regional economic integration of cities. An analysis of the existing research revealed gaps in the following aspects. First, most research on the economic relationship between cities focuses on the amount of urban economic connections. Although some studies involve the main direction of these connections, the focus is only on primary and secondary relationships that show the importance of the contact partners, not the competition between them. e joint relationship means that the direction of the urban spatial economic connection is not specified. Second, in the urban economic connection network, the urban relationship follows the "advantage connection" rule. is research perspective neglects the role of the central city in the urban complex relationship network. Furthermore, research from the perspective of a single central city cannot reflect the complexity of the urban relationship. ese types of "one-to-many" studies highlight the lack of "many-to-many" ones from the perspective of multiple central cities. ird, many urban economic linkage studies follow the analysis framework of points (urban potential)-line (economic linkage axis)-network (economic linkage network) [35,36]; however, the analytical framework of these works does not respond positively to the development direction of the city's economic connections, and research on the complex competition or cooperation between cities is weak. Finally, while the use of high-speed rail and aviation data, online goods services, and intercompany investment data has important practical significance for the study of intercity economic links [37][38][39][40][41][42], the measurement 2 Complexity of urban economic links based on traffic flow, product flow, and capital flow is restricted by limited data accumulation. ese data reflect the spatiotemporal evolution of urban economic relations over a long period. erefore, based on the urban connection theory and regional development theory, three important time nodes of 2007, 2012, and 2017 were selected. e Northeast region was selected as the research area for this study, and the four regions of Shenyang, Dalian, Changchun, and Harbin were chosen as the central cities. en, using the urban economic connection strength model and economic connection membership model, the importance of the economic connection between the four major regional central cities and other cities in the Northeast region was measured. Following this, based on the urban geoeconomic relationship model, the direction of the economic competition and cooperation between the four major regional central cities and other cities in Northeast China was measured. Finally, based on the matching relationship between urban spatial economic connections and urban geoeconomic relations, we examined the complexity of urban economic relations in the Northeast region. is study hopes to provide a reference for the regional economic integration of Northeast China and improve the misaligned development of central and peripheral cities, and complementary advantages.

Study Area.
Northeast China, as an important old industrial base in China [43], is also a relatively complete regional economic sector. From the perspective of the national development strategy, historical development accumulation, and geographical development environment, Northeast China has a very important strategic position. However, the region is facing structural difficulties and institutional contradictions, and the administrative system and government functions are becoming increasingly unsuitable for marketization. Furthermore, the phenomenon of a "strong government and weak market" in cities in Northeast China is very prominent [44].
e Northeast China, referred to in this paper, includes 40 prefecture-level cities (regions, autonomous prefectures, and leagues) in Liaoning Province, Jilin Province, Heilongjiang Province, and Inner Mongolia Autonomous Region, as shown in Figure 1. Some leading cities in the Chinese urban system act as command and control centers, and the unidirectional control relationship from the core city to the small-and medium-sized cities is stronger, and the horizontal connection between the cities appears slightly weaker [45]. e regional spatial development of this area is unbalanced. Shenyang, Dalian, Harbin, and Changchun, as four subprovincial cities in Northeast China, are not only the economic centers of this area, but also the core hub cities of regional transportation. e flow of resources such as transportation and human resources has a radiating effect on other cities in the region and plays a dominant role in the region through agglomeration and diffusion effects [46,47]. Northeast China is a complete geographical unit. us, the functional positioning and coordination of the development of the four central cities involve the overall development of the region [48]. To achieve high-quality development in Northeast China, the leadership of the four regional central cities must be brought into play.

Data Sources.
e administrative boundary data was derived from the national geographic information resource directory service system (http://www.webmap.cn).
is study focuses on the spatial interaction of cities in Northeast China, where highway passenger and freight transportation account for the largest proportion of transportation modes in the region, and spatial distance changes significantly with the level of economic development [16]. Compared with the spatial distance based on the length of road mileage, the time-cost distance is a time metric for evaluating a certain city node in comparison to others. is metric is used to measure the city's level of accessibility from a time-saving time perspective and can intuitively express accessibility and changes therein [49][50][51]. erefore, to determine the distance between cities, time-cost distance was measured by converting the highway operating mileage between the urban areas of the two cities according to the highway speed in different periods. According to the highway engineering technical standards (JTG B01-2003 and JTG B01-2014), and the road and actual driving conditions in Northeast China, the driving speed of highway transportation in 2007, 2012, and 2017 was set and the time-cost per kilometer calculated (Table 1). e flow and connection of factors between regions generally flow from areas with low production efficiency to those with high production efficiency, and from areas with relatively abundant factors to those with relatively few elements. With reference to previous research results [31,52,53], this study used the time cross-sectional data of 40 prefecture-level administrative units in the northeast region in 2007, 2012, and 2017, including regional GDP; secondary and tertiary industry regional GDP; and socioeconomic data such as total fixed asset investment, year-end financial institution deposit balance, total employee wages, and annual import and export total. Five comprehensive indicators were selected to reflect the liquidity of products and resources, as shown in Table 2. Excel2019, SPSS23.0, and ArcGIS10.7 were used for the mathematical analysis, model calculation, and visual expression.

