Spatial Correlation Network and Influencing Factors of Industrial System Modernization in China

Construction of Index System

Industrial system modernization has some important characteristics such as innovation drive, integrated development, structural optimization, green intelligence, safety and controllability, high-level openness, strong competitiveness, and good benefits. It can not only continuously promote the advancement of industrial foundation, the rationalization of industrial structure, the modernization of industrial chain as well as integrated development of digital and real economy, but also provide good conditions for achieving coordinated promotion between high-quality economic development and efficient ecological protection.

Based on this understanding, and in combination with a series of work requirements for China’s development, such as optimizing the industrial structure, promoting the development of strategic emerging industry integration cluster, building a digital industrial cluster with core competitiveness, and tamping infrastructure deployed (CGTN, 2026a, 2026b), we build an index system of ISML (Table 1). This not only considers the adjustment of industrial structure, digital economy, and other development drivers, but also takes into account of security issues, environmental protection, opening up to the outside world, and infrastructure development needs.

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Table 1.

Index system for measuring ISML.

First-Level Indicators	Secondary Indicators	Tertiary indicators	Measure	Type	Weight Coefficient
Industrial high-end	Advanced industrial structure	Industrial structure optimization	Value added of the second and third industries/GDP	+	0.0036
		Productivity improvement	Report period total labor productivity/base period 2010 total labor productivity	+	0.0505
	Industrial added value	Value added rate of industrial enterprise operations	(Industrial Enterprise Main Business Income − Industrial Enterprise Main Business Cost)/Industrial Enterprise Main Business Income	+	0.0076
Industrial digitalization	Industrial digitalization investment	R&D personnel input	Full time equivalent of R&D personnel in industrial enterprises above designated size	+	0.0384
		R&D funding investment	R&D expenses for industrial enterprises above designated size	+	0.0361
		Computer investment	Number of computers used by enterprises per 100 people	+	0.0136
		Website investment	Number of websites owned by every hundred enterprises	+	0.0028
	Industrial digitalization capabilities and applications	Electronic information manufacturing level	Integrated circuit production	+	0.0882
		Industrial Internet	Length of long-distance optical cable	+	0.0109
		Platform economy	E-commerce sales	+	0.0414
		Digital logistics	Express delivery volume	+	0.0685
		Post and telecommunications business volume	-	+	0.0366
		Digital public service	Number of automatic weather stations	+	0.0119
		Geographic information data production	Surveying and mapping benchmark results	+	0.0428
		Income of Software business	-	+	0.0555
	Industrial digitalization infrastructure	Telephone penetration rate	-	+	0.0083
		Internet penetration	Number of Internet broadband access users/number of permanent residents at the end of the year	+	0.0106
		Financial support	Local fiscal science and technology expenditure/local fiscal general budget expenditure	+	0.0179
	Industrial digitalization governance	Number of enterprises in the context of enterprise informatization and e-commerce	-	+	0.0226
Industrial security	Industrial chain resilience	Ability to resist risks and interference	Urbanization rate	+	0.0065
			Per capita gross domestic product	+	0.0123
		Recovery Ability	Urban registered unemployment rate	-	0.0078
		Discovering new path capabilities	Number of personnel engaged in scientific and technological activities in high-tech enterprises	+	0.0373
	Industrial security and guarantee	Public safety	Public security expenditure of local finance/general budget expenditure of local finance	+	0.0070
		Social security	Expenditure on social security, employment, and housing security in local finance/general budget expenditure in local finance	+	0.0069
		Talent security	Average length of education	+	0.0011
		Financial security	(Original insurance premium income − original insurance payout expenses)/Original insurance premium income	+	0.0034
		Policy environment	Main business taxes and surcharges of industrial enterprises above designated size/total profit of industrial enterprises above designated size	-	0.0007
Industrial openness level	Technology openness	Technology introduction	Transaction amount of absorption technology/total transaction amount of absorption and output technology	+	0.0078
	Foreign trade openness	Import and export trade level	Total import and export value/GDP	+	0.0250
	Foreign investment openness	Foreign investment utilization	Actual utilization of foreign investment	+	0.0542
Advanced industrial foundation	Infrastructure	Transportation foundation	Road mileage	+	0.0115
		Hydroelectric foundation	Number of libraries and hydropower stations	+	0.0321
		Network Foundation	Number of Internet broadband access ports	+	0.0176
	High-tech development foundation	Number of high-tech enterprises	-	+	0.0482
		Registration status of technical contracts	Transaction amount of technical contract registration	+	0.0277
	Funding foundation	Fixed assets investment	Fixed assets investment (excluding farmers) increased over the previous year	+	0.0008
	Market environment	Consumer price index	Resident consumer price index	+	0.0071
		Sales price index	Retail price index of goods	+	0.0034
		Investment price index	Fixed assets investment price index	+	0.0051
Industrial ecology	Green living	Popularity rate of rural sanitary toilets	-	+	0.0042
		Green travel	Every ten thousand people have public transportation vehicles	+	0.0067
		Public books	Per capita ownership of public library collections	+	0.0199
	Reduction of pollution emissions	Main pollution emissions per unit of GDP	Main pollution emissions/GDP	-	0.0017
	Efficient resource utilization	Energy efficiency	Energy product consumption/GDP	-	0.0028
		Per capita water consumption	-	-	0.0015
	Metabolic cycle	Level of agricultural waste treatment	-	+	0.0294
		Harmless treatment rate of household waste	-	+	0.0017
	Ecological protection and environmental governance	Green intensification	Industrial pollution control completed investment/GDP	+	0.0242
		Financial environmental protection expenditure	Local fiscal expenditure on environmental protection/General budget expenditures of local finance	+	0.0030
		Forest coverage rate	-	+	0.0117
		Area of National Nature Reserve	-	+	0.0021

