Study on the Effects and Influencing Factors of the Economic Spatial Correlation Network in the Yellow River Basin

Renquan HUANG, Qian ZENG, Yinong SI

Journal of Systems Science and Information ›› 2024, Vol. 12 ›› Issue (5) : 690-708.

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Journal of Systems Science and Information ›› 2024, Vol. 12 ›› Issue (5) : 690-708. DOI: 10.21078/JSSI-2023-0163
 

Study on the Effects and Influencing Factors of the Economic Spatial Correlation Network in the Yellow River Basin

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Abstract

This paper constructs high-quality development assessment indicators based on the perspective ternary system, including economic development, technological innovation, and ecological environment systems. Based on the data of 51 regions in the Yellow River Basin from 2010 to 2021, the economic spatial correlation relationships were constructed. By using social network analysis and the QAP method, the economic spatial correlation characteristics and the influencing factors are deconstructed. The results show that: 1) The regions exhibit significant variations in comprehensive quality and economic connectivity. Zhengzhou, Xi'an, Jinan, Luoyang, and Zibo are the top five regions. Regions with high comprehensive quality tend to have stronger economic ties. The economic links show an obvious "upstream-midstream-downstream" three-tier structure. 2) Regions such as Xi'an, Zhengzhou, Jinan, Taiyuan, Ordos, Luoyang, Baotou etc., exhibit high degree and betweenness centrality, and low closeness centrality. Those are the core regions of high-quality development in the Yellow River Basin. Block Ⅰ is the core block and spills to Block Ⅱ, Block Ⅲ, and Block Ⅳ. Block Ⅱ plays an essential bridge role to Block Ⅲ. 3) The factors of spatial adjacency, fixed asset investment, employment, informatization, and innovation are key to spatial correlation, and explain 40.5% of the spatial correlation.

Key words

Yellow River Basin / spatial correlation / social network analysis / QAP regression

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Renquan HUANG , Qian ZENG , Yinong SI. Study on the Effects and Influencing Factors of the Economic Spatial Correlation Network in the Yellow River Basin. Journal of Systems Science and Information, 2024, 12(5): 690-708 https://doi.org/10.21078/JSSI-2023-0163

1 Introduction

The Yellow River Basin, as one of the most important economic regions in China, plays a significant role in the country's development[1,2]. Grasping the impact and factors of the Yellow River Basin's economic spatial correlation network is vital for advancing regional integration and sustainability. According to Outline of the Yellow River Basin's Ecological Protection and High-quality Development Plan[3], it points out that the economic connectivity among provinces and regions along the Yellow River has historically been limited due to geographical constraints and other factors. Additionally, there is a lack of awareness regarding regional division of labor and cooperation, and the mechanism for efficient and coordinated development remains incomplete. Spatial effects between regions impact China's regional economic growth[4]. The central government emphasizes coordinated regional development and enacts strategies to enhance economic ties and interactions, including in the Yellow River Basin[5]. Market reforms promote the free movement of production factors and goods, with the market's "invisible hand" creating complex economic connections in the region.
Some research has been done on the ecological protection and high-quality coordinated development of the Yellow River Basin. Scholars have studied the coordinated development among various systems in the Yellow River Basin, including economic growth, industrial development, and ecological environment[6], agroforestry economic and ecological environment[7], population, economy and environment[8]. The coupling coordination among these systems shows an increasing trend but remains at a relatively low level overall. The coordinated development of city clusters in the Yellow River Basin has been explored. City clusters have become the most dynamic and promising core areas in the economic development pattern of the Yellow River Basin[9]. However, there are disparities in the high-quality development among the seven major city clusters in the basin[10], and significant internal differentiation within the city clusters[11]. It is necessary to promote the high-quality development of the Yellow River Basin by integrating city clusters with industrial transformation and development space[12]. The spatial correlation in the Yellow River Basin has been studied. Scholars have constructed spatial correlation network models of the Yellow River Basin based on the ideas of multipolar network spatial organization[13], gravity model[14], population migration[15], and coupling coordination[16]. They have used theories such as social network analysis (SNA) and complex networks to study the network characteristics. The results suggest that the spatial coordination problem in the Yellow River Basin is prominent, and exploring spatial coordinated governance mechanisms is key to achieving high-quality development.
Scholars have extensively investigated spatial correlation concerns pertaining to ecological protection and high-quality development in the Yellow River Basin, yet several limitations persist. Firstly, the assessment of high-quality development in the Yellow River Basin mainly relies on the Five Development Concepts (innovation, coordination, green development, opening up, and sharing)[11], and the research focuses on provinces and regions, with less emphasis on prefecture-level areas. Secondly, some scholars have used traditional spatial econometric models for research, which limits the spatial correlation to geographical "adjacency" or "proximity". Thirdly, the existing research mainly focuses on the analysis of spatial correlation characteristics, with insufficient research on the factors influencing spatial correlation relationships.
In this regard, this paper may contribute in the following aspects: Firstly, it evaluates the quality of development based on the synergistic development concept of the ternary systems, which include economic development, technological innovation, and ecological environment. It analyzes the economic spatial correlation characteristics based on the modified gravity model. Secondly, it uses SNA to reveal the structural characteristics of the spatial correlation network for 51 regions in the Yellow River Basin. Thirdly, to objectively reflect the laws of economic spatial correlation in the Yellow River Basin and identify the key areas for efficient and coordinated development, the Quadratic Assignment Procedure (QAP) model is used to explore the main factors influencing spatial correlation relationships.
The remainder of this paper is organized as follows: Section 2 presents the research methods. Section 3 analyzes the characters of the spatial correlation. Section 4 presents the results of the social network analysis. Section 5 analyzes the influencing factors by QAP. Section 6 presents the conclusions and suggestions.

