Spatial Correlation Network and Driving Mechanisms of New Quality Productive Forces and Digital Transformation: Evidence from China

Abstract

Against the backdrop of deep digital economic integration, the synergistic agglomeration of new quality productive forces (NQPFs) and digital transformation (DT) has become a key engine for regional high-quality development. Based on data from 31 Chinese provinces during 2011–2023, this study measured the synergistic level of NQPF and DT. Using a modified gravity model, we convert attribute data into relational data and analyze driving mechanisms via social network analysis and quadratic assignment procedures. The results show that the synergistic agglomeration network presents club convergence rather than homogeneous dispersion, forming a structure comprising “polar-core absorption, hub transmission, hinterland integration, and peripheral marginalization.” Eastern regions act as net beneficiaries; Guangdong, Fujian, and other hubs become net-spillover brokers; central and western regions achieve element equilibrium, yet traditional industrial bases face a widening digital divide. Targeted policy implications are proposed. This study provides references for breaking regional digital barriers and optimizing the spatial layout of high-quality development.

1. Introduction

Amid the accelerated evolution of a new round of global scientific and technological revolution and industrial transformation, digital technologies, including artificial intelligence, big data, and the industrial Internet, have achieved in-depth penetration, giving rise to new business forms such as smart manufacturing and the platform economy and driving a fundamental shift in the allocation of production factors from traditional geospatial agglomeration to cross-border networked collaboration. New quality productive forces (NQPFs)—a distinctively strategic Chinese economic concept first articulated by President Xi Jinping in September 2023 and subsequently elevated to a core national strategy in the 2024 Government Work Report—have become a pivotal force in reshaping the global competitive landscape [1]. As a paradigmatic departure from traditional factor-driven growth, NQPF is fundamentally characterized by a “three-high” orientation: high technology as the primary driving force, with frontier innovations in artificial intelligence, quantum computing, and advanced manufacturing serving as revolutionary engines of productivity advancement; high efficiency as the core operational logic, demanding substantial leaps in total factor productivity through intelligent resource allocation and digital process optimization; and high quality as the overarching developmental objective, prioritizing sustainable, inclusive, and green growth over mere quantitative expansion. Unlike traditional productive forces that emphasize incremental improvements within existing paradigms, NQPF explicitly requires revolutionary breakthroughs across all three constitutive elements—innovative laborers, new labor objects (including data assets), and next-generation means of labor (including digital platforms and intelligent manufacturing systems).

Crucially, NQPF serves as a key endogenous driver for accelerating the green transition. Unlike traditional productive forces that have historically prioritized output expansion at the cost of ecological degradation, NQPF explicitly incorporates green development as a constitutive element rather than an external regulatory constraint. The high-technology dimension directly stimulates green technological innovation, where breakthrough advances in photovoltaic technology, hydrogen energy, new energy vehicles, and carbon capture constitute manifestations of NQPF and core enablers of decarbonization. The high-efficiency dimension promotes the ecological transformation of industrial structures by selecting against energy-intensive processes that depress total factor productivity. Furthermore, the digitalization inherent in NQPF development facilitates precision environmental governance through intelligent energy management, carbon emission monitoring, and data-driven regulatory mechanisms. The synergistic coupling of NQPF and DT further amplifies this green catalytic effect: Digital transformation enables real-time cross-regional pollution coordination, intelligent supply chain carbon footprint optimization, and platform-based green finance allocation. Consequently, understanding the spatial correlation network of NQPF–DT synergistic agglomeration has direct relevance for comprehending the diffusion pathways of green development across China’s regional landscape.

Globally, advanced economies are actively harnessing digital transformation to reconfigure production networks and upgrade industrial competitiveness. Germany’s “Industry 4.0,” for instance, exemplifies how cross-regional smart manufacturing networks can be orchestrated through digital technologies to enhance total factor productivity and capture higher positions in the global value chain [2]. In the Chinese context, this global trend has been theorized through the lens of NQPF—a distinctively Chinese conceptual framework rooted in the Marxist political economy. The full implementation of China’s “East Data West Computing” project explicitly takes digital transformation as the starting point to cultivate NQPF and optimize the spatial allocation of digital productive factors [3]. China’s national policy has increasingly prioritized the integration of the digital economy with the real economy, and recent strategic planning documents have further underscored the spatial optimization of digital economy development, in addition to building a regional synergy and urban–rural integration development pattern.

At present, the cultivation of NQPF and digital transformation at the provincial level in China exhibits significant regional imbalance characteristics. There are not only prominent digital divides and productivity gradient differences, but also a complex, unbalanced spatial correlation network formed by cross-regional factor interactions. In the explicit dimension, the proportion of the digital economy in the GDP of core eastern provinces such as Beijing, Shanghai, and Zhejiang is much higher than that of central and western regions; in the implicit dimension, eastern regions have formed a strong siphon effect by virtue of digital technology advantages, continuously absorbing high-end talents and innovation capital from central and western regions, resulting in the low-end lock-in dilemma and dependence on industrial transfer processes in the central and western regions [4,5]. Existing studies mostly focus on the local attribute characteristics of NQPF or the digital economy in a single region and rarely analyze the spatial correlation structure, block evolution, and driving mechanism of inter-provincial “NQPF–Digital Transformation” synergistic development from the perspective of relational networks. Practical issues such as the identification of core radiation nodes and edge recipient nodes, as well as the driving role of multi-dimensional spatial distance, urgently need to be scientifically answered from the network perspective.

Theoretically, this study breaks through the limitations of traditional regional economic constucts that rely on attribute data and static geographical perspectives, and it constructs a relational network analysis framework for the “synergistic evolution of NQPF and digital transformation”. It innovatively introduces social network analysis (SNA) and quadratic assignment procedures (QAPs) to realize a methodological leap from “node attributes” to “network relationships”. The QAP non-parametric test is used to deconstruct the driving mechanism of multi-dimensional matrices such as geographical distance, economic gap, and digital infrastructure difference on the synergistic agglomeration network, which effectively avoids the endogeneity and multicollinearity defects of traditional spatial econometric models and enriches the connotation of network spillover theory with respect to new economic geography in the digital economy era [6,7]. In practice, the research conclusions are closely linked to the needs of regional coordinated development strategies and the construction of a unified national market, accurately portray the topological roles and block affiliations of provincial nodes in the network, provide empirical support for the formulation of differentiated policies for “net spillover” core blocks and “edge dependent” blocks, identify inter-provincial synergy barriers based on the driving mechanism revealed by QAP, and provide feasible implementation paths for optimizing the national spatial layout of NQPF [8].

Before proceeding to the empirical design, it is essential to clarify the conceptual boundary and operationalization logic of “synergistic agglomeration” as employed in this study. In traditional economic geography, “agglomeration” typically refers to the spatial clustering of economic activities within bounded geographic areas, measured by static concentration indices such as location quotients or spatial Gini coefficients (Martin and Sunley, 2003) [9]. However, in the digital economy era, production factor flows increasingly transcend geographical boundaries, rendering purely distance-based agglomeration metrics inadequate for capturing the networked, cross-regional interdependencies that characterize modern productive systems (Boschma, 2005; Balland et al., 2019) [10,11].

Accordingly, this study reconceptualized “synergistic agglomeration” as a relational network phenomenon comprising two analytically distinct but methodologically integrated dimensions:

(1) The “synergy” dimension captures the intra-provincial coupling coordination between the NQPF and DT system. It is operationalized through the coupling coordination degree (CCD) model, yielding a composite synergistic development index $S_i$ for each province i in each year t. This index quantifies the degree to which a province’s NQPF advancement and DT progression are mutually reinforcing rather than developing in isolation.

(2) The “agglomeration” dimension captures the inter-provincial spatial clustering and hierarchical structuring of these synergistic linkages across the national network. Rather than being measured by a single static index, agglomeration is operationalized through the emergent topological properties of the spatial correlation network itself—namely, network density (reflecting the overall intensity of cross-regional factor flows), degree and betweenness centrality (identifying hub nodes that concentrate connectivity), and the CONCOR blockmodel partitioning (revealing how provinces cluster into hierarchical functional blocks with asymmetric spillover relationships). In this framework, a densely connected, hierarchically stratified network with identifiable core–periphery blocks constitutes empirical evidence of spatial agglomeration—not in the traditional geographic sense but in the relational network sense.

This dual operationalization is consistent with the network-based agglomeration perspective in evolutionary economic geography (Boschma, 2005) [10], which holds that modern agglomeration dynamics are driven not merely by geographical proximity but by multidimensional relational linkages, including cognitive, institutional, and organizational proximities. It also resonates with Balland et al.’s (2019) [11] emphasis that production networks exhibit “club convergence,” where nodes with similar relational profiles cluster into cohesive subgroups regardless of physical distance.

Taking 31 provinces (autonomous regions and municipalities directly under the Central Government) of China from 2011 to 2023 as research samples and focusing on the synergistic development of NQPF and digital transformation, this study systematically answers three progressive core questions: first, the overall and individual topological characteristics of the inter-provincial spatial correlation network of synergistic development between NQPF and digital transformation; second, the spatial clustering blocks of provincial nodes and the energy flow and dependency relationship between core and edge blocks; third, the relational driving mechanism of multi-dimensional distances such as geographical proximity, economic development difference, and digital infrastructure gap on the formation and evolution of the network. The research follows a rigorous technical “attribute measurement–relational reconstruction–network dissection–driver test” route: the coupling coordination degree model is used to calculate the synergistic development level; the modified gravity model is adopted to transform attribute data into a 31 × 31 spatial correlation gravity matrix; SNA and CONCOR blockmodels are applied to analyze the network topology and block structure; finally, QAP analysis is used to eliminate multicollinearity interference and accurately identify the deep-seated spatial relational drivers of network evolution.

2. Literature Review

To notably delineate the spatial correlation characteristics and blockmodel evolution of the synergistic agglomeration between NQPF and DT in China, this study systematically synthesizes cutting-edge literature from information systems (ISs), economic geography, and innovation economics. The extant research predominantly unfolds along three logical trajectories: the reconfiguration of spatial economic landscapes driven by DT, the theoretical evolution and international mapping of NQPF, and the paradigm of industrial synergistic agglomeration via SNA.

2.1. Digital Transformation and the Reconfiguration of Spatial Economic Landscapes

With the profound advancement of the Fourth Industrial Revolution, data—acting as a novel production factor—has fundamentally subverted the core assumptions of traditional spatial economics. At the frontier of international literature, a plethora of studies focus on the “spatial spillover effects” of digital technologies. In their authoritative review on digital economics, Goldfarb and Tucker (2019) argue that although digital technologies drastically reduce the marginal cost of information transmission, they do not entirely obliterate geographical boundaries; rather, the agglomeration of digital infrastructure precipitates a novel “digital divide” [12]. From an IS perspective, Vial (2019) and Verhoef et al. (2021) conceptualize the multidimensional connotations of DT, emphasizing that it transcends mere technological adoption to constitute a fundamental reconfiguration of organizational value creation logic [13,14]. Hanelt et al. (2021) further substantiate that the boundary-spanning empowerment mechanisms of digital platforms are orchestrating a reconfiguration of innovation resource allocation networks [15]. To reap benefits from the digital deluge, cultivating dynamic capabilities is perceived as the core engine to overcome spatial disadvantages (Warner and Wäger, 2019) [16]. Concurrently, domestic scholars primarily explore this phenomenon within the macroeconomic transition context unique to China. At the macroeconomic level, Wang et al. (2024) empirically demonstrate that the digital economy significantly stimulates urban entrepreneurial activity, providing micro-foundational evidence that digital dividends can catalyze regional economic vitality and factor reconfiguration [17]. At the micro-mechanism level, Liu et al. (2024) demonstrate that enterprise digital transformation significantly enhances stock liquidity through improved corporate governance, revealing the capital market response to DT adoption [18]. Complementarily, Zhang et al. (2023) provide micro-level evidence from the Chinese manufacturing sector, showing that digital inputs substantially boost enterprise green productivity, thereby extending the “spatial ripple effects” of DT from financial markets to real-economy efficiency gains [19]. Nevertheless, highly developed digital networks may also empower eastern developed provinces to accelerate the extraction of primary factors from central and western regions. This dual nature provides the theoretical provenance for exploring the “polar-core absorption” phenomenon within spatial networks in this study.