Note: if the content in column 4 is repeated in column 3 of the table, it can be represented as - in column 4.

Fixed Base Difference Entropy Weight Method

Considering the rationality, accuracy, and availability of weighting results, a fixed base difference entropy weight method (Wang et al., 2021) is adopted to measure China’s ISML. The fixed base difference entropy weight method is a combination of entropy weight method and fixed base difference method, which is a relatively objective weighting method. It can not only avoid subjective influence to ensure the scientific and effective weighting, but also effectively achieve the comparability for measurement results in the dual dimensions of time and space as well as dynamic changes, and also prevent weighting errors caused by significant differences in time length and the number of spatial units. The specific steps are as follows:

Y ij t = X ij t - min { X 1 j t , … , X n j t } max { X 1 j t , … , X n j t } - min { X 1 j t , … , X n j t }

(1)

Y ij t = max { X 1 j t , … , X n j t } - X ij t max { X 1 j t , … , X n j t } - min { X 1 j t , … , X n j t }

(2)

Formulas (1) and (2) respectively perform dimensionless standardization on tertiary indicators with positive and negative attributes in Table 1; t represents year, i denotes provinces, and j stands for specific indicator; X^t_ij is the original data of indicator j in province i, while max{X^t_1j,…, X^t_nj} and min{X^t_1j,…, X^t_nj} are the maximum and minimum values of X^t_ij, respectively; Y^t_ij is the standardized value of indicator j in province i.

P ij t = Y ij t / ∑ Y ij t

(3)

Where P^t_ij is the specific proportion, and if P^t_ij = 0, then lim_(Y^t_ij→0) P^t_ij × ln(P^t_ij) = 0 is defined.

E j = - 1 ln n × ∑ [ P ij t × ln ( P ij t ) ]

(4)

Where E_j represents the information entropy of indicator j, and n stands for the product of the length of time and the number of provinces.

Wj = 1 - E j k - ∑ j = 1 k E j

(5)

Where W_j is the weight of indicator j, as shown in the last column of Table 1; K denotes the total number of indicators.

Z j t = X j t - min ( X j 2011 ) max ( X j 2011 ) - min ( X j 2011 )

(6)

Where X^t_j is the original data of indicator j in year t, whereas max(X²⁰¹¹_j) and min(X²⁰¹¹_j) are the maximum and minimum values of indicator j in the base year, respectively; Z^t_j is the data of indicator j in year t after being processed by the fixed base difference method.

A = ∑ W j Z j t

(7)

Where A is the comprehensive evaluation index of ISML. The higher its value, the higher the ISML.