2 Methods

2.1 Assessment of Development Quality

Based on the literature review on high-quality development[17], it is found that economic development, technological innovation, and ecological environment are the core systems of high-quality development. There is a continuous exchange of economic, technological, and material energy among these three systems. Figure 1 shows the synergistic development mechanism of the ternary systems. The ecological environment system provides material for economic development and technological innovation systems. The economic development system provides economic support for technological innovation and the ecological environment systems. The technological innovation system provides technical support for the economic development system and ecological environment system.
Figure 1 The synergistic development mechanism of the ternary systems

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High-quality development assessment is complex, especially for the indicators. Based on the research of Huang and Dong[18], this paper constructs high-quality development assessment indicators that include three subsystems: Economic development, technological innovation, and ecological environment system. The indicators of high-quality development are structured into three layers: System layer, criterion layer, and indicator layer. These layers are outlined in Table 1 for a comprehensive understanding.
Table 1 The index of comprehensive quality evaluation
System layer Criterion layer Indicator layer
Economic development Economic level Gross regional product (GDP) (100 million Yuan)
GDP per capita (Yuan)
GDP growth rate (%)
Reduction rate of energy consumption per unit of GDP(%)
Investment in fixed assets (%)
Resident savings deposits (100 million Yuan)
Local revenues (100 million Yuan)
Average consumer spending per person (Yuan)
Industrial structure Secondary sector/regional GDP (%)
Tertiary sector/regional GDP (%)
Gross industrial output (100 million Yuan)
Total profit of industrial enterprises (100 million Yuan)
Employment in secondary industry/employment (%)
Tertiary employment/employment (%)
Domestic and international trade The total value of foreign trade imports and exports (10 thousand Yuan)
Actual utilization of foreign direct investment (10 thousand US dollars)
Total retail sales of consumer goods of the whole society (10 thousand Yuan)
Social development Number of employed persons/total population (%)
Annual disposable income per urban resident (Yuan)
Average wage of employees (Yuan)
Technological innovation Innovative resources R&D personnel (person)
Number of R&D organizations (unit)
Number of domestic listed companies (unit)
Number of graduates from general higher education institutions (10 thousand people)
Financial sector employees (10 thousand people)
Innovative input Internal Expenditures on R&D Funding (10 thousand Yuan)
Expenditures on science and technology (100 million Yuan)
R&D government funding/internal expenditure on R&D funding (%)
Innovative finance Balance of RMB loans to financial institutions (100 million Yuan)
Total securities transactions (100 million Yuan)
Gross market value of shares (100 million Yuan)
Premium income from insurance organizations (10 thousand Yuan)
Innovation output Amount of technology market contracts (100 million Yuan)
Number of scientific and technical papers (unit)
Patent applications authorized (case)
Ecological environment Ecological pressure Industrial wastewater discharge (10 thousand tons)
Industrial sulfur dioxide emissions (ton)
General industrial solid waste generation (ton)
Ecological level Forest area/total population (hectares)
Urban per capita green space in parks (square meters)
Greening coverage of built-up areas (%)
Ecological protection Total investment in environmental pollution control (10 thousand Yuan)
Total sewage charge revenue (10 thousand Yuan)
Forestry investment completion for the year (10 thousand Yuan)
The indicators reflecting economic development include economic level, industrial structure, domestic and international trade, and social development[19,20]. There are a total of 20 indicators at the indicator layer, all of which are positive indicators. The indicators reflecting technological innovation include innovation resources, innovation input, innovation finance, and innovation output[2123]. There are a total of 15 indicators at the indicator layer, all of which are positive indicators. Since finance plays an important role in technological innovation, some indicators reflecting technology finance are included in the technological innovation system. The indicators reflecting the ecological environment include ecological pressure, ecological level, and ecological protection[2426]. At the indicator layer, there are a total of 9 indicators, out of which 3 indicators reflect ecological pressure and are considered negative indicators. The remaining six indicators are positive. Based on the above, the comprehensive quality of a region could be obtained by the TOPSIS model[27,28].

2.2 Modified Gravitational Model

The gravity model is widely used in the fields of regional economic spatial connection and geographic distance attenuation[29]. Based on the research of Peng[30], a revised model has been derived as follows:
Fij=GMiMjeβijdij,
(1)
Fi=jFij=jGMiMjeβijdij,
(2)
where Fij is the intensity of economic spatial action between regions i and j; Fi is the sum of economic spatial action intensity to region i; G is the gravitational parameter, which is taken as 1; βij is the attenuation factor to the intensity of economic correlation between regions i and j, which is taken as 0.001; dij is the distance between regions i and j, which is expressed in kilometers; Mi and Mj are the comprehensive qualities of regions i and j, respectively, obtained by the TOPSIS. With the average value of each indicator from 2010 to 2021, the comprehensive quality of each region Mi was calculated.
To further characterize the direction of "radiation" and "absorption" between regions in the Yellow River Basin, the interaction relationship is further subdivided:
Rij=GMiMi+MjMiMjeβijdij,
(3)
Pi=jRij=jGMiMi+MjMiMjeβijdij,
(4)
Rij=GMjMi+MjMiMjeβijdij,
(5)
Ni=jRij=jGMjMi+MjMiMjeβijdij,
(6)
where Rij indicates the intensity of region i to j, which is manifested as the "radiation" effect, i.e., radiative force; Pi represents the total "radiation" intensity from region i to other regions; Rij indicates the intensity of region j to i, which can be regarded as the "absorption" effect, i.e., absorptive force perceived by region i; Ni is the sum of the external "absorption" intensity to region i.