Measuring Method of Urban Spatial Economic
Connection. To measure the strength of economic ties between cities, the gravitational model was used to reflect the radiation capacity of the central city and degree of acceptance of the surrounding cities [10]. Based on the first law of geography, the gravitational model further considers the dual effects of city size and spatial distance [54]. e effectiveness of the gravitational model in expressing humane economic phenomena has been confirmed, and many reasonable theoretical deductions have been obtained therefrom. e model is favored for its simple form and high Complexity generalization of spatial interaction phenomena [55]. Two indicators-urban economic connection strength and economic connection membership-were employed to quantify the central city's ability to radiate the economy of surrounding cities and the surrounding city's ability to accept the central city's radiating ability. e following are the calculation formulas for the strength of urban economic ties and membership of economic ties [16,56]:

Complexity
where R ij is the strength of economic ties between cities i and j, L ij is the degree of affiliation of economic ties between cities i and j, P i and P j are the population of cities i and j, respectively, G i and G j are the regional GDP of cities i and j, D ij is the time distance between cities i and j, n represents the number of cities studied, andα is the gravitational constant with a value of 1.0. Finally, β is the distance attenuation index, and when the values are 1.0 and 2.0, respectively, it can more truly reflect the urban radiation effect at the national and provincial scales [15,57]. Since this study focused on the Northeast region, it is closest to the provincial scale; thus, the value of β is 2.0.

Measuring Method of Urban Geoeconomic
Relationship. e widely used Euclidean distance [17,30,52,53,[58][59][60][61] is scientifically valid and has become the main method for measuring the geoeconomic relationship between cities or regions [62]. us, Euclidean distance was employed in this study to evaluate the geoeconomic relationship between Shenyang, Dalian, Harbin, Changchun, and other cities.
Here, "distance" does not refer to the geographic spatial distance, but the difference between cities measured by selected economic indicators. e smaller the distance, the smaller the difference between the two cities and the stronger the competition. Conversely, the larger the distance, the greater the difference between the two cities and the stronger the complementarity.
To effectively reduce dimensional differences in data processing, the five comprehensive indicators in Table 2 were standardized, and the five processed indicators were X * , Y * , Z * , T * , and S * . e formulas are as follows: whereX * is the standardized value of the data of X, X is the average value of the data of X, S X is the standard deviation of the data of X, and n is the number of each piece of data. Similarly, the standardized values ofX, Y, Z, T , and S can also be obtained.
are the central cities of the study, then the formula for calculating the Euclidean distance from another city is where i is the serial number of other cities except the central city, and To facilitate the judgment of the results, the value of the Euclidean distance is standardized, and the calculation formula is as follows:  Total wages of employees in a certain area/gross GDP for that year Regional labor efficiency T GDP of the secondary and tertiary industries in a certain area/GDP of that area in the current year Regional urban economic development capacity S Total annual export volume of a certain area/total annual import volume of that area Regional resources' and products' outward flow capacity Complexity where D i is the average value of the Euclidean distance from the city to other cities, and S D i is the standard deviation of the Euclidean distance from the city to other cities.