Dagum Gini Coefficient and Decomposition Method

In China, regional differences are the foundation for forming spatial connections. This difference provides an original driving force for trans-regional flow of various factors, and improves resource circulation level, strengthens network connections and others for building a industrial system through human flow, logistics, capital flow, information flow, and other carriers. And as mentioned earlier, to some extent, spatial correlation network of ISML already exists. However, due to currently no clear research on this point, we refer to the researches of Wei and Miao (2023), Ma et al. (2022) as well as Zhou et al. (2022), and use Dagum Gini coefficient and its decomposition method for quantitative confirmation to investigate whether China’s ISML can form spatial network connection and its formation is scientific. This method is a core tool for analyzing regional differences through overall, inner-regional and inter-regional Gini coefficients, as well as inner-regional, inter-regional, and hypervariable density contribution degrees (Dagum, 1997; Mussard & Richard, 2012; Zhang et al., 2022). Due to word count limitations, we will not elaborate too much on this mature method. Please refer to the literature mentioned above for specific steps. The only difference lies in the first step, as this paper divides China’s 30 provinces into four regions: east, central, west, and northeast, according to the classification standard of National Bureau of Statistics (National Bureau of Statistics, 2021). Namely, Beijing, Tianjin, Hebei, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan in the eastern region; Shanxi, Anhui, Jiangxi, Henan, Hubei and Hunan in the central region; Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, Guangxi, Inner Mongolia, and Xinjiang in the western region; and Jilin, Liaoning, Heilongjiang in the northeast region.

Formation Mechanism of Spatial Correlation

If the method presented in section “Dagum Gini Coefficient and Decomposition Method” demonstrates the results we envision, then subsequent analysis should be based on this network. Modernized industrial system with networked characteristics is essentially a complex system of points, lines and surfaces formed by the joint action of a series of factors. Let’s take a simplified network and see how it forms. Figure 1 shows a simplified complex connection network for ISML among region A, adjacent region B of region A, adjacent region C of region A, as well as adjacent regions B and C but not adjacent region D of region A, under the three key factors of geographical proximity, technological innovation, and carbon emission efficiency.

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Figure 1.

Formation mechanism of spatial connection.

Specifically, first, the modernization construction activities of industrial system among adjacent regions have natural geographical connections, which is not only reflected in their proximity and similar natural environments, but also in their similar basic conditions, strong policy consistency, small differences in development levels, and others. This facilitates the low-cost absorption of resource elements from adjacent regions and cooperation with them, forming a basic transmission path with natural properties and high efficiency characteristics for spatial correlation network for ISML.

Second, technological innovation is the core driving force for building a modernized industrial system (CGTN, 2026a). It can accelerate the upgrading and transformation of traditional industries, cultivate and strengthen strategic emerging industries, actively develop modernized industrial clusters, so as to promote the formation of a modernized industrial system with local characteristics. This further means that through spatial spillover effects, participating entities such as enterprises and governments in other regions can learn, imitate, and create, thereby forming the network connection and comprehensively improving China’s ISML. Of course, the higher ISML, the easier it is for regions to establish communication channels with other regions, the more a region forms communication with multiple parties, and the more information it can obtain. This not only facilitates the systematic analysis and judgment of ISML for the local region, but also affects the flow of knowledge, talent and other factors among regions, providing supporting conditions for the region to leverage its local advantages and improve its local disadvantages.

Third, economic and ecological factors have a significant impact on China’s ISML and its formation of spatial correlation network. Building a modernized industrial system requires both ecological and economic benefits. In this regard, this paper analyzes carbon emission efficiency with both economic and ecological attributes (Cai et al., 2025; Wang et al., 2025). Improving carbon emission efficiency can provide a good external environmental foundation for overall improving ISML and its formation of spatial correlation network, help guide the flow of green elements in a positive direction, narrowing the gap between core and peripheral regions, and promoting the maximization of overall social benefits. Conversely, high ISML and its spatial correlation network can upgrade industrial structure, improve production efficiency, promote industrial greening and ecologicalization, thereby effectively improving carbon emission efficiency.