2.3 Social Network Analysis Method

Social network analysis (SNA) is a quantitative analysis method developed by sociologists based on mathematics, and graph theory[31]. It is used to analyze the structure of social relations and their attributes. In recent years, it has been widely used in the study of various types of network organization structures. Some scholars have employed this method to analyze regional spatial correlation networks, examining the fundamental network characteristics exhibited by the associated regional correlation network[32,33]. This paper applies SNA to analyze the network properties, centrality, cohesive subgroups, and block models based on the regional economic spatial correlation network in the Yellow River basin. The analysis of network properties focuses on network density, average distance, transferability, clustering coefficient, etc., to analyze the network characteristics. The centrality analysis of the network is carried out in the following three aspects. First, degree centrality describes the connectivity ability of nodes (regions); Betweenness centrality describes the control ability of nodes (regions); while closeness centrality portrays the ability of nodes (regions) to be uncontrolled. Second, in cohesive subgroup analysis, the core-edge analysis could identify whether the regions in the Yellow River Basin are in the core or edge position of development. Third, block model analysis can divide the regions of the Yellow River Basin into different blocks and study the interlinkages between the blocks.

2.4 Quadratic Assignment Procedure Analysis Method

The quadratic assignment procedure (QAP) is a technique used to assess the similarity between individual elements in two square matrices. This involves comparing the correlation coefficients derived from the comparison of individual elements in the square matrices. The resulting coefficients are then subjected to a nonparametric test[34]. In order to perform a comprehensive QAP analysis, it is necessary to establish a relationship matrix that encapsulates the various attributes of distinct regions. The specific method is: For a specific attribute of regions i and j, such as GDP, the attribute value at the intersection of regions i and j in the matrix is coded as 1 if the value is both greater or less than the mean value, and 0 otherwise. QAP is a hypothesis testing method about the correlation of two relationships. This paper applies this method to correlation analysis and regression analysis of the influencing factors to the economic spatial correlation network in the Yellow River Basin. QAP correlation analysis is used to test the correlation between the area attribute relationship matrix and the spatial association network relationship matrix. QAP regression analysis is used to quantitatively identify the extent to which area attribute relationship matrices influence spatial association network relationships. In this paper, the number of random samples in QAP is set to 5000 times. The significance level is evaluated by the matrix fitting coefficient and regression equation determination coefficient R2 in the random test.

2.5 Data Description

Considering the availability of the data, this paper selects 51 regions in the Yellow River Basin from 2010 to 2021 as the research object. The data involved in this paper is mainly from the EPS data platform and the statistical yearbook of each region. In certain years where data is missing, it is obtained through trend extrapolation and interpolation methods. The distance between regions is taken as the straight-line distance between the governmental seats, the latitude and longitude of which are obtained from the Gaode map. The spatial adjacency data is obtained as to whether the regions are geographically adjacent. If they are adjacent, the value is taken as 1. Otherwise, it is 0.