Spatial and Temporal Evolution of Urban Spatial Economic Relations in Northeast
China. Using formula (1), the strength of economic ties and degree of economic affiliation of 39 cities with the central cities of Shenyang, Dalian, Changchun, and Harbin can be calculated separately. Based on the degree of economic ties between two cities, they can be divided into four categories: very strong connection type (L ij > 5%), generally strong connection type (1% < L ij ≤ 5%), generally weak connection type (0.5% < L ij ≤ 1%), and very weak connection type (L ij ≦ 0.5%), as shown in Figure 2.
For economic ties, for the three time points from 2007 to 2017, Shenyang ranks first among the four major cities from the beginning to the end, followed by Changchun and Harbin, and then Dalian. However, the growth rate of Changchun's total economic ties is the fastest, followed by Harbin and Dalian, and Shenyang has the slowest. Regarding economic affiliation, of the four central cities, Shenyang and Dalian have an economic affiliation with a higher proportion of cities in the province than with those outside it, but this proportion is gradually declining. Outside the province, Changchun and Harbin have a high degree of economic affiliation. at in Changchun Province is slowly increasing, while Harbin is showing a downward trend.
For the central city of Shenyang, the total amount of economic connections is increasing, although this first increased and then decreased as follows: an increase of 2. is was 19.29%, 19.96%, and 21.83% at the three time points, respectively. Shenyang, Anshan, and Changchun have always had strong links with Dalian, but in 2017 Changchun surpassed Anshan and took the second place. From a spatial viewpoint, Dalian is closely connected with the cities in the province, while outside the province it has strong ties with Changchun and Harbin. For the central city of Changchun, the total amount of economic ties has continued to increase: from 926.3 million in 2007 to 2876.7 million in 2017, a 3.1-fold increase in 10 years. At the three time points from 2007 to 2017, the economic affiliation of Changchun and the cities in the province demonstrated a growth trend: 32.12%, 33.61%, and 33.29%, respectively. Changchun and other cities in Jilin province had a relatively low total degree of affiliation, while the total degree of affiliation with cities outside Jilin province is 66%, among which the degree of affiliation with Liaoning is the highest: 35.48%, 34.7%, and 32.83% at the three time points, respectively. Although there is a downward trend, it still accounts for a high proportion. Among the 39 cities, Harbin, Jilin, and Shenyang have always had relatively strong economic ties with Changchun. From a spatial viewpoint, except for the cities of Baicheng and Yanbian and the prefectures in Jilin Province, the links between cities and Changchun were slightly weaker, and the strength of economic links between other cities and Changchun was relatively high. In addition to the strength of the economic links between Changchun and Shenyang, Harbin, and Dalian, the cities of Daqing, Suihua, Tongliao, Anshan, Fushun, and Tieling have relatively strong economic ties. From a spatial viewpoint, Changchun has strong ties with Jilin and Songyuan in the province, economic ties with other cities in the province are relatively weak, and ties with Shenyang and Harbin outside the province are relatively strong.
For the central city of Harbin, the total amount of economic ties has increased 2.84 times in 10 years, from 916.6 million in 2007 to 2606.23 million in 2017. e affiliation of Harbin and cities in the province is declining slightly: 37.51%, 36.91%, and 37.14% at the three time points, respectively. Furthermore, the degree of affiliation with cities outside the province is relatively high: the province has the largest city subordination, followed by Liaoning, and the five cities in the Inner Mongolia District have the smallest. e top three cities with economic ties to Harbin are Changchun, Daqing, and Suihua. In 2017, Suihua surpassed Daqing to become its second-largest economically connected city. From a spatial perspective, except for the six cities of Qiqihar, Jixi, Daqing, Jiamusi, Mudanjiang, and Suihua, the economic strength of Harbin and other cities in the province is not very strong.

Spatial and Temporal Evolution of Urban Geoeconomic
Relations in Northeast China. Using formulas (2)-(4), the Euclidean distance and its normalized value between Shenyang, Dalian, Changchun, and Harbin and 39 other cities in Northeast China can be calculated separately. According to the classification scheme of other scholars [63,64], combined with the actual situation in the Northeast region and  2012, and 2017, Changchun's geoeconomic relations with the province and Liaoning have generally tended to compete, but the degree of competition has eased. In contrast, competition with Hulunbeier in Inner Mongolia has intensified. Although the relationship with Tongliao City is complementary, the degree is decreasing, and while the relationship with Heilongjiang is mostly complementary, the overall degree of complementarity is also decreasing.
With Harbin as the central city, the geoeconomic relationship between Harbin and other cities from 2007 to 2017 changed from being more competitive than complementary to more complementary than competitive. In 2007, 24 cities were in competition with Harbin and 15 were complementary. By 2017, the number of cities in competition with Harbin decreased to 17, and the number of complementary cities increased to 22. is shows that the geoeconomic relationship between Harbin and other surrounding cities is gradually becoming complementary, and the possibility of cooperation with other cities is increasing. From a spatial perspective, in 2007, 2012, and 2017, the geoeconomic relationship between Harbin and Liaoning Province has tended to be complementary. Except for Benxi, Panjin, and Yingkou, the other cities were complementary in 2017. e cities in Jilin Province were all competing in 2017, except for Songyuan City, which was complementary. Furthermore, the degree of competition is intensifying. e four urban areas of Inner Mongolia are both complementary and competitive, although the overall degree of competition is gradually intensifying. Finally, the degree of competition between Harbin and the cities in the province is also intensifying, except in Hegang and Yichun.