Gravity Model

Gravity model can not only determine the correlation and its intensity, but also characterize the network features of spatial correlation (Gu et al., 2023), numerically confirming that inter-provincial ISML has spatial connection and forms a complex connection network. Therefore, a gravity model is used to study whether there is spatial correlation among 30 provinces in ISML, as well as their corresponding correlation intensity. The specific formula is as follows:

I ij = g M i M j d ij b

(8)

Where I_ij is the gravitational value of ISML between province i and province j (viz. spatial connection intensity); M_i and M_j denote the comprehensive evaluation index value of ISML in province i and province j, respectively; d_ij represents the distance between the provincial administrative division points of province i and province j; g = M_i/M_i + M_j.

In order to accurately analyze the spatial connection path and intensity among provinces, eliminate the dimensional influence and enhance the comparability of results, gravitational values are standardized by [0,1]. The specific formula is as follows:

I ij * = I ij - Min { I 1 j , ⋯ , I n j } Max { I 1 j , ⋯ , I n j } - Min { I 1 j , ⋯ , I n j }

(9)

Where n denotes total number of provinces; I_ij^* is the standardized gravitational value, while max {I_1j,…, I_nj} and min {I_1j,…,I_nj} are the maximum and minimum values of I_ij, respectively.

Social Network Analysis

Social network analysis (SNA) can reflect the overall structure, relationship characteristic and interaction strength of element nodes, and is an important method for exploring network geographic feature and spatial effect (Hu et al., 2024; Huang et al., 2024). For a more complete study, a spatial correlation matrix will be constructed based on the above gravity model, and the spatial correlation characteristics and evolution of China’s ISML can be further analyzed through SNA. Notably, we first obtain the gravitational value I_ij through formula (8) to construct a 30 × 30 spatial correlation matrix for ISML. Afterward, it is to reshape the 30 × 30 spatial correlation matrix using a cumulative algorithm to perform binary transformation. That is, if the element value of reshaping matrix is greater than 0, it is denoted as 1; otherwise it is denoted as 0. From this, a 30 × 30 spatial binary matrix for ISML is constructed with one province as a network node, as a foundation of social network analysis. Here, the reason for using a province as a network node is: China’s provinces are important nodes in forming regional connections, and inter-provincial resource allocation can go up to the national level and down to the urban level.

Then, based on the aforementioned spatial binary matrix, four parts of analysis are conducted. First, overall network structure feature analysis. Specifically, network size (NS) is measured by the number of network nodes, and the larger NS is, the more provinces will participate in the modernization of industrial system as well as form network connection; network density (ND) represents the degree of closeness between provinces, and the larger ND is, both the greater the impact of the network for ISML on ISML of a certain province and the closer the connection between provinces in terms of ISML will be; network efficiency (NE) refers to the connection efficiency of each node in a spatially correlated network, reflecting the redundancy of connections in a network, and the higher NE is, both the looser the connection between ISML in each province and the more unstable this network structure will be; network correlation degree (NC) reflects the stability and fragility of a network structure, and a larger NC indicates a more stable network structure; network hierarchy (NH) is used to reflect the main position of a network node in the spatial connection network, and the higher NH is, the stricter the hierarchical structure in the network related to ISML will be; average distance length (ADL) measures the degree of tightness or separation between nodes in a network, meanwhile a shorter ADL usually means that in a network, nodes are more tightly connected, and information or resources may spread more quickly and efficiently; clustering coefficient of a node ( LCC_i) is the ratio of actual number of edges between its neighbors to the maximum possible number of edges, and a high LCC_i means that it is easy to form tight clusters or community structures; clustering coefficient (GCC) of a network is usually the average of clustering coefficients of all nodes, and the higher GCC, the stronger the network cohesion of ISML.

Second, network centrality analysis relies on three relative centrality. Degree centrality (DC_i) reveals network control ability of province i, that is, the larger DC_i is, both the higher the importance of province i in this network for ISML and the wider the scope of cooperation will be. Betweenness centrality (BC_i) reflects the ability of network media of province i, and the higher BC_i is, the stronger the inter-provincial liquidity will be, which is more conducive to resource allocation. Closeness centrality (CC_i) shows the degree to which a certain node i is not controlled by other nodes, and a larger CC_i indicates that province i is more able to establish more direct connections without being constrained by other provinces.