3 Characters of the Spatial Correlation

3.1 Differences in the Comprehensive Quality and Economic Correlation Intensity Between Regions

Based on the TOPSIS model and Eqs. (1)(6), the comprehensive quality and economic correlation intensity of each region in the Yellow River Basin are presented in Table 2 (sorted by comprehensive quality Mi) from 2010 to 2021. According to of regions, the first region is Zhengzhou (80.96), which is 18 times of Zhongwei (4.50). The last five regions are Tongchuan, Wuwei, Wuzhong, Baiyin, and Zhongwei, with an average value of the comprehensive quality of 5.49. The top five regions are Zhengzhou, Xi'an, Jinan, Luoyang, and Zibo, with an average value of the comprehensive quality of 57.01. It is 10.39 times the average value of the last five regions.
Table 2 Characteristics of the regions during 2010–2021
Regions Mi Pi Ni PiNi Fi Regions Mi Pi Ni PiNi Fi
Zhengzhou 80.96 38048.61 11910.38 26138.23 49958.99 Baoji 14.08 2920.46 4802.07 1881.61 7722.53
Xi'an 72.38 29900.17 10143.04 19757.13 40043.21 Xining 13.70 2094.40 3308.84 1214.44 5403.24
Jinan 58.40 23659.79 10759.06 12900.73 34418.86 Yuncheng 12.77 2956.72 5545.14 2588.41 8501.86
Luoyang 41.01 16098.67 10491.21 5607.46 26589.88 Changzhi 11.99 2762.64 5564.95 2802.31 8327.59
Zibo 32.31 10088.22 8427.13 1661.09 18515.36 Qingyang 11.79 2382.69 4566.75 2184.06 6949.44
Ordos 31.23 9793.70 7583.18 2210.52 17376.88 Linfen 11.53 2578.01 5274.40 2696.39 7852.41
Jining 30.58 10047.50 8854.60 1192.90 18902.10 Yan'an 11.35 2409.09 4846.92 2437.83 7256.01
Taiyuan 29.46 10235.74 8753.90 1481.84 18989.64 Lvliang 11.00 2338.69 4899.17 2560.48 7237.86
Dongying 28.31 7928.05 7471.37 456.68 15399.41 Wuhai 10.95 1888.84 3729.34 1840.50 5618.18
Heze 27.91 9262.92 8852.85 410.08 18115.77 Datong 10.83 1997.10 4261.60 2264.50 6258.70
Dezhou 26.25 8171.52 8174.32 2.79 16345.84 Hebi 10.38 2153.23 5051.27 2898.04 7204.51
Lanzhou 24.89 5817.41 5375.23 442.18 11192.65 Jincheng 9.77 1977.01 4837.59 2860.58 6814.59
Yulin 23.62 7101.03 7213.55 112.52 14314.58 Shuozhou 9.04 1571.01 3936.28 2365.27 5507.28
Taian 23.02 6639.70 7656.49 1016.79 14296.19 Tianshui 8.62 1261.48 3175.96 1914.49 4437.44
Liaocheng 22.94 6970.27 7965.26 994.98 14935.53 Dingxi 8.50 1192.81 2975.81 1783.00 4168.62
Xinxiang 21.96 6886.73 8146.31 1259.57 15033.04 Xinzhou 8.22 1411.20 3908.88 2497.69 5320.08
Hohhot 21.38 5392.74 6038.75 646.01 11431.49 Shizuishan 7.48 1030.77 2871.71 1840.94 3902.48
Jiaozuo 21.31 6617.07 8010.19 1393.13 14627.26 Bayannur 7.34 939.44 2694.51 1755.07 3633.94
Baotou 21.31 5384.71 5956.29 571.58 11341.00 Shangluo 6.85 985.52 3270.76 2285.24 4256.28
Binzhou 20.02 5044.40 6586.36 1541.96 11630.77 Tongchuan 6.46 918.78 3147.42 2228.64 4066.20
Xianyang 20.01 5397.75 6662.40 1264.66 12060.15 Wuwei 6.19 617.02 2004.40 1387.38 2621.42
Anyang 18.96 5547.35 7444.37 1897.02 12991.72 Wuzhong 5.57 642.95 2352.17 1709.23 2995.12
Kaifeng 17.09 4583.21 6897.10 2313.89 11480.31 Baiyin 4.73 437.83 1846.48 1408.65 2284.32
Yinchuan 16.25 3572.29 4906.26 1333.97 8478.55 Zhongwei 4.50 423.46 1875.70 1452.24 2299.15
Sanmenxia 15.54 3981.78 6285.07 2303.29 10266.85 Average value 19.63 5874.14 5874.14 0.00 11748.27
Puyang 15.34 3924.85 6476.72 2551.87 10401.57 Standard deviation 15.55 7198.11 2473.14 5356.13 9336.51
Weinan 14.97 3593.60 5791.41 2197.81 9385.01 Variation coefficients 0.79 1.23 0.42 0.79
Ranked by Fi, the first region is Zhengzhou (49,958.99), which is 21.87 times that of Baiyin (2,284.32). The last five regions are Bayannur, Wuzhong, Wuwei, Zhongwei, and Baiyin, with an average value of 2,766.79. The top five regions are Zhengzhou, Xi'an, Jinan, Luoyang, and Taiyuan, with an average value of 34,000.11, which is 12.29 times more than the average value of the last five regions. The correlation coefficient between Fi and Mi is 0.99, suggesting that regions with high comprehensive quality tend to have stronger economic ties, as indicated by the total intensity. Similarly, there are also large differences in the "radiation" and "absorption" of regions. The level of economic development is an important factor influencing the comprehensive quality. Therefore, regions with higher comprehensive quality are mainly distributed in the economically developed midstream and downstream regions of the Yellow River basin, further influencing the region's "radiation" and "absorption".
From the variation coefficients of the data1, the variation coefficients of Mi, Ni, and Fi are greater than 0.35, which is in the high variation interval. While the variation coefficient of Pi is 1.23, which is in a state of strong variation. Based on the above, there are significant differences in the comprehensive quality and the intensity of economic correlation among the regions in the Yellow River Basin, i.e., the differentiation of economic development among the regions is obvious.
1The variation coefficient is divided as follows: Weak variation is [0, 0.15]; Moderate variation is (0.15, 0.35]; High variation is (0.35, 1]; Strong variation is greater than 1.