2.2. Theoretical Evolution of NQPF and Its International Mapping

NQPF represents a major theoretical innovation recently proposed within the Chinese political economy context, and it is rooted in Marxist productive forces theory and adapted to China’s contemporary development stage. As a concept with specific Chinese policy connotations, NQPF is not directly equivalent to any single Western industrial paradigm. Nevertheless, its theoretical core—leveraging frontier technologies to achieve substantial leaps in total factor productivity—resonates with and can be meaningfully mapped onto established international discourses on technological innovation and AI-driven productivity effects. Hong and Wang (2024) posit that the core of NQPF lies in scientific and technological innovation, which must rely on the deep integration of digital technologies and the real economy to achieve a substantial leap in total factor productivity (TFP) [20]. From a macro-logical standpoint, Huang and Sheng (2024) emphasize three pivotal dimensions: high-tech orientation, high efficiency, and greenization [21]. Yang et al. (2022) further note that the digital economy era has imposed transformative challenges on enterprise management paradigms, particularly in financial market risk management, where big data capabilities have become indispensable for navigating the complexities introduced by new productive forces [22]. While NQPF remains a distinctively Chinese construct, its analytical dimensions find conceptual parallels in the international literature. Specifically, the emphasis on technology-driven productivity leaps resonates with research on “frontier technological innovation” and the “Artificial Intelligence (AI) productivity effect,” although these international frameworks do not carry the same political economy connotations as NQPF. Acemoglu and Restrepo (2020) deeply dissect the reconfiguration mechanisms of automation technologies on labor markets, highlighting the complex interplay between “productivity effects” and “displacement effects” [23]. Brynjolfsson et al. (2017) offer a profound reflection of the “productivity paradox” in the AI era, pointing out the time lags inherent in realizing technological dividends [24]. Empirically, Mikalef and Gupta (2021) and Bolanos et al. (2024) validate the decisive role of AI and big data governance capabilities in elevating enterprises’ disruptive innovation [25,26]. Furthermore, Appio et al. (2021) and Nambisan et al. (2019) confirm that digital affordances significantly broaden the spatial boundaries of innovation and entrepreneurship [27,28]. Liang and Li (2024) also indicate that digital empowerment is the core driver propelling the next-generation industrial paradigm shift [29]. This robust body of literature lays the logical foundation for this study to conceptualize DT and NQPF as a “dual-helix ecosystem” of synergistic empowerment.

2.3. Industrial Synergistic Agglomeration and Spatial Network Evolution

Traditional research on industrial agglomeration and regional synergy relies heavily on geographical concentration metrics or static spatial econometric models. Grounded in evolutionary economic geography (EEG), Boschma (2005) proposes that inter-regional synergistic innovation networks frequently exhibit “club convergence” characteristics, where multidimensional proximities (cognitive, institutional, and geographical) notably dictate knowledge spillovers [10]. Leveraging complex systems theory, Balland et al. (2019) note that early-mover regions easily forge technological barriers, making it exceedingly difficult for latecomers to penetrate core networks [11]. Martin and Sunley (2003) sharply point out that traditional attribute data analysis often fragments the cross-boundary interactive ties between regions, failing to capture the authentic topological structures of industrial clusters [9]. In recent empirical applications, Li et al. (2024) employ the modified gravity model combined with SNA to comparatively deconstruct the spatial correlation network structure and formation mechanisms of urban high-quality economic development across the Yangtze River Economic Belt and the Yellow River Basin [30]. Ji et al. (2025) explored the network structure and drivers of NQPF to provide references for its enhancement and high-quality socio-economic development [31].

2.4. The SNA Paradigm and the Application of the CONCOR Algorithm

To shatter the bottlenecks of static geographical measurements, social network analysis (SNA) has been rapidly adopted as a relational data mining paradigm. Borgatti et al. (2009) systematically articulate the application potential of SNA in the social sciences [32]. Regarding the identification of node roles within networks, Freeman’s (1978) centrality theory [33], Burt’s (2004) “structural holes” theory [34], and Granovetter’s (1973) “strength of weak ties” [35] provide a robust bedrock for distinguishing “hubs” and “bridges.” For the partitioning of network blockmodels, Finn (2021) proposes multilayer network analyses as a comprehensive toolkit for measuring social structure, demonstrating the versatility of iterative subgroup algorithms such as CONCOR in capturing multidimensional relational patterns [36]. Complementarily, the core–periphery model proposed by Borgatti and Everett (2000) [37] has become the golden standard for deconstructing the hierarchical distribution of complex networks (Wasserman and Faust, 1994) [38]. Gao et al. (2016) further demonstrate how the structural characteristics of complex networks impact systemic resilience [39]. In recent years, these classic methodologies have found renewed vitality in digital networks and supply chain domains. Ivanov et al. (2019) apply SNA to dissect risk propagation in digital supply chain networks [40]. Constantinides et al. (2018) and De Reuver et al. (2018) explore the network evolution effects of digital platform architectures [41,42]. Furthermore, scholars such as Duan et al. (2019), Urbinati et al. (2020), Mehta et al. (2022), and Bresciani et al. (2021) have extensively utilized network algorithms to capture dynamic value within AI decision-making, big data innovation ecosystems, and digital analytics [43,44,45,46]. In the Chinese context, Li et al. (2014) were among the first to combine a modified gravity model with SNA to reveal the spatial correlation laws of China’s regional economy [47]. Xia et al. (2024) empirically investigate the effect and mechanism through which industrial intelligence reshapes industrial structure, providing direct evidence that the intellectualization of production networks is reconfiguring cross-regional factor allocation patterns [48]. These classic and cutting-edge methodological studies provide strong technical support for constructing the “synergistic agglomeration gravity matrix” in this study.

2.5. Literature Synthesis and Points of Departure

Before delineating the research gaps, it is important to acknowledge and differentiate this study from two closely related recent publications. Zhao, Zheng, and Dai (2025) [49] investigate the causal impact of NQPF on regional economic disparities using panel econometric methods (system GMM and threshold regression), demonstrating that NQPF development can reduce and exacerbate regional disparities depending on institutional quality thresholds. While their study provides valuable causal evidence, it treats each province as an independent observation and does not examine the inter-provincial relational network structure governing how NQPF-related spillovers flow across space. More directly relevant, Wang Z, Liu W, and Yang N et al. (2025) [50] construct a spatial correlation network of NQPF at the provincial level using a gravity model and SNA, identifying network structural characteristics and correlation mechanisms. Their pioneering work confirms the value of network analysis for NQPF research. However, the present study differs from and extends Wang et al. (2025) [50] in three critical respects: (1) conceptual scope—we examine the synergistic agglomeration between NQPF and DT (operationalized through the coupling coordination degree) rather than NQPF alone, capturing interaction effects that neither dimension individually represents; (2) methodological innovation—our modified gravity model incorporates a dual-distance weighting mechanism (geographic distance + digital development disparity) and a digital contribution coefficient ($k_{ij}$) absent from their specification; (3) temporal depth—our 13-year panel (2011–2023) enables systematic dynamic evolution analysis, including the identification of how major policy initiatives (e.g., “Internet Plus” 2015, “New Infrastructure” 2020) reshape the correlation structure over time.

In summary, while the extant literature provides a fertile theoretical soil, significant gaps remain. First, existing studies frequently treat “Digital Transformation” as a unidirectional explanatory variable, rarely juxtaposing it with “New Quality Productive Forces” as parallel systems to investigate their synergistic agglomeration evolution. Second, traditional spatial econometrics fail to delineate the asymmetric, bidirectional spillovers of production factors across geographical confines, thus falling short of revealing the deep-seated hierarchical transitions within networks. Third, there is a paucity of research applying micro-level network analytics to macro-regulatory scenarios in China, such as the “East Data West Computing” project or the “Revitalization of Old Industrial Bases.” Addressing these lacunae, this study pioneers the construction of a synergistic agglomeration correlation network for both systems. Relying on SNA and the CONCOR algorithm, it dissects the characteristics of four heterogeneous blocks, aiming to bridge the existing void in the literature regarding spatial hierarchical evolution.

3. Materials and Methods

3.1. Data Sources and Preprocessing

Based on a panel of 31 Chinese provinces, autonomous regions, and municipalities (excluding Hong Kong, Macao, and Taiwan) from 2011 to 2023, this study constructed a comprehensive dataset encompassing multidimensional indicators such as economic development, innovation inputs, digital infrastructure, and policy texts. The primary data were systematically collated from authoritative sources, including the China Statistical Yearbook, China Statistical Yearbook on Science and Technology, Statistical Report on the Development of China’s Internet and Communications Industry, provincial statistical communiqués on national economic and social development, and publicly available datasets from the National Intellectual Property Administration (CNIPA) and the China Internet Network Information Center (CNNIC). To ensure the integrity and reliability of the panel, missing values for certain years were robustly imputed using linear interpolation of adjacent years and regression estimation techniques.

The evaluation indicator systems for the NQPF and DT subsystems are adopted from our previously published and peer-reviewed study (Dai et al., 2025) [51], which systematically developed and validated a comprehensive measurement framework for assessing the coupling coordination between new quality productivity and digital transformation across China’s 31 provinces.

The NQPF evaluation subsystem is theoretically grounded in the “three elements of productive forces” framework from Marxist political economy, decomposing new quality productive forces along three criteria layers: laborers (encompassing economic output, employment structure, educational attainment, cultivation expenditure, innovation spirit, and entrepreneurship spirit), labor objects (covering informatization level, green ecology, and green production), and means of labor (including infrastructure, energy utilization potential, technological innovation level, and digitalization level), totaling 20 third-level indicators. This tripartite decomposition is theoretically complete—exhaustively covering the human agent, the material target, and the instrumental medium of production—and empirically validated in the NQPF measurement literature (Hong and Wang, 2024 [20]; Huang and Sheng, 2024 [21]).

The DT evaluation subsystem follows the widely recognized “digital infrastructure–digital industrialization–industrial digitalization” framework, corresponding to the “penetration–integration–output” evolutionary logic of digital technology diffusion, comprising 17 third-level indicators. This dimensional structure is firmly grounded in international IS scholarship (Vial, 2019 [13]; Verhoef et al., 2021 [14]) and established domestic digital economy measurement practices.

The complete indicator definitions, measurement methods, data sources, and attribute classifications for both subsystems are presented in Appendix A (

Table A1. Evaluation index system for new quality productive forces (NQPFs).

1st-Level Index	2nd-Level Index	3rd-Level Index	Measurement Method	Direction
Laborers	Economic Output	A1: Per Capita GDP	GDP/Total Population	+
	Economic Income	A2: Per Capita Wage	Average Wage of Employees on Duty	+
	Employment Structure	A3: Proportion of Employment in Tertiary Industry	Number of Employees in Tertiary Industry/Total Number of Employees	+
	Educational Attainment	A4: Proportion of People with Higher Education	Average Years of Education per Capita	+
	Cultivation Expenditure	A5: Intensity of Education Expenditure	Education Expenditure/Total Fiscal Expenditure	+
	Innovation Spirit	A6: Innovation Human Input	Full-time Equivalent of R&D in Industrial Enterprises above Designated Size	+
	Entrepreneurship Spirit	A7: Entrepreneurship Activity	Number of Innovative Enterprises per 100 People	+
Labor Object	Informatization Level	A8: Enterprise Informatization Level	Number of Enterprises Engaged in E-commerce Transactions/Total Number of Enterprises	+
	Green Ecology	A9: Effort in Environmental Protection	Environmental Protection Expenditure/General Fiscal Expenditure	+
	Green Production	A10: Pollution Prevention Quality	Chemical Oxygen Demand Emission/GDP	-
		A11: Pollution Prevention Quality	Sulfur Dioxide Emission/GDP	-
		A12: Green Invention Achievements	Number of Green Patent Applications/Number of Patent Applications	+
Means of Labor	Infrastructure	A13: Traditional Infrastructure	Highway Mileage	+
		A14: Traditional Infrastructure	Railway Mileage	+
		A15: Digital Infrastructure	Length of Optical Cable Lines	+
		A16: Digital Infrastructure	Number of Internet Access Ports per Capita	+
	Energy Utilization Potential	A17: Pollution Prevention Ability	Treatment Capacity of Waste Gas Treatment Facilities	+
	Technological Innovation Level	A18: Number of Patents per Capita	Number of Authorized Patents/Total Population	+
		A19: Economic Input in New Products	New Product Development Expenditure/GDP	+
	Digitalization Level	A20: Digital Economy	Digital Economy Index	+

and

Table A2. Evaluation index system for digital transformation (DT).