Third, core-periphery analysis and cohesive subgroup analysis. The main analysis contents are as follows: some provinces located in a core region have obvious resource endowment advantages and are prone to forming cohesive subgroups, while other provinces located in a periphery region have the opposite; the existence of cohesive subgroups indicates the emergence of closely connected small groups, namely, there are regional collaborative strategic partners for improving ISML.

Fourth, block model divides all provinces into some blocks to analyze the position and function of blocks in the network, as well as their relationship and connection method with other blocks. According to the status and role of block, it is divided into four types of blocks: the number of relationships overflow from net beneficiary block to other blocks is much smaller than that it receives from the others; net spillover block has significantly fewer relationships with internal members than those with other blocks, and receives fewer relationships from other blocks; bidirectional spillover block has both spillover relationships to other blocks and internal blocks, but receives fewer outgoing relationships from other blocks; broker block not only sends out relationships to other blocks, but also receives more spillover relationships from other blocks, playing a mediating and bridging role in a network.

Given the word limit and the maturity of this method, we will not elaborate further. The relevant calculation formulas can be directly referenced to the research of Hu et al. (2024) and Huang et al. (2024).

Temporal-Spatial Characteristics

The comprehensive evaluation index of China’s ISML calculated by the fixed base difference entropy weight method, and corresponding results are shown in Figure 2.

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Figure 2.

Measurement result of China’s ISML.

From temporal characteristic, China’s ISML and its growth rate showed an upward trend year by year from 2011 to 2020. In 2020, China’s ISML doubled, with a growth rate of 47.2209%, far higher than the average annual growth rate of 19.1198% during this period. For each province, the growth rate of ISML has also been increasing year by year. The positive development of China’s ISML is closely related to the implementation of a series of policies in the country. In 2012, the “‘12th Five-Year Plan’ for the Development of National Strategic Emerging Industries” was proposed to promote industrial prosperity from multiple dimensions such as green, digitalization and economy (The Central People’s Government of the People’s Republic of China, 2012); in 2017, the report of the 19th National Congress of the CPC encouraged China to unanimously promote the construction of modernized industrial system and improve ISML (CGTN, 2026a). However, in 2021, although China’s overall ISML was improving, the overall growth rate had dropped to 22.3288%; even though there were some provinces with growth, such as Beijing, Guangdong, Gansu, Ningxia and Xinjiang, with the growth rate of Xinjiang reached 369.1485%, most provinces’ ISML grew against the trend, with Inner Mongolia recording a particularly sharp decline of −77.2923%. This is because the global public health security epidemic occurred at the end of 2019, the epidemic fully broke out in 2020, and after 2021, China changed the overall epidemic control methods, which gradually drove industrial recovery and development, propelled the economy into a stable recovery phase, and improved ISML. Meanwhile, some provinces with strong economies, such as Beijing and Guangdong, could withstand the impact of the pandemic better and maintain stable or even improve ISML, while economically weaker provinces could not. Thus, China’s policy tends to support the provinces with weaker economies, such as Gansu, Ningxia and Xinjiang, to prevent more unfavorable factors from existing in underdeveloped areas, and ultimately alleviate the overall impact on a country. At present, the potential for improving ISML is still affected by the previous epidemic. In the future, promoting the construction of modernized industrial system and comprehensively improving ISML is a major issue and challenge.

From spatial characteristic, there are significant differences in ISML among provinces, and these gaps are widening year by year, with a clear regional differentiation pattern of “high in the east and low in the west.” By 2022, the difference reached 8.6490 between Ningxia with the highest level of industrial system modernization, and Inner Mongolia with the lowest level. Although China’s ISML is constantly improving, it has long been characterized by imbalanced and insufficient development within China, and regional strategies can only alleviate but cannot completely solve the crux differences, such as technological and geographical differences. Therefore, these ultimately leads to a significant inter-provincial difference in ISML, and the gap is still widening. In the future, regional imbalances cannot be ignored.