3.2 The Spatial Gradient Structure and City Cluster Effect of the Yellow River Basin Are Obvious

In the Yellow River Basin, 12 regions have a higher value (Mi) than the three-quarter quartile value (24.89). These regions include 6 in Shandong, 2 in Henan, 1 in Shanxi, 1 in Shaanxi, 1 in Gansu, and 1 in Inner Mongolia, which are ranked ahead of Lanzhou. Divided basin-wise, there are 2 in the upstream, 3 in the midstream, and 7 in the downstream of the Yellow River. Between the 51 regions, there are 1,275 economic intensity links. 14 economic intensity values are greater than 1,500, mainly concentrated between the regions of Shandong and Henan the downstream of the Yellow River. In the midstream, Taiyuan, Xi'an, and Luoyang are connected with the downstream regions. However, there are no such connecting links observed in the upstream areas. Therefore, the economic links among the regions along the Yellow River Basin show an obvious "upstream-midstream-downstream" three-tier structure. The upstream regions have lower comprehensive quality and weaker inter-regional economic spatial interaction strength. The midstream regions have relatively higher comprehensive quality and stronger inter-regional economic spatial interaction strength. The downstream regions have the highest comprehensive quality and the strongest inter-regional economic spatial interaction strength. The reason is mainly that there are inter-provincial spatial influences and inter-regional spatial correlations in China's regional economic growth, and the inter-regional economic development of the Yellow River Basin follows this law.
According to Equations (4) and (6), Pi refers to the sum of the "radiation" intensity and Ni refers to the sum of the "absorption" intensity. Therefore, PiNi could reflect the integrated "radiative force" of region i. If the value of PiNi is positive, it means that the comprehensive "radiation" of the region is stronger, and is in the center of regional development. If the value is negative, it means that the comprehensive "radiation" is weaker, and is in a relatively marginal position. According to the results in Table 2, 11 of 51 regions, including Zhengzhou, Xi'an, Jinan, Luoyang, Ordos, Zibo, Taiyuan, Jining, Dongying, Lanzhou, and Heze, have positive values. It indicates that the above regions play an important role in promoting high-quality economic development. According to the national "13th Five-Year Plan", the Yellow River Basin region includes seven city clusters. In terms of city cluster distribution, the above regions belong to specific city clusters: Jinan, Zibo, Jining, Dongying, and Heze belong to the Shandong Peninsula City Cluster; Zhengzhou and Luoyang belong to the Central Plains City Cluster; Xi'an belongs to the Guanzhong Plain City Cluster; Taiyuan belongs to the Jinzhong City Cluster; Erdos belongs to the Hubao-Eyu City Clusters; Lanzhou belongs to the Lanxi City Cluster. This indicates that the planning and construction of Yellow River Basin City Clusters have had a significant impact, with these regions playing a leading role in driving the economic development of their respective city clusters. Furthermore, it is worth noting that the Shandong Peninsula City Cluster has 5 cities, all of which have made significant progress in economic development. However, none of the cities in Ningxia Along the Yellow River City Cluster have been designated as regional center, indicating the need for further strengthening in this aspect. These differences are not only due to the location of the regions, but are also influenced by the level of regions. To achieve high-quality development of the urban agglomeration in the Yellow River basin, it is necessary to fully consider the differences in natural environment and socio-economic conditions between the upstream, midstream, and downstream regions. Different regions need to formulate precise policies based on their actual situations in order to achieve the desired results.

4 Results of Social Network Analysis

4.1 Properties of the Networks

Considering the directionality of the interaction between regions, this paper constructs the network of the Yellow River Basin based on Equation (3). Where, the maximum value of Rijmax is 1,954.27; The minimum value of Rijmin is 9.53; The quarter-quartile value(Q1) of Rij1/4 is 35.64; The two-quarter-quartile value(Q2) of Rij2/4 is 79.95; The average value of Rijaver is 149.02; The three-quarter quartile value(Q3) of Rij3/4 is 170.37. Table 3 presents the fundamental characteristics of the network under different connection thresholds. Indicators such as the network edges and network density demonstrate notable nonlinear variations, indicating instability within the regional economic correlation network.
Table 3 Basic network properties at different connection thresholds
Parameters Q1 (35.64) Q2 (79.95) Average value (149.02) Q3 (170.37)
Network edges 1938 1285 731 643
Network density 0.76 0.50 0.29 0.25
Average distance 1.16 1.34 1.50 1.52
Transferability 56.00% 25.74% 8.91% 7.05%
Clustering coefficient 0.76 0.81 0.80 0.81
Reciprocity 0.72 0.60 0.43 0.42
Network centralization 2.71% 3.90% 10.20% 10.82%
This study utilizes a threshold value of Rij3/4=170.37 to construct the economic correlation network, taking into account the following factors. On the one hand, this threshold ensures the absence of isolated nodes or regions in the network, thereby ensuring the completeness of the economic correlation network. On the other hand, it effectively filters out 1,907 low-value linkage relationships or edges, while retaining the primary economic correlation relationships within the region. The structure of the radiative network for each region in the Yellow River Basin is depicted in Figure 2. Based on the properties of this network, the following conclusions can be drawn.
Figure 2 Structure of the Radiative Network in the Yellow River Basin

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1) The network is relatively sparse. The network that has been established consists of 51 nodes or regions, with a total of 643 edges or connections, which are formed using a threshold value of Rij3/4=170.37. On average, each node has 12.61 connections. The network density is calculated to be 0.25, indicating relatively sparse connectivity relationships. However, it is important to note that there are no isolated nodes in the network.
2) The network cohesion is high. The network exhibits a clustering coefficient of 0.81, indicating that 81% of the triads in the network are stable. The result indicates the presence of a "small group" phenomenon within the economic correlation network of the Yellow River Basin. The average distance between nodes in the network is 1.52, meaning that on average, 1.52 nodes need to be traversed to establish a connection between any two regions. The transferability of the network is 7.05%, indicating a relatively low transfer efficiency after eliminating low-value correlations.
3) Network reciprocity is low. At the critical value, the network reciprocity is measured to be 0.42, indicating that only 42% of the associations in the network are bidirectional. Additionally, when using a threshold value of Rij2/4=79.95, the reciprocity increases to 0.60, suggesting that the reciprocal relationships among the regions in the Yellow River Basin remain relatively low.
4) The centrality of the network is high. As the threshold value increases, the intermediate centrality potential increases from 2.71% to 10.82%. Therefore, it indicates that within the Yellow River Basin region, when a part of the low-value economic correlations is removed, the network has a strong central tendency, i.e., some regions have absolute advantages (or influence) on regional development.