1st-Level Index	2nd-Level Index	3rd-Level Index	Measurement Method	Direction
Digital Transformation	Digital Infrastructure	B1: Internet Broadband Access Rate	Number of Internet Broadband Access Ports/Permanent Resident Population in the Region	+
		B2: Internet Broadband Penetration Rate	Number of Internet Broadband Access Users/Permanent Resident Population in the Region	+
		B3: Mobile Phone Facility Scale	Mobile Phone Switching Capacity	+
		B4: Length of Long-Distance Optical Cable Lines	Length of Long-Distance Optical Cable Lines	+
		B5: Number of Web Pages	Number of Web Pages	+
	Digital Industrialization	B6: Mobile Phone Penetration Rate	Mobile Phone Penetration Rate	+
		B7: Number of Legal Entities in Information Transmission, Software, and IT Services	Number of Legal Entities in Information Transmission, Software, and IT Services	+
		B8: Proportion of Employees in Information Software Industry	Employees in Information Transmission, Software, and IT Services (Urban Units)/Urban Unit Employees	+
		B9: Domestic Patent Application Acceptance Quantity	Domestic Patent Application Acceptance Quantity	+
	Industrial Digitization	B10: Digital Inclusive Finance	Peking University Digital Inclusive Finance Index	+
		B11: Proportion of Enterprises with E-commerce Transactions	Proportion of Enterprises with E-commerce Transactions	+
		B12: E-commerce Sales Amount	E-commerce Sales Amount	+
		B13: Number of Websites per 100 Enterprises	Number of Websites per 100 Enterprises	+
		B14: Added Value of Secondary and Tertiary Industries	Added Value of Secondary Industry + Added Value of Tertiary Industry	+
		B15: Investment in Technological Innovation	R&D Expenditure of Industrial Enterprises Above Designated Size	+
		B16: Express Delivery Volume	Express Delivery Volume	+
		B17: Digital Economy Index	Digital Economy Index	+

). All raw data were extracted from the China Statistical Yearbook, China Science and Technology Statistical Yearbook, China Population and Employment Statistical Yearbook, provincial statistical yearbooks, the EPS database, and the Peking University Digital Inclusive Finance Index, covering 31 provinces (excluding Hong Kong, Macao, and Taiwan) over the period 2011–2023.

Regarding data processing, the following standardized protocol was applied, consistent with Dai et al. (2025) [51]:

Step 1: Missing value treatment: Sporadic missing values (affecting less than 3% of total observations, concentrated in 2011–2013 for indicators A8, B10, and B11) were imputed via linear interpolation between adjacent years. No indicator had more than two consecutive missing years for any province.

Step 2: Directionality harmonization and normalization: All indicators were classified as either positive (higher values indicate better performance) or negative (higher values indicate worse performance); see the “Direction” column in Table A1 and Table A2. Positive indicators were normalized via $x_{ij}^{\prime }=\left(x_{ij}-{\mathrm{m}\mathrm{i}\mathrm{n}}_j\right)/\left({\mathrm{m}\mathrm{a}\mathrm{x}}_j-{\mathrm{m}\mathrm{i}\mathrm{n}}_j\right)$; negative indicators were normalized via $x_{ij}^{\prime }=\left({\mathrm{m}\mathrm{a}\mathrm{x}}_j-x_{ij}\right)/\left({\mathrm{m}\mathrm{a}\mathrm{x}}_j-{\mathrm{m}\mathrm{i}\mathrm{n}}_j\right)$. The min and max values are computed globally across all provinces and all years (2011–2023) to ensure temporal comparability—that is, a given normalized score retains consistent meaning across years.

Step 3: Entropy weight method (EWM): Indicator weights were determined using the full pooled panel (31 provinces × 13 years = 403 observations) as a single cross-section, yielding a time-invariant weight vector for each subsystem. The pooled approach is adopted rather than year-by-year weighting because of the following reasons: (a) it avoids artificial discontinuities in composite scores caused by annual weight fluctuations, (b) it ensures that changes in composite scores over time reflect genuine changes in underlying indicators rather than mechanical shifts in weighting structure, and (c) it is consistent with the dominant practice in the NQPF measurement literature (Ji et al., 2025 [31]; Wang Z, Liu W, Yang N et al., 2025 [50]). The key EWM formulas are presented in Appendix B.

Step 4: Composite score computation: Final composite scores for the NQPF and DT subsystems were obtained using weighted linear aggregation, $U_i^t={\sum }_{j=1}^n{w}_j\cdot x_{ij}^t$, where $w_j$ is the entropy-derived weight for indicator $j$, and $x_{ij}^t$ is the normalized value of indicator $j$ for province $i$ in year $t$.

These two indicator systems not only maintain their independent functional positioning within their respective dimensions but are also intrinsically interdependent at their underlying logical core. Together, they provide robust data support for the subsequent delineation of the provincial spatial correlation network and the deconstruction of its evolutionary drivers.

3.2. Methodology

3.2.1. Construction of the Spatial Correlation Network: Modified Gravity Model and SNA

To accurately capture the interactive correlations between provinces, this study refined the traditional gravity model by incorporating a dual-weighting mechanism comprising geographical distance and digital distance, thereby constructing a directed spatial correlation matrix. This methodological design directly operationalizes the dual dimensions of “synergistic agglomeration” defined above. The CCD-derived synergistic index ($S_i$) serves as the “mass” parameter in the gravity model, encoding the “synergy” dimension into the relational data. The modified gravity model then translates these node-level synergistic attributes into a dyadic correlation matrix, which—after binarization and SNA—yields the network topological indicators (density, centrality, and blockmodel structure) that collectively operationalize the “agglomeration” dimension. Thus, the analytical pipeline can be expressed as follows: Synergy (CCD→$S_i$)→Gravity Model→Correlation Matrix→SNA Topology (=Agglomeration Measurement). This ensures that “synergistic agglomeration” is not merely a rhetorical label but a construct with clear, traceable operationalization at each analytical stage. Consequently, drawing upon the relevant literature [52,53,54,55], the modified gravity model introduces “digital economic distance” alongside geographical spatial distance to calculate the inter-provincial correlation intensity (gravity) as follows:

$$F_{ij}=k_{ij}{\displaystyle \frac{\sqrt[3]{C{odigi}_i\ast {GDP}_i}\times \sqrt[3]{{Codigi}_j\ast {GDP}_j}}{{(d_{ij}/g_{ij})}^2}}.$$

(1)

$F_{ij}$ denotes the inter-provincial spatial correlation intensity. $k_{ij}$ represents the digital contribution coefficient, formulated as $k_{ij}={\displaystyle \frac{C{odigi}_i}{C{odigi}_i+{Codigi}_j}}$. This parameter is introduced to modify the traditional gravity model, specifically highlighting the asymmetric and differentiated impact of DT on inter-provincial linkages; that is, provinces exhibiting a higher synergistic index are assigned greater mathematical weights in the correlation intensity, notably reflecting the catalytic role of digital proficiency in accelerating factor mobility and strengthening economic interconnectedness. $C{odigi}_i$ and ${Codigi}_j$ stand for the synergistic development indices of “NQPF–DT” for province $i$ and province $j$, respectively. These are precisely calculated via a modified CCD model. This overarching index integrates the NQPF evaluation system (covering dimensions such as innovation drive, efficiency enhancement, and industrial upgrading) with the DT indicator system (encompassing infrastructure, technological application, and environmental support). The index values are normalized within the range of [0, 1], where a higher value signifies a superior level of synergy. ${GDP}_i$ and ${GDP}_j$ signify the per capita gross domestic product (GDP) extracted directly from provincial statistical yearbooks. These parameters capture the regional economic scale, functioning as the fundamental “economic mass” that drives inter-provincial correlations. $d_{ij}$ indicates the geospatial distance between provincial capital cities (measured precisely via latitude and longitude coordinates), while $g_{ij}$ denotes the digital development disparity (calculated as the absolute difference in digital economy indices between the two provinces). These two components are mathematically synthesized into a “composite distance” matrix, clearly capturing the dual spatial friction imposed by geographical boundaries and digital divides.

A methodological note on the cube-root transformation is warranted. In Equation (1), the synergistic development indices ($C{odigi}_i$, ${Codigi}_j$) and per capita GDP values (${GDP}_i$, ${GDP}_j$) are subjected to a cube-root transformation (i.e., raised to the power of 1/3). This transformation is motivated by three complementary considerations.

First, from a distributional perspective, provincial-level comprehensive indices and economic aggregates in China exhibit pronounced right-skewed distributions. A small number of eastern provinces (e.g., Guangdong, Jiangsu, Beijing) possess disproportionately large values relative to the vast majority of central and western provinces. Without transformation, these extreme values would dominate the gravity matrix, inflating the correlation intensities between a few core provinces while compressing the ties between peripheral provinces to near-zero levels. This would result in a degenerate network where meaningful inter-provincial linkages outside the eastern core are systematically obliterated during the binarization step. The cube-root function (x^1/3) effectively compresses the upper tail of the distribution while preserving the ordinal ranking, relative spacing, and non-negativity of the original data, thereby ensuring that the gravity matrix retains sufficient variance across all provincial pairs.

Second, from a comparative perspective, the cube-root transformation offers a distinct advantage over the commonly used logarithmic transformation. Several provinces in the early years of the sample period (2011–2013) exhibit synergistic index values at or very close to zero. The logarithmic function is undefined at zero and approaches negative infinity near zero, necessitating arbitrary adjustments (e.g., adding a small constant) that introduce systematic bias. In contrast, the cube-root function is naturally defined for all non-negative values, including zero (0^1/3 = 0), preserving the integrity of the original data without ad hoc modifications. Compared with the square-root transformation (x^1/2), the cube root provides a moderately stronger compression effect for highly skewed data, which is more appropriate given the extreme inter-provincial disparities observed in China’s digital economy landscape.

Third, from a literature precedent perspective, the application of power transformations (including cube-root and similar fractional exponents) in modified gravity models for spatial correlation network construction is well established. Huo et al. (2022) [6] adopt an analogous power transformation in their modified gravity model to construct the spatial correlation network of China’s building carbon emissions. Zhang and Yao (2023) [54] apply a similar approach in analyzing the spatial correlation networks of carbon emissions in emerging economies. Li et al. (2024) [30] and Bi et al. (2024) [52] also employ comparable gravity model specifications with power-transformed variables in their studies of urban economic development and carbon emission networks, respectively.

To facilitate SNA, the calculated gravity matrix must undergo a 0–1 binarization process. Specifically, the annual mean of the correlation intensities ($F_{ij}$) is adopted as the threshold. If $F_{ij}$ is greater than or equal to this mean value, it is assigned a value of 1 (indicating the existence of a valid network tie); otherwise, it is assigned 0. This procedure ultimately yields the definitive 31 × 31 directed spatial correlation matrix for each respective year.

3.2.2. Social Network Analysis (SNA)

Global network characteristics: This study calculates network density (the ratio of actual ties to the maximum possible ties), network connectedness (the robustness of connected subgraphs), and network hierarchy (the extent of asymmetric control exerted by core nodes) to reveal the overall connectivity and hierarchical architecture of the synergistic network. Individual network characteristics: By measuring degree centrality (the number of direct connections), betweenness centrality (the frequency a node acts as an intermediary), and closeness centrality (the shortest path from a node to all others), this study precisely identifies core hubs, critical bridges, and peripheral nodes within the network. Core–periphery structure analysis: As a pivotal method for identifying network stratification and “dominance-dependence” node relationships, the core–periphery model distinguishes between the core block (a densely connected set of nodes with strong resource control) and the peripheral block (a sparsely connected set highly dependent on the core). This reveals the network’s hierarchical resource allocation and interaction paradigms. Drawing on the relevant literature [55], this study utilized the binarized spatial correlation matrix as input. By iteratively optimizing the partition of core and peripheral nodes, the algorithm maximizes the discrepancy between intra-core density and inter-periphery sparsity. Simultaneously, the structural fitness is verified via the correlation coefficient, thereby notably dissecting the hierarchical positioning, resource radiation, and dependency logic of provinces within the “NQPF–DT” spatial correlation network.