Dagum Gini Coefficient and Decomposition Results

The results of Dagum Gini coefficient and its decomposition method are shown in Figure 3. In terms of the overall Gini coefficient (G), we can find that there are significant regional differences in ISML. And except for a slight decrease in 2018 and 2021, the coefficient increased in all other years, and reached 0.6345 in 2022 that exceeded the mean value of 0.3958 during the inspection period. In terms of the Gini coefficient within region j (Gj), during the sample period, the Gini coefficient in the eastern region was the highest and exceeded 0.7239, while those for other regions were significantly lower. This result likely stems from the fact that China’s eastern region is economically more advanced and industrialized, allowing it to lead the implementation of policies for modernized industrial construction in the country. From the Gini coefficient between region j and region h (Gjh), there is a significant difference in ISML between China’s eastern region and other regions. However, over time, this difference tends to stabilize and only shows a significant increase in 2022. This result indicates that the central, western, and northeastern regions are accelerating and have the potential to reach or surpass the high modernization level of industrial system in the eastern region. In addition, the Gini coefficient between the central region and western region, northeast region, as well as the western and northeastern regions, is smaller than that between the eastern region and central region, the western region, northeastern region, but China’s ISML still shows an overall regional imbalance. In fact, this is consistent with the actual situation of industrial development in the country. The favorable developmental foundation of the eastern region resulted in economic, ecological and social benefits, while other regions such as Guizhou, which has rich natural resources but lacks industrial variety, has weak digital foundation and high debt, resulting in a low level of industrial system modernization and an unclear growth trend.

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Figure 3.

Dagum Gini coefficient and its decomposition results.

From the perspective of contribution, the regional differences in ISML from 2011 to 2020 mainly come from inter-regional differences, and the contribution rates of this part were all above 65%; during the sample period, the contribution of within-regional differences (Gw) presented a stable upward trend, but they didn’t exceeded the contribution of inter-regional differences (Gnb); the contribution of inter-regional differences was less than 65% in 2021 and 2022, and the main source of regional differences in ISML in 2021 became contribution from hypervariable density (Gt); in 2022, the regional differences of ISML were very close to inter-regional differences and within-regional differences, and the overlapping effects between different regions were less pronounced.

Through analysis, it is concluded that there are differences in China’s ISML between regions, within regions and among provinces within different regions. On this basis, when promoting China’s ISML as a whole, no province should fall behind. This also prompts a province to form inter-provincial and cross-regional flow channels as well as cooperation platforms with provinces both within a region and in other regions. The aim is to learn from the experiences and lessons of other provinces, optimize resource allocation efficiency, promote smooth flow of factors and others, thereby improving ISML in the province and also collaborating with other provinces to improve ISML by obtaining essential external resources and driving the outward flow of local resources for profit. Thus it can be said that China’s ISML has formed a complex connection network, and subsequent analysis should also be based on this.

Overall Network Structure Characteristic Analysis

As shown in Figure 5, from 2011 to 2022, the values of network size (NS), network density (ND), and other measurement indicators for the spatial network structure characteristic of China’s ISML were relatively stable, with slight fluctuations around the corresponding mean values. It should be noted that, the above indicators fluctuated more frequently from 2019 to 2022, which is also in the post-epidemic period. Among them, network efficiency and network hierarchy fluctuate the most, and the number of ineffective connections has increased. This means the important role of doing a good job of prevention and control in the future, especially in dealing with unknown public health security threats. To sum up, China’s provinces have crossed geographical boundaries and formed complex network connections among provinces. And overall, inter-provincial connection is relatively close, while inter-provincial communication is smooth and cohesive, with stable connections and channels between provinces, and the spatial connection network structure is robust.

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Figure 5.

Overall network structure characteristic indicators from 2011 to 2022.

Network Centrality Analysis

It is to utilize such three indicators as degree centrality (DC), betweenness centrality (BC), and closeness centrality (CC) to investigate the relative central positions of 30 provinces in China for spatial correlation network of ISML. The results are shown in Figure 6. In terms of time evolution, the average level of the above three central indicators continued to rise nationwide, their mean values were respectively 23.5333, 11.3333, and 35.7333 in 2022, and the three centrality indicators in most provinces exceeded the corresponding mean values. This hints that the spatial network relationship of ISML is constantly becoming more complex in China, and the status and role of provinces in the network are overall improved. And this situation is consistent with the ISML time trend.

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Figure 6.

Network centrality of China’s ISML: (a) DC, (b) BC, and (c) CC.