Discussion
To better investigate the complexity of urban connections in Northeast China, the above classification of economic connections and level of geoeconomic relations was used to match and analyze these connections and relations of the four central cities in Northeast China. Figure 2 provides the matching results. e five categories of matching relationships were as follows: Deepening cooperation type with strong economic connection and strong complementarity; adjustment strategy type with strong economic connection and strong competitiveness; strengthening cooperation type with strong complementarity and weak economic connection; strengthening cooperation adjustment strategy type with strong competition and weak economic connection; strengthening cooperation and strengthening complementarity type with weak economic connection and general competition or complementarity.
According to the matching situation of the four central cities' economic ties and geoeconomic relations, Harbin has the best matching situation, with good cooperation relationships or cooperation space with 39 other prefecture-level administrative units. Furthermore, while Shenyang has close economic ties with other regions, it has more competitive relationships, especially with other cities in Liaoning Province.
In 2017, the central city of Shenyang had a deepened cooperation with Harbin. e number of cities that For the central city of Changchun, no cities had deepened cooperation with Changchun in 2007, two did so in 2012, and one in 2017. Four cities strengthened cooperation with Changchun, and the number of cities categorized for the three types of strategic adjustment remained four. Cities that strengthened cooperation and adjusted their strategic strategies with Changchun increased from 2 to 3, and those that strengthened cooperation and enhanced complementarity decreased from 29 to 27. e four cities of Shenyang, Harbin, Jilin, and Siping are economically connected with Changchun and have competitively adjusted their strategic geoeconomic matching relationships. Shenyang and Harbin, as the capitals of Liaoning and Heilongjiang Provinces, are closely connected with Changchun's economic ties, and their competition is relatively strong. Songyuan and Changchun are categorized as having a deepening cooperation-based geoeconomic matching relationship. Songyuan is adjacent to Changchun and is the destination of industrial transfer in Changchun. e industrial division of labor and cooperation between the two cities is close.
For the three time points of 2000, 2012, and 2017, the number of cities that have deepened cooperation with Harbin has decreased from 4 to 2, the number of cities that have strengthened cooperation has been stable at 4, the number of cities that have adjusted their strategy has increased from 0 to 3, the number of cities that have strengthened cooperation and adjusted their strategy has remained 2, and the number of cities that have strengthened cooperation and enhanced complementarity has decreased from 29 to 28. In the three time points from 2000 to 2017, Shenyang, Changchun, Jilin, Suihua, and Daqing have had strong economic ties with Harbin, but the competitiveness of these five cities has changed greatly. Until 2017, Shenyang and Suihua had a deepened cooperation with Harbin, while the ties with Changchun, Daqing, and Jilin are categorized as the strategic adjustment type.