3.2.3. Driving Mechanism Analysis: The QAP Regression Model

The spatial correlation network of the synergistic agglomeration between NQPF and DT exhibits typical network interdependence; that is, inter-provincial ties do not exist in isolation but are intricately shaped by the complex interplay of geographical space, factor endowments, and institutional environments. Traditional ordinary least squares (OLS) regressions strictly hinge on the independent and identically distributed (IID) assumption. Applying OLS directly to dyadic network data inevitably triggers severe endogeneity and multicollinearity issues due to spatial autocorrelation. Conversely, the QAP is a non-parametric testing method based on random matrix permutations. It effectively circumvents the non-independence bias of network data, precisely identifying the causal linkages and correlation intensities between the explanatory and dependent matrices. Aligning with the theme of this study, the high applicability and cutting-edge nature of the QAP regression model are manifested in three dimensions. Suitability for “relational” data structures: The dependent and explanatory variables in this study are 31 × 31 inter-provincial relational matrices, perfectly satisfying QAP’s core data requirements. Transcending the independence trap: By generating standard errors through thousands of random matrix permutations, QAP effectively isolates the autocorrelation interference inherent in spatial network data. Unboxing the “relation-to-relation” driving mechanism: QAP can directly delineate the mapping between multidimensional inter-provincial potential gaps and synergistic network intensity, notably resonating with the theoretical essence of cross-regional synergistic interactions of “NQPF–DT.” Based on this logic, this study employs the QAP regression model to examine the impact of multidimensional driving factors on the formation of the spatial correlation network. The specific steps are as follows:

• Selection of Driving Factors and Matrix Construction:

Guided by theoretical mechanisms and data availability, this study constructed seven core explanatory variable matrices from two dimensions: geographical spatial distance and multidimensional socio-economic disparities. The geographical distance matrix (Geo) was constructed based on the spherical distance between capital cities to measure the friction effect of physical spatial barriers on network ties. The economic disparity matrix (Econ) was represented by the absolute difference matrix of per capita GDP, measuring the gravitational pull of economic potential gaps on cross-regional factor mobility. The digital infrastructure disparity matrix (Dig) was captured by the absolute difference in broadband penetration rates (or length of long-distance optical cables), reflecting the impact of the inter-provincial digital divide. The technological innovation disparity matrix (Inno) was measured by the absolute difference in invention patents per 10,000 people, gauging the gap in knowledge spillovers and technological potential. The human capital disparity matrix (Hum) was represented by the absolute difference in average years of schooling, depicting the support of cross-regional mobility of high-quality labor for network linkages. The financial development disparity matrix (Fin) was measured by the absolute difference in the ratio of deposit and loan balances of financial institutions to GDP, reflecting the spatial asymmetry of capital allocation. The government intervention disparity matrix (Gov) was captured by the absolute difference in the ratio of local general public budget expenditure to GDP, measuring the disparities in local institutional environments and policy barriers.

2.

Model Specification and Parameter Estimation:

Utilizing Ucinet 6.0 software, this study conducted QAP regression analysis, setting the “NQPF–DT” synergistic spatial correlation matrix (Net) as the dependent variable to construct the following multiple matrix regression model:

$$Net={\beta }_0+{\beta }_{1}Geo+{\beta }_{2}Econ+{\beta }_{3}Dig+{\beta }_{4}Inno+{\beta }_{5}Hum+{\beta }_{6}Fin+{\beta }_{7}Gov+\epsilon .$$

(2)

where Net is the spatial correlation matrix, ${\beta }_0$ is the constant term, ${\beta }_i$($i$ = 1, 2, …, 7) represents the standardized regression coefficients for each driving factor matrix, and ε is the residual matrix. During estimation, 5000 random permutations are selected to test the significance of the coefficients. The focus is placed on the directional signs (positive drivers or negative inhibitors) and relative intensities of the regression coefficients, thereby precisely isolating the key structural forces dictating the evolution of the inter-provincial synergistic network.

3.3. Methodological Applicability and Data Reliability

The methodological system of this study achieves a paradigm shift from the surface to the core and from isolated “points” to an interconnected “network.” Specifically, it boasts three significant advantages. Scientific rigor and objectivity of the measurement system: By deeply coupling the political economy connotations of NQPF with the evolutionary characteristics of the digital economy, this study circumvents the one-sidedness of single indicators. Furthermore, employing the entropy weight method for objective dynamic weighting effectively eliminates subjective evaluation biases, accurately and authentically reconstructing the spatiotemporal asymmetric attributes of China’s provincial “NQPF–DT.” Multidimensionality and dynamics of spatial network delineation: Breaking away from the static presets of traditional spatial economics that rely merely on “0–1 geographical adjacency” or pure physical distance, this study adopts a modified gravity model nesting “geographical–economic (or digital)” dual potential gaps. This achieves a qualitative leap in data morphology—from isolated “attribute nodes” to complex “relational links.” Combined with SNA and blockmodeling, it not only precisely measures global and local topological features but also dissects the dynamic evolutionary laws of inter-provincial factor flows, block clustering, and asymmetric spillovers. Methodological frontier in driving mechanism analysis: This study completely abandoned the limitations of traditional spatial econometric models (e.g., SDM), which inevitably suffer from endogeneity and multicollinearity when processing high-dimensional network matrices. Instead, it innovatively introduces the QAP non-parametric testing method. By elevating the analytical perspective from traditional “attribute variable regression” to “relational matrix fitting” through multidimensional spatial difference matrices (e.g., digital divides, economic gaps, institutional barriers), it successfully achieves the precise isolation and scientific inference of the deep-seated “relational drivers” propelling the formation and evolution of the provincial synergistic network. Regarding data reliability, the research sample spanned 13 years (2011–2023), with comprehensive data sourced from authoritative national statistical archives, such as the China Statistical Yearbook and the China Statistical Yearbook on Science and Technology. For core variables (e.g., digital innovation output, NQPF inputs), cross-validation across multiple databases was systematically conducted. Minor missing values were scientifically imputed using linear interpolation and smoothing techniques, strictly ensuring the continuity and integrity of the strongly balanced panel data. Consequently, the robustness and reproducibility of the empirical inferences and research conclusions are guaranteed.

4. Results

4.1. Trend Analysis of the Synergistic Agglomeration Development

To intuitively unveil the spatial differentiation and evolutionary characteristics of the synergistic agglomeration between NQPF and DT in China from a macroscopic perspective, this study utilizes spatial analysis tools to map the 3D trend surface fitting perspectives of the relevant indices for 2011, 2017, and 2023 (Figure 1). The inclusion of the intermediate year 2017—corresponding to the phased peak of network density (0.2323,

Table 1. Eigenvalues of network density and correlation characteristics of the synergistic agglomeration of NQPF and DT in China.

Indicators	2011	2014	2017	2020	2023
Network Size	31	31	31	31	31
Number of Network Ties	211	204	216	200	209
Network Density	0.2269	0.2194	0.2323	0.2151	0.2247
Network Connectedness	1	1	1	1	1
Network Hierarchy	0.2857	0.4211	0.4211	0.4211	0.4211
Network Efficiency	0.7448	0.7379	0.7264	0.7356	0.7241

)—enables direct visual verification of the non-monotonic evolutionary trajectory. Observing the fitted curves along the longitudinal (East–West) axis, the synergistic agglomeration level exhibits a pronounced “high in the East, low in the West” incremental spatial gradient. Empowered by profound endowments in digital infrastructure and innovation capital, the eastern coastal regions have constructed a distinct high ground, with agglomeration degrees vastly surpassing those of the central and western regions. Along the latitudinal (North–South) axis, a classic “inverted U-shaped” nonlinear distribution emerges, forming prominent spatial “uplift zones” (agglomeration peaks) in China’s middle-latitude belts (e.g., the Yangtze River Delta and the middle reaches of the Yangtze River urban agglomerations).

Critically, the three-period comparison reveals a non-linear evolutionary trajectory rather than simple monotonic convergence. From 2011 to 2017, the overall elevation of the trend surface increased substantially—particularly in the central transition zone—reflecting the strong momentum generated by the “Internet Plus” initiative (2015) and the rapid deployment of digital infrastructure during the 12th and 13th Five-Year Plans. The East–West gradient, while still pronounced, exhibited measurable narrowing as central provinces (e.g., Hubei, Henan, Anhui) experienced accelerated digital-productive synergy growth. However, from 2017 to 2023, the pace of convergence decelerated, and the spatial pattern consolidated rather than continued its earlier convergence trajectory. This deceleration is consistent with the W-shaped density fluctuation documented in Table 1: the exogenous shock of 2020 disrupted cross-regional factor flows, temporarily widening the spatial friction between core and peripheral regions before partial recovery by 2023.

Comparing the beginning (2011) and end (2023) of the research period, although the overarching spatial orientation and the “core–periphery” bedrock have not fundamentally reversed—demonstrating certain “spatial path dependence” and “lock-in effects”—it is noteworthy that the disparity in synergistic agglomeration along both axes exhibits a definitive downward trend. This dynamic evolution not only signifies that the disequilibrium in DT’s empowerment of NQPF is undergoing substantial amelioration, converging towards a holistic improvement, but also preliminarily corroborates that digital dividends are breaching traditional geographical friction, releasing initial “trickle-down effects” and spatial spillover dividends to adjacent regions. Synthetically, this highly complex spatial disequilibrium—characterized by overall improvement yet persistent regional disparities and non-monotonic intermediate dynamics—cannot be adequately decoded by traditional non-spatial econometric models. This necessitates the deployment of SNA and QAP regression for a profound, structural dissection in the subsequent sections of this study.

4.2. Global Network Structure Characteristics of Synergistic Agglomeration

Having established the synergistic development index (the “synergy” dimension) in Section 4.1, we now turn to the spatial correlation network analysis, which operationalizes the “agglomeration” dimension by revealing how provinces with varying synergistic levels cluster into hierarchical network structures. Based on the asymmetric gravity matrix measured using the modified gravity model, this study leverages ArcGIS software 10.8 to delineate the spatial correlation network topology maps of the inter-provincial “NQPF–DT” synergistic agglomeration for 2011, 2017, and 2023 (Figure 2), systematically unveiling its complex network characteristics and evolutionary laws. The inclusion of 2017—the year exhibiting the highest network density (0.2323) within the sample period—provides direct visual evidence for the non-monotonic W-shaped fluctuation documented in Table 1, responding to the need for intermediate-year corroboration of dynamic claims.

From the perspective of temporal progression, two analytically distinct trends must be completely differentiated. On the one hand, the weighted correlation intensity (i.e., the gravity values before binarization) exhibits a dramatic exponential growth trajectory: The maximum inter-provincial gravity value surged from approximately 24,000 in 2011, continued to grow substantially through 2017, and reached nearly 835,000 by 2023, reflecting a massive consolidation of the underlying “mass” driving synergistic agglomeration. On the other hand, the binary network structure (i.e., the number of ties and network density after binarization) does not exhibit monotonic densification. As Table 1 explicitly shows, the number of ties fluctuates in a W-shaped pattern, and density correspondingly oscillates around 0.22. Visually, the 2017 network map (Figure 2b) displays noticeably denser connectivity than the 2023 map (Figure 2c), providing direct graphical corroboration of this non-monotonic pattern. This distinction is substantively important: It indicates that while the strength of existing inter-provincial correlations has intensified enormously over the decade, the breadth of the network (how many provincial pairs exceed the mean threshold) has remained relatively stable, suggesting that the absolute correlation threshold itself has risen in tandem with the overall gravity scale. In 2011, the maximum network gravity was merely around 24,000; by 2023, this peak value had skyrocketed to nearly 835,000. This notably reflects that, over the past decade, accompanied by the pan-domain penetration of digital technologies and the leapfrog deployment of novel infrastructures, the “mass” foundation driving the synergistic agglomeration of both systems has been massively consolidated. Consequently, the interactive frequencies of cross-regional factor mobility and network interdependence have been elevated to unprecedented heights.

It is important to note that the four-tier stratification below describes the weighted gravity values (i.e., the continuous correlation intensities before binarization) and not the binary network ties. The dramatic increases in tier thresholds between 2011 and 2023 reflect the exponential growth in weighted intensity rather than an expansion in the number of binary network connections. To precisely dissect the hierarchical stratification and dynamic evolution of correlation intensity, coupled with the magnitude leaps in the legend values, this study stratifies the network ties into four progressive gradients:

Tier 1: Polar-core backbone network: In 2011, this was primarily constituted by orange ties with gravity values exceeding 500; by 2023, it evolved into red ties breaching the 50,000 thresholds. This tier is predominantly anchored within and across the three paramount urban agglomerations (Beijing–Tianjin–Hebei, Yangtze River Delta, and Pearl River Delta). Relying on top-tier digital ecosystems and innovation capital, these regions have clearly obliterated geographical friction, forging high-intensity “leapfrog” empowerment correlations. They serve as the absolute hubs driving national synergistic agglomeration.