In terms of spatial evolution, the influence of Chinese provinces in the spatial correlation network is unbalanced, and the influence of provinces in the eastern and northeastern regions is relatively high, but there are still some provinces with high influence in the central and western regions. For example, the above three central indicators were relatively high in Beijing and Sichuan, and at least two of them presented an upward or stable trend. The reason is that under the guidance of regional strategy and inter-provincial collaborative engineering proposed by China, with the continuous development of China’s socio-economy, the cross regional obstacles of factor flow are gradually being broken, each region has formed some provinces with the core goal of developing its own region and effectively connecting other regions according to development requirements, thereby ensuring the overall development of local region and whole country. This is conducive to building a modernized industrial system where the fruits of development are shared by the nation and comprehensively improving ISML.

Core-Periphery Analysis and Cohesive Subgroup Analysis

The results of core-periphery analysis and cohesive subgroup analysis are shown in Figure 7. First, China’s ISML presented a typical “core-periphery” spatial pattern. Among the 30 provinces in China, the number of core provinces increased every year, and this number reached 18 in 2022. On the one hand, this indicates that China has gradually formed many growth poles that drive the development of industrial system, and the effective utilization for resource advantages of each province has become a reality. On the other hand, this implies that the complexity and stability of spatial connection network reflecting the inter-provincial ISML in China are gradually increasing, which is very compatible with China’s current and future development. Second, in 2011, 2014, 2017, 2020, and 2022, some provinces consistently belonged to core provinces, such as Beijing, Chongqing, and Sichuan, while some provinces consistently to peripheral provinces, such as Guangxi and Gansu, but most provinces moved frequently towards core province targets, such as Shanxi, Jiangsu, and Xinjiang. However, due to the influence of their geographical locations, economic development, cultural customs, and other factors, some provinces are facing difficulties in reversing their position. For example, Xinjiang, although the three centrality indicators in 2022 were high, has limited resources and insufficient catching up strength, which makes it difficult to become a growth pole to drive the development of industrial system and that of surrounding provinces. Third, core provinces always form cohesive subgroups with periphery provinces, and the latter is always led by the former with higher ISML as well as economic, technological, and talent advantages. And although China’s eastern, central, western, and northeastern regions have their core provinces, the cohesive subgroups are mainly centered around the developed eastern provinces. This implies that in building a modernized industrial system, each province and region should promote economic, cultural, and other aspects of development and improve ISML. All in all, China should establish inter-regional and inter-provincial collaborative strategic partners to break the shackles of economic, technological, geographical, and other conditions, form close connections through “highland” leading, “bottom” following and local cooperation under the strategic characteristics of regional cooperation and exchange in China, and finally improving ISML as a whole.

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Figure 7.

Core-periphery analysis and cohesive subgroup division of China’s ISML: (a) 2011, (b) 2014, (c) 2017, (d) 2020, and (e) 2022.

Block Model Analysis

In this section, we adopt CONCOR algorithm in UCINET and simultaneously set a maximum segmentation depth to 2 as well as a concentration standard to 0.2000 to obtain four blocks (viz. corresponding to the above four cohesive subgroups), then to conduct an in-depth analysis of the internal structure for spatial correlation network of China’s ISML and the roles played by each province. According to Table 2, block 1 belonged to a broker block, and played an intermediary and bridge role in the spatial connection network of China’s ISML; block 2 belonged to the bidirectional spillover block, indicating that the provinces within this block can form significant spatial connections with other blocks through industrial transfer, talent flow, commercial cooperation, etc; block 3 was a net benefit block, meaning that the provinces in this block mainly promote the comprehensive improvement of ISML and form network connections through absorbing other block’s favorable spillover, such as “technological dividend”; and block 4 was a net spillover block, which belongs to the block that delivers dividends to other blocks.

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Table 2.

Results of Block Spillover Effects.