4.2 Centrality Analysis

The purpose of the centrality analysis is to examine the position and role of regions within the Yellow River Basin in regional economic development. It provides insights into the influence and impact of each node on other regions, as well as its contribution to the overall economic development. By normalizing the point centrality, betweenness centrality, and closeness centrality of each node (relative to the maximum value of each index), we can compare the economic correlation network within the Yellow River Basin. The results are presented in Figure 3.
Figure 3 Centrality characteristics of regions in the Yellow River Basin

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4.2.1 Degree Centrality

The degree centrality could reflect the node's connection ability in the network. Considering the 51 nodes in the spatial correlation network, the maximum degree is 75 of Xi'an, and the minimum is 1 of Wuwei, with the average value 25.22. Five regions with the highest degree centrality are Xi'an (75), Zhengzhou (73), Luoyang (65), Jinan (62), and Ordos (61), which are the top five regions of the comprehensive quality except Ordos.The distribution of degrees in each region is shown in Figure 3. The correlation coefficient between the degree and the comprehensive quality is 0.86, which indicates that the regions with higher comprehensive quality have a larger number of degrees. Generally, they are important nodes in the network.
The degree class of a node could be categorized into in-degree and out-degree. The out-degree reflects the influence of the region on other regions (radiation effect), and the in-degree reflects the influence of other regions on the region (absorption effect). There are 17 regions in the network, where the value of the out-degree is larger than the in-degree (difference value), including Zhengzhou (25), Xi'an (25), Ordos (25), Jinan (24), Baotou (20), Taiyuan (19), Luoyang (19), Zibo (18), Jining (17), Dongying (14), Hohhot (11), Heze (11), Dezhou (8), Xinxiang (8), Tai'an (5), Liaocheng (5), and Binzhou (2). It indicates that the above regions have a strong radiation effect on the economic development of the Yellow River Basin, which can drive the development of the regional economy. From this perspective, Xining (6), and Yinchuan (11), as the upstream central cities, need to be further strengthened in driving the development of upstream city clusters.

4.2.2 Betweenness Centrality

The betweenness centrality of a node reflects the ability to control "resources". Figure 3 illustrates the betweenness centrality of the economic spatial correlation network within the Yellow River Basin. The maximum betweenness centrality is observed at Xi'an 273.86, while Zhongwei, Wuwei, and other regions have a minimum betweenness centrality of 0. The average betweenness centrality is 13.88. Notably, 8 regions exhibit a betweenness centrality higher than the average value. These regions are Xi'an (273.86), Zhengzhou (179.36), Luoyang (84.46), Erdos (34.96), Jinan (34.77), Taiyuan (18.32), Baotou (17.48), and Jining (15.50). It suggests that these regions exert significant control over the regional economic development within the Yellow River Basin and play a crucial role as bridges in regional economic development.

4.2.3 Closeness Centrality

Figure 3 displays the closeness centrality of the economic spatial correlation network within the Yellow River Basin. The maximum closeness centrality is observed in regions such as Zhongwei and Wuwei, with a value of 200. Xi'an has the minimum closeness centrality at 50. The average closeness centrality is 134.47. Notably, there are 24 regions with a closeness centrality of 200, primarily located in the midstream and upstream areas of the Yellow River Basin. This indicates that these regions are "marginalized" within the network and serve as weak links that limit regional economic development. Regions with a closeness centrality below 60 include Xi'an (50), Zhengzhou (51), Jinan (57), Ordos (57), and Luoyang (58). These regions occupy central positions within the network and exhibit strong independence in economic development. Furthermore, regions with lower values of closeness centrality generally correspond to higher degree centrality, betweenness centrality, and comprehensive quality. This illustrates the significant role played by these regions in regional economic development from various perspectives.

4.3 Core-Edge and Block Model Analysis

In order to reveal the characteristics of the economic correlation network in the Yellow River Basin at different levels, the core-edge method is applied to analyze its cohesive subgroups. In addition, the block model is applied to study the interrelationships between different blocks.

4.3.1 Core-Edge Analysis

The economic spatial correlation network of the Yellow River Basin was analyzed by using core-edge analysis, resulting a fit value of 0.98. This indicates the presence of a highly structured core cluster and an edge cluster. The core cluster comprises 17 regions, including Zhengzhou, Xi'an, Luoyang, Jining, Taiyuan, Jinan, Dezhou, Xinxiang, Liaocheng, Tai'an, Zibo, Heze, Ordos, Baotou, Binzhou, Dongying, and Hohhot. Meanwhile, the edge cluster consists of the remaining 34 regions. The core cluster exhibits a network density of 0.9963, with 271 edges, indicating strong economic connectivity among the core regions. Conversely, the edge cluster demonstrates a network density of 0.0045, with 5 edges, suggesting relatively weak economic connectivity among the edge regions. Notably, the core cluster sends 309 edges to the edge cluster, while the edge cluster only sends 58 edges to the core cluster. This highlights the significant radiation effect of the core regions, which play a crucial role in driving the regional economic development of the Yellow River Basin. Furthermore, the core degree value of each region was measured, revealing a significant positive correlation coefficient of 0.75 between the core degree and comprehensive quality.