Tier 2: Sub-core radiation network: Represented by light-blue ties (50–500) in 2011, this tier was wholly upgraded to orange ties (5000–50,000) by 2023. It vividly captures the energy transmission from the eastern coastal core to central pivotal provinces (e.g., Henan, Hubei, Hunan, Sichuan). It intuitively maps the trickle-down effects of digital dividends and innovation factors driven by national strategic layouts, such as the “East Data, West Computing” project and industrial gradient transfers.

Tier 3: Large-span wide-area transmission network: Transitioning from light-green ties (0.5–50) in 2011 to light-blue ties (1000–5000) in 2023, this tier presents an extensively interwoven, dense cobweb-like topology. It signifies that the vast central–western hinterlands and sub-developed eastern provinces have gradually broken through the constraints of traditional geographical adjacency, establishing highly resilient, multiple correlation flows.

Tier 4: Bottom-tier peripheral weak-tie network: Situated at the absolute bottom of the network (grey ties < 0.5 in 2011, replaced by light-green ties < 1000 in 2023), this tier primarily involves northwestern (e.g., Xinjiang, Tibet, Qinghai) and certain remote northeastern provinces. Constrained by the classic law of geographic distance decay and the digital divide stemming from local factor endowment scarcity, these regions still face severe risks of marginalization or even passive detachment within the global spatial network.

The three-period visual comparison (Figure 2a–c) provides particularly compelling evidence for the W-shaped oscillation. In 2017 (Figure 2b), the sub-core radiation ties (Tier 2, orange) are visibly more extensive than in 2023 (Figure 2c), with central provinces such as Hubei, Henan, and Hunan exhibiting denser inward connections from the eastern core. This graphically corresponds to the peak density of 0.2323 in 2017. By contrast, the 2023 network (Figure 2c), despite its substantially higher maximum gravity values, shows a slightly reduced number of visible moderate-intensity ties—a direct manifestation of the rising binarization threshold absorbing proportionally more ties as overall gravity escalates. This three-panel visualization thus resolves the apparent tension between “strengthening weighted intensity” and “oscillating binary density” by demonstrating that both phenomena are simultaneously observable in the network’s topology.

In conclusion, although China’s “NQPF–DT” synergistic spatial correlation network exhibits substantial intensification in weighted correlation strength alongside relatively stable binary network density (oscillating around 0.22 with W-shaped fluctuations), the node hierarchy persistently maintains an extremely salient “core–periphery” asymmetric ring structure, exhibiting a pronounced Matthew effect. The Matthew effect—a concept originally articulated by sociologist Robert K. Merton (1968) to describe cumulative advantage processes—refers to the self-reinforcing mechanism whereby entities that already possess advantageous positions progressively accumulate further advantages at the expense of less-endowed entities. In the specific context of this NQPF–DT spatial correlation network, the Matthew effect operates through the following mechanism: provinces already possessing superior digital infrastructure, advanced innovation ecosystems, and higher coupling coordination levels progressively attract disproportionate shares of inter-provincial knowledge flows, capital investment, and high-skilled talent migration, which further consolidates their central network positions and makes them even more attractive as collaboration partners in subsequent periods. Conversely, provinces with initially lower synergistic development levels face a vicious cycle—limited digital connectivity reduces their attractiveness, restricting their access to technological spillovers necessary for catch-up development, thereby further widening the gap. Moving forward, it is imperative to strengthen cross-regional synergy mechanisms and digital channel construction to break the shackles of factor mobility in peripheral areas, thereby fully activating and unlocking the network multiplier effect of inter-provincial synergistic agglomeration.

To further unveil the evolutionary laws of the overarching structure, this study utilizes UCINET 6.0 software to calculate the global spatial network correlation characteristics of China’s “NQPF–DT” synergistic agglomeration from 2011 to 2023 (see Table 1). Throughout the research period, the network size (31) and network connectedness (1) consistently maintained their theoretical maximum values. This indicates that all provinces nationwide have been systematically integrated into the spatial spillover network of synergistic agglomeration. Cross-regional linkages exhibit a ubiquitous globalized nature, completely eliminating the phenomenon of isolated nodes or “structural holes” at the provincial level.

This maximum-integration result (connectedness = 1) warrants explicit interpretation from three perspectives. First, methodologically, the modified gravity model (Equation (1)) assigns a positive correlation intensity to every provincial pair, since all constituent variables—per capita GDP, synergistic indices, and distances—take strictly positive values. The binarization threshold (annual mean) retains approximately 40–50% of potential directed ties, ensuring that even provinces with few direct connections maintain indirect pathways through intermediary nodes. A connectedness value below 1 would require some provinces to have uniformly below-threshold correlations with all other provinces simultaneously—a highly unlikely scenario given China’s integrated economic system. Second, substantively, China’s unified fiscal transfer mechanisms, centralized industrial policy coordination (e.g., Five-Year Plans, “East Data West Computing”), comprehensive national transportation networks, and substantial inter-provincial labor mobility create fundamental economic interdependencies preventing any province from complete structural isolation. Even the most geographically remote provinces (e.g., Tibet, Qinghai) maintain meaningful linkages through Central Government transfer payments and resource trade. Third, comparatively, a connectedness value of 1 is consistently reported in provincial-level spatial correlation network studies within China: Huo et al. (2022) [6], Li et al. (2024) [30], Zhang and Yao (2023) [54], and Bi et al. (2024) [52] all document fully connected networks at the provincial level. This convergent finding suggests that full connectedness is an inherent structural property of provincial-level analysis in China’s centralized economic system rather than an anomaly. Crucially, however, connectedness = 1 does not imply a homogeneous network. The simultaneously high hierarchy values (0.2857–0.4211) and the markedly uneven degree distribution demonstrate substantial internal stratification—the network is fully connected but profoundly asymmetric.

However, beneath this veneer of perfect connectivity, the overall cohesion of the network remains relatively sparse and exhibits an oscillating pattern. The network density and the number of network ties display a pronounced “W-shaped” fluctuation, hovering around 0.22 and 210, respectively. They reached a phased peak in 2017 (0.2323)—propelled by the substantial dividends of national digital infrastructure layouts—yet hit a phased trough in 2020 (0.2151) due to the severe spatial friction triggered by exogenous public health emergencies. This trajectory starkly reflects that the highly efficient, synergistic flow of cross-regional factors is still highly susceptible to macroeconomic environmental shocks, leaving substantial room for improvement.

Simultaneously, the spatial polarization of the internal power paradigm has become increasingly prominent. Network hierarchy surged sharply from 0.2857 in 2011 to 0.4211 in 2014, persistently solidifying at a high level thereafter. This reveals that the synergistic network has not evolved towards a flattened architecture. Instead, it has forged a rigid “core–periphery” structure, wherein eastern coastal provinces—leveraging profound digital foundations and innovation capital—have established an absolute central dominant position, exerting a continuous siphoning effect on the central and western peripheral provinces.

Notably, despite this hierarchical stratification, network efficiency exhibited a steady downward trend, declining from 0.7448 to 0.7241. Within the theoretical context of SNA, a decline in network efficiency paradoxically signifies a proliferation of multiple, overlapping “redundant correlation pathways.” Inter-provincial factor spillovers no longer heavily rely on single linear transmission routes. Rather, this complexly interwoven, multidimensional topological morphology fundamentally enhances the overarching structural resilience and fault tolerance of the global correlation network against external shocks.

4.3. Individual Network Structure Characteristics of Synergistic Agglomeration

Transitioning to the individual network characteristics, a comprehensive examination of the dynamic evolution of degree centrality, betweenness centrality, and closeness centrality (

Table 2. Centrality analysis of provincial nodes in the synergistic agglomeration network.

	2011						2023
	Degree Centrality			Betweenness Centrality	Closeness Centrality		Degree Centrality			Betweenness Centrality	Closeness Centrality
Region	Out-Degree	In-Degree	Degree		In-Closeness	Out-Closeness	Out-Degree	In- Degree	Degree		In-Closeness	Out- Closeness
Beijing	11	20	66.667	11.634	69.767	14.925	9	19	66.667	8.444	66.667	10.601
Tianjin	3	1	10.000	0.044	46.875	14.286	3	1	10.000	0.042	48.387	10.169
Hebei	4	1	13.333	0.102	46.875	14.706	6	0	20.000	0.000	3.226	11.583
Shanxi	4	1	13.333	0.074	46.875	14.423	4	1	13.333	0.068	48.387	10.239
Neimenggu	4	2	13.333	0.137	50.000	14.423	4	3	16.667	0.202	51.724	10.239
Liaoning	6	3	23.333	0.474	51.724	14.925	3	1	10.000	0.042	48.387	10.169
Jilin	5	4	20.000	0.461	52.632	14.851	5	10	36.667	0.895	60.000	10.381
Heilongjiang	5	5	20.000	0.530	53.571	14.851	5	11	40.000	0.967	61.224	10.381
Shanghai	12	18	63.333	5.965	69.767	15.385	10	15	53.333	3.959	63.830	10.526
Jiangsu	12	24	80.000	9.111	83.333	15.075	11	21	70.000	8.977	76.923	10.490
Zhejiang	13	23	76.667	10.332	81.081	15.228	10	22	73.333	7.570	78.947	10.417
Anhui	4	0	13.333	0.000	3.226	17.442	7	0	23.333	0.000	3.226	11.719
Fujian	10	4	33.333	0.545	41.667	15.385	10	3	33.333	0.504	39.474	10.638
Jiangxi	7	1	23.333	0.218	41.667	15.075	6	0	20.000	0.000	3.226	11.628
Shandong	10	11	40.000	2.514	53.571	15.228	9	11	43.333	2.473	52.632	10.563
Henan	7	0	23.333	0.000	3.226	17.751	7	0	23.333	0.000	3.226	11.538
Hubei	6	0	20.000	0.000	3.226	17.647	7	0	23.333	0.000	3.226	11.719
Hunan	6	1	20.000	0.146	41.667	15.000	9	0	30.000	0.000	3.226	11.765
Guangdong	11	25	83.333	18.980	85.714	15.000	11	27	90.000	17.500	90.909	10.490
Guangxi	5	5	16.667	0.495	53.571	14.634	6	3	20.000	0.329	49.180	10.453
Hainan	6	8	26.667	1.927	57.692	14.778	5	7	23.333	0.919	55.556	10.309
Chongqing	6	5	20.000	0.653	53.571	15.000	6	1	20.000	0.071	40.541	10.453
Sichuan	6	0	20.000	0.000	3.226	17.544	7	0	23.333	0.000	3.226	11.673
Guizhou	6	5	20.000	0.653	53.571	15.000	6	3	20.000	0.329	49.180	10.453
Yunnan	6	5	20.000	0.653	53.571	15.000	6	5	20.000	0.684	53.571	10.453
Xizang	7	10	36.667	2.387	60.000	15.152	6	13	43.333	1.682	63.830	10.453
Shaanxi	5	0	16.667	0.000	3.226	17.341	5	0	16.667	0.000	3.226	11.538
Gansu	7	7	23.333	1.682	56.604	15.152	7	5	23.333	1.663	54.545	10.526
Qinghai	7	7	23.333	1.682	56.604	15.152	7	9	30.000	2.680	58.824	10.526
Ningxia	6	5	20.000	1.048	53.571	15.000	6	5	20.000	1.383	54.545	10.453
Xinjiang	6	12	40.000	1.691	62.500	15.000	6	13	43.333	1.720	63.830	10.453

) enables a profound dissection of the role differentiation and power dynamics between provincial nodes within the “NQPF–DT” synergistic agglomeration network. The empirical findings reveal that rather than converging towards an idealized equilibrium, the overarching spatial correlation network has crystallized into a highly polarized and rigidly stratified “core–periphery” topological architecture.

Primarily, degree centrality—which captures the breadth and intensity of a node’s direct connections—unmasks a profound “spatial siphoning” phenomenon. Throughout the 2011–2023 period, eastern core provinces and municipalities such as Guangdong, Jiangsu, Zhejiang, Beijing, and Shanghai consistently anchored the top echelon (reaching notable highs of 90.000, 70.000, 73.333, 66.667, and 53.333, respectively, in 2023). A granular dissection of their internally directed structure exposes an overwhelming dominance in in-degree centrality among these developed eastern regions (e.g., in 2023, Guangdong’s in-degree of 27 vastly outstripped its out-degree of 11; similarly, Jiangsu recorded an in-degree of 21 versus an out-degree of 11). This clearly indicates that rather than merely acting as unilateral “radiators,” these regions function as “high-centrality hub nodes”. Leveraging significant digital infrastructure, sophisticated industrial supply chains, and abundant innovation capital, they persistently and aggressively absorb overarching factors from the network.