	Number of overflow relationship (PCS)	Number of receiving relationship (PCS)	Number of internal relationship (PCS)	Expected proportion of internal relationship (%)	Actual proportion of internal relationship (%)
			2011
Block 1	173	101	83	31.0345%	32.4219%
Block 2	119	77	22	17.2414%	15.6028%
Block 3	50	139	35	27.5862%	41.1765%
Block 4	42	67	16	13.7931%	27.5862%
			2014
Block 1	169	102	73	27.5862%	30.1653%
Block 2	119	67	30	17.2414%	20.1342%
Block 3	68	117	40	24.1379%	37.0370%
Block 4	28	98	9	20.6897%	33.3333%
2017
Block 1	168	85	54	24.1379%	24.3243%
Block 2	117	67	30	17.2414%	20.4082%
Block 3	58	129	55	31.0345%	48.6726%
Block 4	22	84	11	17.2414%	33.3333%
			2020
Block 1	181	98	69	27.5862%	27.6000%
Block 2	132	81	40	20.6897%	23.2558%
Block 3	46	126	32	24.1379%	41.0256%
Block 4	29	83	16	17.2414%	35.5556%
			2022
Block 1	155	75	73	27.5862%	32.0175%
Block 2	106	47	34	17.2414%	24.2857%
Block 3	33	133	43	31.0345%	56.5789%
Block 4	18	57	14	13.7931%	43.7500%

To further investigate the interactions between blocks, we calculate the network density and image matrix of each block (Table 3). Among them, this image matrix is obtained from the network density, that is, when the network density of a block is greater than the overall network density, it is assigned a value of 1 in the image matrix, otherwise it is 0. Here, 1 indicates the existence of transitive relation, while 0 indicates the absence of transitive relation. From Table 3, block 1 plays a role of “transmitter” in the spatial connection network of ISML and constructs a complete correlation path with other blocks, in which most of the provinces in this block are China’s main political centers, policy implementation centers, and cultural centers, such as Beijing, Chongqing, and Shaanxi. The spatial connection between block 1 and block 2 in China’s ISML is very active, and they can form two-way connection with other blocks. However, block 3 and block 4 are mainly one-way connection, which may be due to greater advantages resulting from the connection with a certain block in the network in comparison to that between certain blocks, as a result of factors such as the level of economic development, infrastructure configuration, and other factors.

OPEN IN VIEWER

Table 3.

Density Matrix and Image Matrix.

Year	Block	Density matrix				Image matrix
		Block 1	Block 2	Block 3	Block 4	Block 1	Block 2	Block 3	Block 4
2011	Block 1	0.8110	0.8830	0.8670	0.8400	1.0000	1.0000	1.0000	1.0000
	Block 2	0.8830	0.5330	0.9260	0.5330	1.0000	0.0000	1.0000	0.0000
	Block 3	0.3670	0.1480	0.3610	0.2000	0.0000	0.0000	0.0000	0.0000
	Block 4	0.3000	0.5330	0.2440	0.5500	0.0000	0.0000	0.0000	0.0000
2014	Block 1	0.8890	0.8520	0.9310	0.8890	1.0000	1.0000	1.0000	1.0000
	Block 2	0.8330	0.8000	0.8540	0.7860	1.0000	1.0000	1.0000	1.0000
	Block 3	0.5560	0.1460	0.5710	0.1610	0.0000	0.0000	0.0000	0.0000
	Block 4	0.0790	0.3330	0.1610	0.1670	0.0000	0.0000	0.0000	0.0000
2017	Block 1	0.8210	1.0000	0.9380	0.9380	-
	Block 2	0.8330	0.8000	0.8170	0.7780
	Block 3	0.5250	0.0830	0.5220	0.1830
	Block 4	0.0630	0.3890	0.0830	0.1670
2020	Block 1	0.8330	1.0000	0.9310	0.9440	-
	Block 2	0.8570	0.7860	0.9110	0.6430
	Block 3	0.5140	0.0710	0.4290	0.1040
	Block 4	0.1300	0.3330	0.1670	0.3330
2022	Block 1	0.8890	0.7410	0.8890	0.7780	-
	Block 2	0.7410	0.9330	0.7500	0.7000
	Block 3	0.3220	0.0500	0.3670	0.0200
	Block 4	0.1330	0.1330	0.1600	0.4500

Note: if the results of Image Matrix in 2017, 2020 and 2022 are the same as those for 2014, they can be expressed as.

In short, the construction of modernized industrial system is closely related to China’s ISML and its dynamic correlation among provinces. In the future, China should have effective measures according to local conditions to enhance the position of each province in the spatial correlation network of ISML and its correlation with other provinces, promote inter-provincial and inter-regional exchanges and cooperation, and balance local and overall benefits, so as to improve ISML.