Conclusions
Based on urban spatial economic connections and urban geoeconomic relationships, as well as the matching results, the complexity of the urban economic relationship between the four central cities in Northeast China and other cities was analyzed in three dimensions. e following conclusions were drawn. For the period 2007-2017, the economic links between the four central cities in Northeast China and other cities became closer, reflecting the acceleration of regional integration in Northeast China. Shenyang had the highest number of economic links, followed by Changchun, Harbin, and Dalian. Changchun has the fastest growth rate, followed by Harbin, Dalian, and Shenyang. Shenyang's economic ties with Anshan, Fushun, and Liaoyang are important, and they are in competition with cities in the province and demonstrate complementarity with those outside the province. Shenyang has a strong competitive relationship with cities with strong ties, and weak economic links with those with strong complementarity. Dalian has prominent connections with Shenyang, Anshan, and Changchun. Its geoeconomic relationship with other cities is more complementary than competitive, and it is most competitive with cities in the province. e three cities with the strongest economic ties with Changchun are Harbin, Jilin, and Shenyang, which are central cities with more competitive than complementary cities. ey also have a relatively good matching relationship with other cities; for example, Suihua, Daqing, and Changchun are the three most important cities in economic connection with Harbin. e geoeconomic relations with other cities are generally more complementary than competitive, but the strength of economic ties with complementary cities is weak. In terms of matching relationship types, Harbin is the best performer among the four central cities. Harbin and most small-and medium-sized cities are types that strengthen cooperation and complement each other.
e relationship between cities in Northeast China has obvious complexity. Among the four regional central cities, Shenyang has the most important urban economic connection status in Northeast China, while Dalian is a relatively weak regional central city.
e relative importance of Complexity 9 Changchun and Harbin has been improved significantly over the last ten years. is is closely related not only to the geographical location of the city, but also to the strategic direction of urban and regional development. e basintype city pattern in Northeast China embodies the new urban relationship model under the network development of the urban system. Shenyang is a resource distribution center and communication window for the entire Northeast China, with a very high degree of urban connection and a high urban system [16]. Considering Northeast China as a relatively closed geographical unit, Dalian has the characteristics of being a terminal location, making it a "Continental-driven development city" in Northeast China that "embraces the ocean" based on its location in a coastal area in China. Dalian's future lies in the construction of an ocean-centric city and international shipping hub to stabilize the old industrial base and develop an open economy. Shenyang and Dalian serve as "land windows" and "sea windows" for interregional connections in Northeast China, and as bridges between Northeast China, the Beijing-Tianjin-Hebei region, and China's coastal regions. As such, they continue to weaken the "siphon effect" of the city. Changchun and Harbin, as "middle-stream cities" in Northeast China, should play a leading role in the integrated development of the Kazakh-City agglomeration and north-central part of Northeast China and better connect with the Shenyang economic zone and Liaoning coastal economic zone. To this end, we propose the following three policy countermeasures and suggestions to guide the construction of a new type of urban relationship model in Northeast China and promote the optimal and coordinated development of regional central cities and peripheral smalland medium-sized cities. e first suggestion is to conform to the laws of economic development, regulate the urban ecological potential, and operate overall regional functions. In different stages of urban economic development, the relationship between cities exhibits the evolutionary law of "antagonistic competition-dislocation competition-cooperative competition," and out-of-date or out-of-place development concepts will cause more or less negative harmonious development between cities and regions. It is necessary to make full use of complementary geoeconomic relations and deal with competitive ones. Urban function positioning needs to advance with time, adapt to local conditions, and make strategic adjustments according to the required development factors and the environmental situation. e second suggestion is to actively develop regional central cities and build a new model of urban relations. e formation of a reasonable division of labor system should be accelerated, a cooperative incentive mechanism implemented, comprehensive transportation networks as well as solid and solid industrial support systems optimized, and the vitality of economic development boosted in Northeast China. e focus should be on the construction and maintenance of the four regional central cities of Shenyang, Dalian, Harbin, and Changchun, and the urban group in the middle-southern part of Liaoning Province and the Harbin-Changchun urban agglomeration optimized. is is to form a supporting and coordinated urban regional division of labor between the node and core cities. e background of geographic resources and the environment should be promoted; the flow of social and economic stocks activated; the flow of information, knowledge, and talent promoted; and the endogenous power of high-quality urban development enhanced. Finally, measures should be adapted based on the combination of matching relationships in different cities. For cities that are strategically adjusted, full advantage must be taken of the large amount of connections, and cooperation channels must be actively increased to enhance the complementarity between the two places. Furthermore, the industrial structure should be adjusted to reduce friction losses. For cities with deepened cooperation, it is necessary to actively promote industrial cooperation transfer and allround open cooperation. For cities that are cooperationoriented, it is necessary to increase the degree of economic ties between the two places, with a focus on strengthening cooperation in areas with higher economic ties.
is study focused on the relationship between regional central cities and peripheral small-and medium-sized cities and clarified the impact of urban economic connections and geoeconomic relations on the complexity of urban economic relations. Previous studies did not consider the overall importance and direction of urban economic links in the regional urban system by multiple central cities, especially in Northeast China.
is study addresses this research gap. e complexity research has important reference value and significance. However, in terms of urban spatial economic connections and urban geoeconomic relations, the study has some limitations. e connection between cities is reflected in many aspects such as the flow of commodities, labor, capital, technology, and information. e distance between cities is not only covered by road transport, and the index of measuring city geoeconomic relationship should be improved and supplemented. For example, this study did not consider that manufacturing and service industries have different effects on the uneven development of the urban system [65]. In addition, the classification of various urban economic relations was relatively subjective in this study. erefore, future research should improve the measurement model and evaluation criteria of urban economic connections and geoeconomic relations.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request. Disclosure e funding sources had no role in the study design, data collection, analysis, or interpretation, or the writing of this manuscript.

Conflicts of Interest
e authors declare that there are no conflicts of interest. 10 Complexity