In stark contrast, a vast expanse of central and western provinces (e.g., Hebei, Anhui, Henan, Hubei, Sichuan) have chronically seen their in-degrees approach or equal zero, while their out-degrees hover around 6 to 7. This implies that within cross-regional synergies, these territories are relegated to passive “net out-flow destinations” of factors, confronting severe risks of “hollowing out” as their high-end productive factors and digital resources are relentlessly extracted.

Such clearly asymmetric factor flows directly catalyze the development of a high monopoly over network control. From the perspective of betweenness centrality, core nodes such as Guangdong, Zhejiang, Jiangsu, and Beijing persistently occupy the “structural holes” within the network. They command absolute intermediary discourse power over cross-provincial technology transfers, data circulation, and capital allocation, coercing numerous peripheral provinces to rely heavily on these hubs as relay stations for interactions. Although driven by nationally coordinated regional development strategies during the research period, the intermediary hub functions of certain provinces—such as Jilin (rising from 0.461 to 0.895), Heilongjiang (0.530 to 0.967), and the western province of Qinghai (1.682 to 2.680)—have experienced a nascent awakening, beginning to act as connecting bridges within localized sub-regions. However, this marginal downward shift of power has fundamentally failed to shake the unipolar dominance of the eastern seaboard.

Furthermore, the severe bifurcation in closeness centrality clearly corroborates the structural fossilization of this spatial power paradigm. Empowered by exceptionally high in-closeness centrality (e.g., in 2023, Jiangsu, Zhejiang, and Guangdong all exceeded 76), eastern provinces possess the capability to traverse geographical spatial barriers at exceptionally low transaction costs to aggregate nationwide resources. Conversely, a large swathe of central, western, and northeastern provinces is trapped at a rock-bottom accessibility baseline of 3.226, languishing in a profound “structural periphery” where they struggle to become active targets for synergy initiated by other provinces.

In summary, the individual network of China’s “NQPF–DT” synergistic agglomeration exhibits a typical Matthew Effect that manifests empirically in three observable patterns: (1) degree centrality concentration—the top five provinces (Guangdong, Jiangsu, Zhejiang, Beijing, Shanghai) consistently account for approximately 35–40% of all network ties, and this concentration has intensified over the 2011–2023 period; (2) blockmodel role rigidity—fewer than three provinces changed block membership across the entire 13-year span, indicating that initial advantages have crystallized into persistent structural positions; (3) digital divide amplification—digital transformation exhibits increasing returns to scale and network externalities that disproportionately reward early movers, widening the gap between leading and lagging provinces over time. The core block has achieved comprehensive domination—from the directional absorption of factors to the strict control of circulation channels—whereas the peripheral block is mired in a dependency trap characterized by “high out-degree, zero in-degree, and low betweenness.” Looking ahead, it is urgently imperative to dismantle administrative jurisdictional barriers, fortify digital infrastructure in the central and western regions, and recalibrate regional comparative advantages, thereby substantively elevating their ecological niches within the global network.

4.4. Dynamic Evolution of Spatial Correlation Block Clustering for Synergistic Agglomeration

To notably dissect the underlying spatial clustering characteristics and dynamic evolutionary laws of the “NQPF–DT” synergistic agglomeration network in China, this study conducts a joint observation utilizing the CONCOR (Convergence of Iterative Correlations) iterative cohesive subgroup algorithm alongside the block spillover effect matrix [56,57].

The empirical findings reveal that from 2011 to 2023, rather than exhibiting a simplistic homogeneous divergence, the global network adhered to the “club convergence” law. It clearly evolved into a multidimensional folded spatial architecture characterized by “polar-core absorption, hub transmission, peripheral marginalization, and hinterland integration.” From the perspective of the network’s core driving factions, the circulation of high-end digital factors and innovation resources is jointly orchestrated by the “net-receiving” polar-core and the “net-spillover” transmission hubs. Over the decade, the spatial hierarchical barriers and role divisions between the two have undergone profound structural reshaping.

Specifically, Block I exhibits significant spatial structural rigidity and a persistent core position. Contrary to the conventional assumption that developed regions merely act as unidirectional output engines, the data in

Table 3. Spillover effects of spatial correlation blocks for the synergistic agglomeration of NQPF and DT in 2011 and 2023.

Block Role		2011				2023
		Block I	Block II	Block III	Block IV	Block I	Block II	Block III	Block IV
Received ties	Intra-block	0	1	0	1	0	4	0	1
	Extra-block	94	28	5	82	88	26	2	88
Spillover ties	Intra-block	0	1	0	1	0	4	0	1
	Extra-block	58	20	28	103	49	38	28	89
Expected internal relation proportion (%)		13.33%	3.33%	16.67%	56.67%	13.33%	13.33%	13.33%	50.00%
Actual internal relation proportion (%)		0.00%	4.76%	0.00%	0.96%	0.00%	9.52%	0.00%	1.11%
Number of members		5	2	6	18	5	5	5	16

rigorously verify that Block I is substantively the paramount “Net-Receiving Block” (net beneficiary) within the network. Its external receiving ties consistently maintained the highest global position (from 94 in 2011 to 88 in 2023), vastly outstripping its outward spillover ties (converging from 58 to 49). Furthermore, its actual internal relation proportion (0.00%) was significantly lower than the expected value (13.33%). This asymmetric spillover differential in the results suggests that, leveraging irreplaceable first-mover policy advantages, top-tier digital infrastructure, and elite talent reservoirs, Block I exerts an intense “siphoning effect.” It continuously absorbs NQPF factors nationwide to accomplish its own industrial iterative upgrades. Concurrently, the marginal convergence of its outward spillovers implies that the polar-core’s factor absorption and internal capacity are gradually entering a high-level saturation phase.

Table 4. Classification of the four blocks for the synergistic agglomeration of NQPF and DT in 2011 and 2023.

Year	2011	2023
Block I	Beijing, Shanghai, Jiangsu, Zhejiang, and Shandong	Beijing, Shanghai, Jiangsu, Zhejiang, and Shandong
Block II	Fujian and Guangdong	Fujian, Guangdong, Henan, Anhui, and Hubei
Block III	Hebei, Tianjin, Liaoning, Anhui, Henan, and Hubei	Hebei, Sichuan, Liaoning, Tianjin, and Hunan
Block IV	Neimenggu, Heilongjiang, Jilin, Jiangxi, Hunan, Shanxi, Guangxi, Hainan, Chongqing, Sichuan, Guizhou, Yunnan, Xizang, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang	Jilin, Jiangxi, Neimenggu, Shanxi, Guangxi, Hainan, Chongqing, Heilongjiang, Guizhou, Yunnan, Xizang, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang

shows that the member roster of the five eastern coastal core provinces/municipalities (Beijing, Shanghai, Jiangsu, Zhejiang, and Shandong) remained stable throughout 2011–2023, constituting the “super vanguard” of China’s digital economy and NQPF development.

Meanwhile, a notable spatial reconfiguration emerged in Block II. Serving as the “transmission hub” with the most drastic structural leap and dynamic expansion over the decade, Block II expanded robustly from merely two provinces (Fujian and Guangdong) in 2011 to five provinces in 2023, successfully assimilating three central core hubs (Henan, Anhui, and Hubei) previously belonging to Block III. This geopolitical expansion directly mirrors a qualitative mutation in its network power. In 2011, Block II (Fujian and Guangdong) possessed an actual internal proportion (4.76%) exceeding the expected value (3.33%), categorizing it as a “Bidirectional Spillover Block” with robust internal self-circulation capabilities. By 2023, it successfully transformed into a high-capacity “Net Spillover Block”; its outward spillovers surged to 38, surpassing external receptions (26), while internal interactions also climbed (four). This interlocking data notably unveils the materialization of the “trickle-down effect” in China’s digital economic landscape. Pioneer regions such as Guangdong and Fujian are breaking internal lock-ins, actively undertaking the capacity spillovers from the eastern polar core. Simultaneously, they act as crucial “brokers” and “structural hole” bridges, facilitating the highly efficient, tiered transfer and radiation of NQPF dividends, advanced manufacturing technologies, and DT solutions towards the central hinterland along the Yangtze River Economic Belt and the Beijing–Guangzhou railway. The successful integration of the three central provinces signifies that central–eastern China has preliminarily constructed a digital industrial synergy highland transcending geographical boundaries.

Shifting focus to the vast inland bedrock and traditional industrial zones, the peripheral factions have embarked on starkly divergent evolutionary paths, interwoven with macro-strategic drivers and the challenges of industrial transition. As the largest dependent bedrock in the global network, Block IV (encompassing 16 to 18 provinces across the northwest, southwest, and parts of the northeast) underwent a landmark historical role optimization. Although theoretically maintaining the label of a “Net Spillover Block,” the core of its spatial interaction structure has fundamentally reversed. In 2011, its outward spillovers (103) vastly exceeded external receptions (82), exhibiting clear attributes of factor drain and passive “resource extraction” as the cheap labor and resource backend for the developed East. However, by 2023, its spatial correlation achieved a striking dynamic equilibrium: External receptions leaped to 88, forming an exceptionally rare 1:1 parity with outward spillovers (89). This data reversal forms a perfect logical closed loop with recent national macro-strategies, such as the “East Data West Computing” initiative, the Western Development Strategy, and the construction of a Unified National Market. It indisputably demonstrates that the central–western hinterland is no longer a mere bystander in the digital era. Instead, relying on abundant green energy and computing hub construction, it has deeply integrated into the mainstream circulation system of NQPF resources under a novel identity as the provider of “foundational computing power and data centers.” This marks a historical leap from “unidirectional dependency” to “bidirectional empowerment.”

However, beneath the overarching positive trajectory of global network synergy, the reorganized Block III exposes alarming risks of “structural collapse” and severe agonies of traditional industrial transition. Table 4 reveals that following the upward migration of the three central provinces, Block III in 2023 degenerated into an isolated faction of five provinces (Hebei, Tianjin, and Liaoning—old industrial bases—plus Sichuan and Hunan). The matrix data in Table 3 indicates a risk of structural fragmentation for this block: in 2023, its outward spillovers to other blocks remained at 28, yet its external receiving ties suffered a precipitous plunge, dwindling to a mere two, with internal interactions plummeting to absolute zero. This structural imbalance reveals a concerning pattern. Provinces characterized by high outflow and near-zero internal connections face a growing digital divide and path dependence. Several traditional industrial provinces appear constrained by institutional rigidities, slow development of emerging industries, and talent outflow, resulting in diminishing capacities to attract external network resources. They are forced to regress into “passive blood donors” that unidirectionally export primary factors. Increasingly disconnected from mainstream technology spillover channels, they have become “information silos” and “structural depressions” within the synergistic network.

Synthetically, while the spatial network evolution of China’s NQPF and DT exhibits positive momentum with respect to hub-radiated inland integration, the asymmetric characteristics of inter-block hierarchical fossilization and localized peripheral marginalization remain severe. Moving forward, breaking the “lock-in” dilemmas of old industrial bases and marginalized provinces through targeted assistance, transfer payments, and cross-regional digital infrastructure coordination to eliminate structural network vulnerabilities will be the pivotal breakthrough for constructing China’s new spatial paradigm of high-quality development.

4.5. Analysis of the Driving Mechanisms of the Spatial Correlation Network of Synergistic Agglomeration Between NQPF and DT

4.5.1. Model Construction and Selection of Driving Factors

Multiple forces—encompassing regional geospatial conditions, the digital divide, and socioeconomic factors—jointly drive the formation and evolution of the inter-provincial spatial correlation network of synergistic agglomeration between NQPF and DT. Unveiling these underlying driving mechanisms holds profound practical significance for dismantling cross-regional digital barriers, promoting the pan-territorial empowerment of NQPF, and facilitating the construction of a unified national market.

Tobler’s First Law of Geography posits that “everything is related to everything else, but near things are more related than distant things.” In the digital economy era, although network communication has drastically reduced information transmission costs, the spillover of high-end tacit knowledge and complex technologies—upon which NQPF heavily relies—remains notably constrained by spatial geographic distance. Simultaneously, the formation of the inter-provincial synergistic network is highly contingent upon the potential energy of factor flows across regions.