4.3.2 Block Model Analysis

In UCINET 6.5, the CONCOR method (the maximum segmentation depth is 2, and the convergence criterion is 0.2) is used to divide the 51 regions in the Yellow River basin to get four blocks (the coefficient value of determination R2 is 0.77). Considering the network density of 0.25, if the density value between the plates exceeds 0.25, it is assigned a value of 1. Otherwise, it is assigned 0. According to the block density matrix, the image matrix could be obtained in Table 4. Based on the image matrix, the association relationship between the blocks in the Yellow River Basin could be demonstrated, as shown in Figure 4.
Table 4 The density matrix and image matrix
Blocks Density matrix Image matrix
Block Ⅰ Block Ⅱ Block Ⅲ Block Ⅳ Block Ⅰ Block Ⅱ Block Ⅲ Block Ⅳ
Block Ⅰ 1.00 1.00 0.97 0.352 1 1 1 1
Block Ⅱ 0.94 0.86 0.28 0.00 1 1 1 0
Block Ⅲ 0.10 0.01 0.01 0.00 0 0 0 0
Block Ⅳ 0.00 0.00 0.00 0.00 0 0 0 0
Figure 4 The relationship between the blocks in the Yellow River Basin

Full size|PPT slide

Block Ⅰ is the core block of economic growth in the Yellow River Basin. All 9 regions in this block belong to the core cluster in the core-edge analysis. They are not only internally correlated, but also have spillover effects to blocks Ⅱ, Ⅲ, and Ⅳ. It indicates that cities in Block Ⅰ play an important role in driving the high-quality development of the Yellow River basin, serving as the "engine" of economic growth. Block Ⅱ also plays an important role in regional development, which contains 11 regions. Except for Anyang, Jiaozuo, and Yulin, the other 8 regions are all from the core clusters. This block not only exhibits internal correlation but also serves as a crucial bridge for transferring the momentum of economic growth from Block Ⅰ to Block Ⅲ. Block Ⅲ and Block Ⅳ are mainly from the edge cluster. Block Ⅲ (mainly belongs to the midstream area) receives spillovers from Block Ⅰ and Block Ⅱ. While Block Ⅳ (mainly belongs to the upstream area) receives spillovers from Block Ⅰ only. Therefore, Block Ⅲ is in an advantageous position for economic development. Overall, the spillover effects of high-quality development in various regions of the Yellow River basin exhibit significant gradient characteristics. Each block relies heavily on Block Ⅰ, followed by Block Ⅱ acting as a bridge and hub for Block Ⅲ. Block Ⅳ, mainly in the upstream regions, lacks economic growth momentum.

5 Influencing Factor Analysis by QAP

5.1 Theoretical Assumptions and Methodologies

Based on the analysis of the economic spatial correlation characteristics in the Yellow River Basin, this study further explores the driving factors. Drawing on the findings of Zhang, et al.[35] and Li, et al.[4], this paper posits the following assumptions regarding the primary factors influencing the economic spatial correlation network (Cor) in the Yellow River Basin. 1) Spatial adjacency (Spa), which refers to whether the locations are adjacent in space. 2) Fixed asset investment level (Inv), measured by the ratio of total fixed asset investment to regional GDP. 3) Employment level (Emp), measured by the proportion of urban employees to total employees. 4) Informatization level (Inf), measured by the ratio of internet users to permanent residents. 5) Government revenue level (Gov), measured by the ratio of government fiscal revenue to regional GDP. 6) Wage level (Wag), measured by average worker wages. 7) Innovation level (Inn), measured by the ratio of patent applications to permanent residents. The variables in the assumptions are relational data, and the QAP method is used to test the above assumptions. QAP is a non-parametric test method that does not require the assumption of independence between variables and has more robust advantages compared to parametric methods. From 2010 to 2021, the average values of the indicators in each region are computed, and a relationship matrix between regions is constructed using these average values. Then, QAP correlation analysis and QAP regression analysis are applied to test the assumptions.

5.2 QAP Correlation

During the QAP correlation analysis using UCINET 6.5, 5,000 random permutations are performed to obtain the results presented in Table 5. Spa and Inv are significant at the 1% level, and both correlation coefficients are positive. It indicates that geographic adjacency and fixed asset investment have a significant positive effect on economic spatial correlation. Inf and Inn are significant at the 1% level, and Emp is significant at the 5% level. The correlation coefficients of the above three factors are negative, suggesting that they have a significant negative impact on the economic spatial correlation. In addition, Gov and Wag are not significant, which indicates that they are not the main factors affecting the spatial correlation of the economy. Those factors have little impact on the spillover effect of the regional economy.
Table 5 Economic spatial correlation network and influencing factors correlation results
Variables Correlation coefficient Significance Average correlation coefficient Std Min Max
Spa 0.101 0.000 0.000 0.023 0.071 0.084
Inv 0.281 0.000 0.000 0.029 0.096 0.148
Emp 0.064 0.033 0.000 0.038 0.118 0.182
Inf 0.088 0.005 0.001 0.038 0.115 0.168
Gov 0.019 0.282 0.000 0.029 0.093 0.205
Wag 0.005 0.324 0.000 0.016 0.056 0.101
Inn 0.220 0.000 0.001 0.062 0.193 0.238

5.3 QAP Regression

The results of QAP regression through 5,000 random permutations are shown in Table 6. The coefficient of determination R2 is 0.418, and the adjusted R2 is 0.405. This means that the model can explain 40.5% of the spatial correlation. Spa is significant at the 1% level, indicating that geographic distance is an important factor influencing interconnectedness in the Yellow River Basin. Inv and Inn are significant at the 1% level, suggesting that the similarity of the investment structure in fixed assets and the innovation capacity between regions is conducive to the establishment of the spatial correlation between regions. It is conducive to the establishment of spatial correlation among regions. Emp and Inf are significant at the 10% level, indicating the similarity of employment and informatization are important drivers of the spatial correlation.
Table 6 Results of QAP regression analysis
Variables Unstandardized regression coefficients Standardized regression coefficients Significance
Intercept 0.252
Spa 0.141 0.089 0.001
Inv 0.244 0.281 0.001
Emp 0.043 0.049 0.053
Inf 0.006 0.007 0.090
Inn 0.204 0.230 0.001