The economic development level constitutes a “gravity field” attracting the cross-border flow of digital capital and innovation factors, with economic potential differences accelerating the agglomeration of advanced productive forces towards high-yield regions. Digital infrastructure, acting as the underlying bedrock of the digital economy, exhibits regional disparities (i.e., the digital divide) that directly dictate the friction costs and network docking efficiency of cross-provincial data circulation. Technological innovation serves as the core of NQPF; differences in innovation growth exert a profound impact on the intensity of asymmetric spatial correlations via technological potential and knowledge spillover effects. Human capital level determines a region’s absorptive and transformative capacity for novel factors, making the cross-regional mobility of high-caliber talents and the “talent pool” effect crucial ties for reshaping the spatial network. Financial development level acts as the lifeblood for digital transformation and industrial upgrading; its non-equilibrium distribution dictates cross-regional investment and financing flows, thereby shaping network evolution. Furthermore, differences in government intervention levels (the institutional environment) constitute “invisible barriers” or “policy dividends,” directly affecting unhindered channels for the free flow of production factors. As evidenced by the preceding blockmodeling analysis, the spillover and receiving relationships generated between different blocks are, to a large extent, the macroscopic manifestations of the superposition of these multidimensional spatial divides.

Therefore, drawing upon existing research in the fields of new economic geography and the digital economy [58] and grounded in multidimensional proximity theory and factor flow mechanisms, this study constructs an analytical model. The model sets the synergistic spatial correlation network matrix (Net) as the dependent variable, and it selects the spatial geographic distance matrix (Geo), economic development difference matrix (Econ), digital infrastructure difference matrix (Dig), technological innovation difference matrix (Inno), human capital difference matrix (Hum), financial development difference matrix (Fin), and government intervention difference matrix (Gov) as independent variables (see

Table 5. Driving factors and measurement methods for the spatial correlation network of the synergistic agglomeration of NQPF and DT.

Variable	Definition	Measurement Method	Data Source
$Geo$	Geo-spatial geographic distance matrix	Constructing a spatial weight matrix based on the spherical distance between provincial capitals	National Geomatics Center of China, calculated via ArcGIS
$Econ$	Economic development level difference matrix	The logarithm of per capita GDP	China Statistical Yearbook
$Dig$	China Statistical Yearbook	Internet penetration rate	China Statistical Yearbook
$Inno$	Technological innovation level difference matrix	The logarithm of the number of domestic invention patent authorizations	National Intellectual Property Administration, China Statistical Yearbook
$Hum$	Human capital level difference matrix	Average years of schooling	China Population and Employment Statistical Yearbook
$Fin$	Financial development level difference matrix	The proportion of year-end loan balances of financial institutions to GDP	Almanac of China’s Finance and Banking, China Statistical Yearbook
$Gov$	Government intervention level difference matrix	The proportion of local government general budgetary expenditure to GDP	China Statistical Yearbook

Notes: Except for the Geo matrix, the independent variable matrices are all constructed based on the absolute value of inter-provincial differences for each attribute. The calculation formula for average years of schooling is as follows: (Illiterate population × 1 + Primary school × 6 + Junior high school × 9 + Senior high/technical school × 12 + Junior college, undergraduate and above × 16)/Total population aged 6 and above.

) to further uncover the driving mechanisms of China’s inter-provincial synergistic evolution network.

Given that the aforementioned variables are all matrix variables (N × N) based on “relational data,” traditional ordinary least squares (OLS) regression based on “attribute data” would inevitably fall into the traps of severe autocorrelation and multicollinearity when processing such data. Consequently, this study utilized UCINET 6.0 software to introduce the QAP for empirical testing. As a non-parametric statistical method based on the random permutation of matrix data, QAP regression calculates regression coefficients by synchronously permuting the rows and columns of the matrices. This effectively circumvents multicollinearity interference, endowing the model’s testing results with stronger robustness and scientific validity. The model is specified as follows:

$$Net=f\left(Geo,Econ,Dig,Inno,Hum,Fin,Gov\right).$$

(3)

4.5.2. QAP Regression Analysis

To effectively overcome the endogeneity interferences—such as multicollinearity and autocorrelation—faced by traditional econometric models when processing network “relational data,” this study conducted year-by-year regressions based on 5000 random permutations using UCINET 6.0. The results (

Table 6. QAP regression results for the spatial correlation network of the synergistic agglomeration between NQPF and DT.

Variables	2011	2014	2017	2020	2023
Geo	−0.1564 ***	−0.1408 ***	−0.1715 ***	−0.1424 ***	−0.1677 ***
	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
Econ	0.2453 ***	0.2801 ***	0.2904 ***	0.3362 ***	0.3565 ***
	(0.001)	(0.000)	(0.000)	(0.000)	(0.000)
Dig	0.2221 ***	0.1028 **	0.2709 ***	0.0852 **	0.0399 **
	(0.004)	(0.032)	(0.000)	(0.026)	(0.013)
Inno	0.4418 ***	0.5195 ***	0.3994 ***	0.5289 ***	0.5439 ***
	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
Hum	−0.0634 *	0.0295	0.0040	−0.1003 **	−0.1174 ***
	(0.087)	(0.290)	(0.444)	(0.014)	(0.000)
Fin	−0.1360 ***	−0.1120 **	−0.0849 **	−0.0363	0.0264
	(0.004)	(0.012)	(0.026)	(0.178)	(0.235)
Gov	−0.2193 ***	−0.2307 ***	−0.1233 **	−0.2039 ***	−0.1893 ***
	(0.001)	(0.000)	(0.023)	(0.000)	(0.000)
Observations	930	930	930	930	930
Number of permutations	5000	5000	5000	5000	5000

Notes: The variable coefficients reported are standardized regression coefficients. The values in parentheses represent the probability that the absolute value of the regression coefficient generated by random permutations is greater than or equal to the observed absolute coefficient (i.e., the p-value based on permutation tests). ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively.

) notably unveil the spatiotemporal dynamic evolutionary logic of the direction and intensity of various driving factors.

First, differences in the technological innovation level (Inno) and economic development level (Econ) constitute the most stable and robust “core engines” for cross-regional network ties. Throughout the observation period, both variables remain significantly positive at the 1% level, with their coefficients either maintaining high positions or climbing steadily. This empirical evidence corroborates the “gradient transfer” and “technology spillover” effects in regional economics: developed provinces, leveraging their profound R&D foundations and massive economic volumes, have formed immense “potential energy highlands.” The complementary demand for heterogeneous endowments strongly drives the “trickle-down effect” of digital dividends toward less-developed regions.

However, this cross-regional synergy has not entirely broken free from spatial and institutional shackles; geographic distance (Geo) and government intervention differences (Gov) constitute significant “frictional resistance.” Geographic distance remains significantly negative across all years, indicating that the transmission of tacit knowledge and complex technologies is still constrained by physical friction. The classic “law of distance decay” remains highly applicable in the digital era. Concurrently, government intervention differences are persistently and significantly negative, highlighting the network’s strong preference for “institutional isomorphism.” The closer the marketization processes and business environments of two provinces, the more effectively they can reduce institutional transaction costs for cross-provincial synergy and circumvent local protectionist barriers.

Before interpreting the temporal evolution of driving factors, methodological clarification regarding the digital infrastructure variable (Dig) is warranted. In the gravity model (Equation (1)), digital development disparity ($g_{ij}$) appears in the compound denominator as $d_{ij}$/$g_{ij}$, meaning that a larger $g_{ij}$ mathematically reduces the effective distance, thereby increasing the predicted correlation intensity $F_{ij}$. This design is theoretically intentional: digital disparity between provinces represents asymmetric complementary potential energy rather than symmetric friction. When province i possesses substantially higher digital development than province j, the resulting “digital potential gap” creates strong incentives for cross-regional technology transfer, capital flow, and talent migration—analogous to water flowing from high to low elevations. In the QAP regression, Dig similarly captures this complementarity mechanism: provinces with larger digital infrastructure gaps exhibit stronger spatial correlations due to complementary factor demand. This distinguishes Dig fundamentally from Geo (geographic distance), which represents pure symmetric friction. The compound term $d_{ij}$/$g_{ij}$ thus represents the net effective distance: geographic friction attenuated by digital complementarity. It is highly noteworthy that alongside the deepening of national digital strategies, the driving forces of the underlying infrastructure and the financial environment exhibit a distinct “boundary dissolution and threshold elimination” trend. The positive driving coefficient of digital infrastructure differences (Dig) demonstrates an oscillating decay, while financial development level differences (Fin) evolved from being significantly negative in the early stage to being completely insignificant recently. This dynamic transition powerfully reflects that, bolstered by macro-strategies such as “Broadband China” and “digital financial inclusion,” the underlying computing power network and cross-regional capital flows have shattered traditional physical scale limitations. They have gradually trickled down to become a ubiquitous “common environment,” maintaining the operation of the unified national market.

Finally, while hardware and capital barriers gradually dissolve, the evolutionary trajectory of human capital (Hum) delineates an increasingly stringent “soft absorption threshold.” Human capital differences were insignificant in the initial stage of the observation but leaped to being significantly negative at the 1% high level in 2020 and 2023. This perfectly aligns with absorptive capacity theory in the field of knowledge management. The underlying logic is that as NQPF advances into deep-water zones (e.g., industrial large models), the spillover of high-order tacit knowledge imposes a convergence requirement on the “digital literacy” of receiving regions. A massive chasm in the talent structure between two provinces will directly precipitate an “absorption failure” in the less-developed region.

In summary, the evolution of China’s spatial correlation network of “NQPF–DT” is not the linear outcome of a single factor; rather, it comprises systemic reshaping under the dynamic game of multiple mechanisms: the powerful traction of technological and economic potential differences, the objective obstruction of physical and institutional friction, the universal dissolution of infrastructure and financial boundaries, and the increasingly prominent threshold of human capital absorption.

4.6. Robustness Checks

To verify that the core findings are not artifacts of the specific binarization threshold adopted in the main analysis, three complementary robustness tests were conducted using the 2023 cross-section as the benchmark year. The results of these robustness checks are summarized in

Table 7. Robustness check results.

Indicator/Variable	Baseline (Mean Threshold)	Test 1 (Median Threshold)	Test 2 (Mean + 1SD Threshold)	Test 3 (Weighted QAP)
Network structure
Number of ties	209	453	103
Network density	0.2247	0.4871	0.1108
Top 5 provinces	GD, JS, ZJ, BJ, and SH	GD, ZJ, BJ, JS, and SH	GD, JS, ZJ, BJ, and SH
Block I members	5 (unchanged)	7 (expanded)	4 (contracted)
Block III internal ties	0	0	0
QAP Regression
Geo	−0.1677 ***			−0.1843 ***
Econ	0.3565 ***			0.3812 ***
Dig	0.0399 **			0.0312 **
Inno	0.5439 ***			0.5687 ***
Hum	−0.1174 ***			−0.0981 ***
Fin	0.0264			0.0187
Gov	−0.1893 ***			−0.2056 ***
Adj. R2	0.4224			0.4617
Observations	930	930	930	930
Permutations	5000			5000

Notes: ***, and ** denote significance at the 1% and 5% levels, respectively. Blanks indicate that the test does not apply to that column. GD—Guangdong; JS—Jiangsu; ZJ—Zhejiang; BJ—Beijing; SH—Shanghai. Collectively, the three robustness tests confirm that the main findings—including the hierarchically stratified network structure, the stable four-block architecture, and the multidimensional driving mechanism—are not sensitive to the choice of binarization threshold or the binary/weighted network specification, thereby enhancing confidence in the empirical conclusions.

.

Test 1: Median threshold binarization: Given that inter-provincial gravity values exhibit a pronounced right-skewed distribution, the median provides a threshold that is more robust to extreme observations. Replacing the mean with the median yields a denser network (453 ties; density = 0.4871). Despite this substantial increase in connectivity, the core structural properties remain qualitatively unchanged: (a) the top five provinces by degree centrality are identical in composition (Guangdong, Zhejiang, Beijing, Jiangsu, and Shanghai), with only minor internal reordering between Jiangsu and Zhejiang; (b) all five original Block I members are retained within an expanded seven-member Block I, with the additional members drawn from adjacent Block II transmission hubs—a theoretically expected outcome under a more permissive threshold; and (c) Block III provinces maintain zero internal ties even under this substantially denser network, confirming that their structural marginalization is not an artifact of threshold selection.

Test 2: Mean plus one standard deviation (mean + 1SD) threshold binarization: Due to the extreme right-skewness of the gravity distribution, the arithmetic mean already occupies approximately the 78th percentile position. To ensure a genuinely restrictive test, we adopted the Mean + 1SD as the threshold (approximately the 89th percentile), retaining only the strongest 11% of inter-provincial correlations (103 ties; density = 0.1108). Under this stringent criterion, the top five provinces remain identical regarding composition and ranking order. The CONCOR algorithm contracts Block I to four provinces, identifying the absolute minimum irreducible core. Block III provinces record zero internal ties under this extreme sparsification, validating that their peripherality is robust to the most restrictive analytical conditions.

Test 3: Weighted-network QAP regression: To address potential information loss inherent in binary threshold procedures, the QAP model is re-estimated using the original continuous gravity matrix as the dependent variable (double Dekker semi-partialing method; 5000 permutations). The results demonstrate complete directional consistency with the baseline binary specification. Technological innovation disparity (β = 0.5687, p < 0.001) and economic development disparity (β = 0.3812, p < 0.001) remain the dominant positive drivers with slightly elevated coefficients reflecting amplified signals in continuous-valued outcomes. Geographic distance (β = −0.1843, p < 0.001) and government intervention disparity (β = −0.2056, p < 0.001) maintain significant negative effects. Digital infrastructure disparity (β = 0.0312, p < 0.05) retains significance with continued coefficient attenuation, corroborating the progressive dissolution of digital boundaries. Financial development disparity (β = 0.0187, p = 0.304) remains firmly insignificant, providing definitive confirmation that financial boundaries have been substantively dissolved. The adjusted R² of 0.4617 reflects superior explanatory power attributable to preserved tie-strength variance.

Collectively, the three robustness tests—spanning a more permissive threshold (Test 1), a substantially more restrictive threshold (Test 2), and a continuous dependent variable specification (Test 3)—converge on identical qualitative conclusions, substantially enhancing confidence in the empirical findings.

5. Discussion

5.1. Discussion of Key Findings

This study constructed and analyzed the spatial correlation network of NQPF–DT synergistic agglomeration across China’s 31 provinces over the 2011–2023 period, yielding several findings that merit in-depth discussion in the context of existing scholarship.

Finding 1: The network exhibits full connectedness but significant internal hierarchical stratification.

Our results demonstrate that the spatial correlation network maintains a connectedness value of 1 throughout the entire sample period, indicating that no province is structurally isolated from the NQPF–DT synergistic agglomeration system. However, this full connectedness coexists with pronounced hierarchical asymmetry (network hierarchy values ranging from 0.2857 to 0.4211, as reported in Table 1), suggesting that while all provinces participate in the network, they do so from vastly different structural positions. This finding aligns with Wang Z, Liu W, and Yang N et al. (2025) [50], who similarly report a fully connected yet hierarchically stratified spatial correlation network for NQPF at the provincial level. However, our study extends their finding by demonstrating that the incorporation of the DT coupling dimension intensifies rather than mitigates this hierarchical pattern—provinces with high NQPF and DT levels enjoy disproportionately central positions, while provinces with mismatched development (e.g., moderate NQPF but low DT) are relegated to more peripheral roles than their NQPF levels alone would predict.

Finding 2: The blockmodel analysis reveals a stable four-block structure with limited inter-block mobility.

The identification of “net spillover,” “net benefit,” “bilateral spillover,” and “broker” blocks confirms the theoretical expectation that spatial correlation networks exhibit role differentiation (White et al., 1976) [56]. Notably, the remarkable stability of block membership over the 13-year period suggests the presence of strong path-dependency effects. This is consistent with the broader literature on regional economic lock-in (Martin and Sunley, 2006) [9], which argues that initial advantages in institutional capacity, infrastructure endowment, and human capital tend to self-reinforce over time. Our contribution lies in demonstrating that this lock-in operates not merely through individual provincial characteristics but through relational mechanisms embedded in the network structure itself—a province’s network position shapes its access to innovation spillovers, which in turn reinforces its position.

Finding 3: The QAP regression reveals that digital development disparity and geographic proximity jointly shape network formation.

The QAP results confirm that geographic distance and digital development gaps significantly influence the probability and intensity of inter-provincial spatial correlations. This dual-distance finding resonates with the emerging “digital geography” literature (Huo et al., 2022; Hernandez,2019) [6,7], which argues that digital connectivity creates new forms of spatial proximity that complement rather than replace traditional geographic proximity. Our study empirically validates this theoretical proposition within the specific context of NQPF–DT synergy: provinces may be geographically distant yet strongly connected through shared digital development trajectories, while geographically proximate provinces with divergent digitalization levels may exhibit surprisingly weak correlations.

5.2. Theoretical and Practical Implications

Theoretical implications: This study provides three primary theoretical contributions. First, it advances the conceptualization of NQPF from an individual provincial attribute to a relational and networked phenomenon, demonstrating that the development of new quality productive forces cannot be adequately understood in isolation from inter-provincial spatial interdependencies. Second, it introduces the concept of “synergistic agglomeration” as a theoretically grounded unit of analysis that bridges the NQPF and DT literature through the coupling coordination framework. Third, it contributes to the spatial econometrics literature by proposing a modified gravity model that incorporates dual-distance weighting (geographic + digital), offering a more realistic representation of the friction factors governing inter-provincial knowledge and resource flows in the digital era.

Practical implications: The findings carry direct implications for regional governance. First, the identification of stable “net spillover” provinces (predominantly in eastern China) suggests that these regions should be incentivized to expand their outward-facing collaborative activities through inter-provincial technology transfer programs and cross-regional innovation consortia. Second, the persistent peripheral position of certain western provinces indicates that conventional “trickle-down” assumptions are insufficient; targeted interventions in digital infrastructure development and innovation capacity building are necessary to enable these provinces to establish meaningful network connections. Third, the blockmodel’s “broker” category identifies provinces (typically in central China) that serve as critical intermediaries; policymakers should recognize and leverage this bridging function through dedicated “corridor development” strategies that strengthen the connective tissue between eastern hubs and western peripheries.

5.3. Limitations and Future Research Directions

Despite the contributions outlined above, this study has several limitations that should be acknowledged transparently.

First, although Section 4.6 demonstrates that our core findings are robust to alternative binarization thresholds (median and Mean + 1SD) and to weighted-network specifications, the binarization procedure inevitably involves some degree of information loss. Future research could further explore backbone extraction algorithms or multi-scale network approaches to preserve even more granular information about tie strength heterogeneity.

Second, the provincial level of analysis, while appropriate for capturing macro-level spatial patterns, may mask significant intra-provincial heterogeneity. Large provinces, such as Guangdong and Sichuan, contain substantial internal disparities between their economically advanced cores and less developed peripheries. Future studies could extend this framework to the prefectural city level to capture finer-grained spatial dynamics, though this would require overcoming data availability challenges for sub-provincial DT indicators.

Third, while the QAP regression identifies significant correlates of network structure, it is inherently limited in establishing strict causal inference due to its cross-sectional relational design. Future research could employ temporal exponential random graph models (TERGMs) or stochastic actor-oriented models (SAOMs) to model the dynamic co-evolution of network ties and provincial attributes, thereby providing stronger inferential leverage on the causal mechanisms of network formation.

Fourth, this study focused exclusively on China’s domestic inter-provincial network. Given that NQPF development—particularly in high-technology sectors—is increasingly embedded in global value chains and international technology transfer networks, future research could integrate an international comparative dimension to assess whether the observed agglomeration patterns and driving mechanisms are unique to China’s institutional context or represent more universal spatial dynamics.

Finally, the measurement of NQPF and DT relies on composite indices constructed through the entropy weight method, which, while objective, may not capture all qualitative dimensions of productive force transformations. Future studies could complement this quantitative approach with qualitative comparative analysis (QCA) to identify configurational pathways leading to network centrality or with case studies of specific provincial pairs to elucidate the micro-mechanisms underlying observed spatial correlations.

6. Conclusions

6.1. Conclusions Main Findings

Based on the dual examination of SNA and the QAP spatial econometric model, this study conducts a multidimensional deconstruction of the spatial correlation network of the synergistic agglomeration between NQPF and digital transformation in China from 2011 to 2023. Our research reveals that China’s synergistic agglomeration network notably follows the “club convergence” rule, evolving into a disequilibrium hierarchical bloc structure characterized by “polar-core absorption, hub transmission, hinterland integration, and peripheral marginalization.” From the perspective of bloc transition trajectories, the polar-core bloc, centered on the eastern coastal regions, leverages its first-mover advantages to exert a strong “siphon effect,” essentially becoming the largest “net beneficiary bloc” in the global network. The transmission hub, comprising Guangdong, Fujian, and the central core regions, has emerged robustly, breaking internal self-locking and acting as a “broker” node for cross-regional radiation, which corroborates the “trickle-down effect” in the digital landscape. Driven by macro-strategies such as the “East Data, West Computing” initiative, the vast midwestern inland base has achieved a historic reversal from unidirectional blood loss to a dynamic input–output balance. However, the peripheral island bloc, primarily consisting of some old industrial bases, is deeply mired in a “structural collapse” risk where internal interactions plummet to zero and external receptions sharply drop, facing a severe crisis of being marginalized from the mainstream network. Further QAP mechanism tests reveal that the aforementioned network evolution is the outcome of a dynamic game among multidimensional mechanisms: technological and economic potential differences constitute the stable “core engines” for cross-regional network formation, while geographic distance and government intervention differences (a preference for institutional isomorphism) form significant “frictional resistance.” What warrants particular vigilance is that, although the physical boundaries of digital infrastructure and financial capital are increasingly dissolving, the human capital factor has evolved into an increasingly stringent “soft absorption threshold,” directly determining the success or failure of less-developed regions in undertaking the spillover of NQPF.

6.2. Policy Recommendations

Given the complex multidimensional bloc differentiation and spatial heterogeneity characteristics described above, the findings suggest that undifferentiated national industrial policies are insufficiently responsive to the substantial heterogeneity in provincial network positions revealed by our blockmodel analysis. A province occupying Block I (the “net receiving” polar core) faces fundamentally different development challenges compared to one in Block III (facing structural collapse risks). We therefore recommend differentiated regional governance strategies calibrated to each block’s specific structural role and developmental needs, as detailed below. Regarding the polar-core bloc at the apex of the network, the state should strive to curb its excessive siphoning of low-efficiency elements and innovation resources from the central and western regions. The policy focus must resolutely pivot towards achieving breakthroughs in “bottleneck” frontier technology fields—such as underlying AI algorithms and quantum computing—strengthening its function as the leading role in the global digital economy game and establishing a synergistic innovation community to guide the orderly gradient transfer of mature digital production capacities to the periphery. For the rapidly expanding transmission hub, top-level planning should further fortify its “broker” role of “connecting the East and West, linking the North and South.” Priority should be given to deploying national-level digital technology transfer centers and pilot zones, comprehensively unblocking the main industrial chain artery comprising “R&D in the East–Transformation in the Central–Application in the West.” As for the inland base that has achieved a dynamic balance within the network, the vast midwestern provinces must seize the historical opportunities of the computing power era, actively extending into high-value-added modern digital services—such as big data cleaning and AI multi-modal data annotation—translating the superficial balance of network ties into a substantive leap in TFP. Finally, for provinces that our blockmodel analysis identifies as persistently occupying the peripheral block—characterized by plummeting internal interactions and severely declining external receiving ties (as evidenced by Block III’s regression to zero internal ties and only two external receptions in 2023)—targeted national-level support policies are warranted to prevent entrenchment of structural marginalization. We recommend centrally coordinated interventions through three channels: (a) “digital revitalization” transfer payments dedicated to accelerating industrial Internet and 5G+ smart manufacturing adoption in traditional industrial bases; (b) cross-provincial “digital paired-assistance” mechanisms linking “net spillover” provinces with peripheral provinces for technology transfer and joint R&D; and (c) human capital development programs specifically addressing the “absorption failure” crisis by building advanced digital skills in lagging regions. By introducing “special transfer payments for digital revitalization” and cross-provincial “digital paired-assistance” mechanisms, the deep empowerment of traditional manufacturing by the “Industrial Internet” and “5G + Smart Manufacturing” should be vigorously advanced. This will reshape the comparative advantages of old industrial bases, resolve the “absorption failure” crisis caused by the scarcity of high-order human capital, and thereby construct a new high-quality spatial development paradigm in China characterized by core leadership, hub transmission, hinterland synergy, and island breakthroughs.