6 Conclusions and Suggestions

6.1 Conclusions

This study specifically investigates the economic spatial correlation relationship among 51 regions in the Yellow River Basin from 2010 to 2021. By using social network analysis, the economic spatial correlation characteristics are analyzed. Furthermore, the QAP method is employed to explore the factors influencing the regional spatial correlation relationship. The conclusions drawn from this study are as follows.
There are significant economic spatial correlation characteristics within the Yellow River Basin. There are large differences in the comprehensive quality and economic connectivity strength between regions in the Yellow River Basin. The variation coefficients of Mi, Ni, and Fi are in the high variation interval, and Pi is in a state of strong variation. The economic connectivity between regions shows a significant "upstream-midstream-downstream" structure. The upstream region has lower comprehensive quality and weaker economic connectivity, while the midstream region has relatively higher comprehensive quality and stronger economic connectivity. The downstream region has the highest comprehensive quality and strongest economic connectivity.
The various regions within the associated network hold different positions and play different roles. Cities like Xi'an, Zhengzhou, Jinan, Taiyuan, Ordos, Luoyang, and Baotou have relatively high degree centrality and betweenness centrality in the regional associated network. They are also situated near areas with lower centrality values, positioning them at the center of the network. These cities are distributed across different urban clusters within the Yellow River Basin and play crucial roles in driving the economic development of these urban clusters.
The 51 regions within the Yellow River Basin can be divided into four economic functional blocks. Block Ⅰ consists of 9 regions that belong to the core cluster in the core-edge analysis. Block Ⅰ generate spillover effects to blocks Ⅱ, Ⅲ, and Ⅳ, and it is the core block for economic growth in the Yellow River Basin. Block Ⅱ consists of 11 regions, with 8 of them coming from the core cluster. This block transfer the economic growth momentum from block Ⅰ to block Ⅲ, and play an important bridging role. Block Ⅲ and block Ⅳ come from the peripheral cluster. Block Ⅲ simultaneously receives spillover effects from block Ⅰ and block Ⅱ. It is in a relatively advantageous position.
The economic spatial relationships within the Yellow River Basin are primarily influenced by five major factors. Through QAP correlation and QAP regression analysis, it has been found that spatial adjacency, fixed asset investment level, employment level, informatization level, and innovation level significantly impact spatial relationships, explaining 40.5% of the variance in these relationships. Therefore, geographical proximity, similarities in the levels of fixed asset investment, innovation, employment, and informatization, are conducive to establishing economic linkages among different regions.
Furthermore, there are still some shortcomings about the research: First, due to factors such as data availability, only the economic relationships among 51 regions in the Yellow River Basin were studied, which needs further expansion of the research scope. Second, during the period from 2010 to 2021, the static analysis of network structure characteristics was conducted, lacking the dynamic characteristics analysis. Third, when employing the QAP method to examine the driving factors of network structure, the analysis did not assess the relative significance of each individual factor.

6.2 Suggestions

Firstly, it is crucial to enhance the economic spatial connectivity among the regions in the Yellow River Basin and strengthen the network closeness at a higher level of correlation. Currently, the economic connectivity among the regions in the Yellow River Basin primarily remains at a relatively low level, with insufficient high-level correlation. Provinces and regions in this area should formulate their strategies based on ecological protection and high-quality development in the Yellow River Basin, eliminating local protectionism and firmly embracing the concept of integrated regional development. The government should coordinate the planning of population, resources, environment, and various elements of economic and social development within the basin. Additionally, there should be a vigorous promotion of transportation infrastructure and network infrastructure construction, gradual removal of barriers to the flow of elements within the region, and a boost in the development of high-level economic correlation among the regions.
Secondly, it is essential to leverage the role of city clusters in the Yellow River Basin as carriers and enhance the spatial synergy of regional economic development. Currently, the main city clusters in the Yellow River Basin include the Shandong Peninsula City Cluster, Central Plains City Cluster, Guanzhong Plain City Cluster, Jinzhong City Cluster, Hubao-Eyu City Cluster, Ningxia Along the Yellow River City Cluster, Lanxi City Cluster. These clusters serve as the primary drivers for the future high-quality development of the Yellow River Basin. However, there are significant disparities in the development levels among these city clusters. It is necessary to strengthen the economic interaction between the core regions in the basin to drive the coordination of regional economic development. Simultaneously, it is crucial to further leverage the radiating role of the core regions within the clusters and propel the high-quality development of the basin's economy from a "Point-Line-Plane" approach to a higher level.
Thirdly, there is an urgent requirement to execute the strategy for ecological protection and high-quality development in the Yellow River Basin, concurrently shifting the economic development approach of less developed regions.The economic correlation among regions in the Yellow River Basin is significantly influenced by geographical distance, with stronger connectivity observed among regions with similar economic development patterns. To effectively address this issue, provinces in the Yellow River Basin should prioritize the implementation of the strategy for ecological protection and high-quality development, guided by the concept that "clear waters and green mountains are as valuable as mountains of gold and silver". This includes accelerating industrial upgrading in the basin through technological innovations and transforming the economic development mode of underdeveloped regions. By doing so, the aim is to reduce disparities in economic development conditions among regions in the basin, which will contribute to enhancing the spillover effect of regional economic development.

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Funding

Humanities and Social Science Fund of Ministry of Education of China(22YJC790008)
Soft Science Research Project of Xi'an Municipal Science and Technology Bureau(24RKYJ0007)
Soft Science Research Project of Shaanxi Province Science and Technology Department(2022KRM116)
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