Spatial Correlation Network Assessment of the New Quality Productive Forces Among 283 Chinese Cities: Network Characteristics and Structural Resilience Features

Abstract

Cities, being elementary concentrations of socio-economic activities and resource-environmental pressures, confront significant challenges in promoting new quality productive force (NQPF) development because technology, resource, and information conditions may be spatially associated across cities. Although the nexus among cities has gained widespread recognition in China’s high-quality development such as in innovations and low-carbon transformation, a critical gap exists in quantitatively assessing how model-estimated inter-city spatial correlations relate to high-quality development within an integrated framework. To bridge this gap, this study constructs an urban social correlation network (SCN) analysis framework, integrates spatial correlation methods to overcome the limitations of traditional heterogeneity assessment, and applies it to 283 Chinese cities from 2010 to 2023 to measure network characteristics and structural resilience related to NQPF. The results show that the network density rose from 0.0608 in 2010 to 0.1577 in 2023. By 2023, the SCN featured higher connectivity and reciprocity, comparatively high but lower efficiency, low hierarchy, and no obvious core–periphery structure. The 283 cities were divided into four blocks, exhibiting denser intra-regional than inter-regional links, and strengthened inter-regional interactions over time. The displayed node-removal trajectories declined faster under centrality-ordered removal than under one reported random-removal sequence. The network was more vulnerable to intentional attacks than to random attacks. Motif analysis indicates that M1 and M2 dominated and contributed to low network density, while the shift from open structural holes toward a mix of open and closed structures was associated with network evolution. These findings indicate that cultivating key node cities and improving inter-city coordination mechanisms to enhance network resilience are critical pathways for advancing NQPF development with Chinese characteristics, providing quantitative evidence for targeted inter-city coordination policymaking.

1. Introduction

In the era of rapid technological advancement and global urbanization, cities have become pivotal hubs for the convergence of innovative factors, productive resources, and socio-economic activities, forming the fundamental foundation for the cultivation of new quality productive forces (NQPF). The Third Plenary Session of the 20th Central Committee of the Communist Party of China in 2024 called for institutional mechanisms that support locally adapted NQPF development. Subsequently, integrating the development of NQPF adapting to local realities into the annual work tasks was further specified in the 2025 Government Work Report delivered by the State Council. The Fourth Plenary Session further emphasized optimizing the regional economic landscape, fostering coordinated development, and refining major productivity layouts, providing strategic guidance for the spatially coherent advancement of NQPF. For urban areas, keeping pace with these evolving productivity paradigms is crucial for achieving developmental leapfrogging [1]. NQPF development, central to China’s sustainable and high-quality growth, is defined by its innovative essence and advanced quality [2,3]. The principle of “adapting to local conditions” serves as a critical governance instrument, acting as a key mechanism to address deep-seated regional and inter-urban development imbalances in China [4]. As spatial inequity increasingly constrains sustainable economic progress, urban-centric coordination strategies that acknowledge spatial heterogeneity and promote resource complementarity have gained prominence. Major urban agglomerations, such as the Beijing–Tianjin–Hebei Region and the Yangtze River Delta, exemplify this approach and play a pivotal role in national quality development [5,6]. Their implementation accelerates the reshaping of spatial patterns from monocentric to polycentric models [7], where strengthening inter-city linkages and leveraging strategic synergies are paramount. NQPF represent an advanced form of productive forces. They are innovation-driven, characterized by high technology, efficiency, and quality, and align with the new development philosophy. Emerging from technological breakthroughs, innovative factor allocation, and industrial upgrading, they position the national productivity system as a complex, interactive entity of “factors, structure, and functions” [8]. A multi-dimensional analysis of this system from a city perspective is therefore foundational for implementing locally grounded NQPF strategies. It also provides critical insights for national resource optimization aimed at building NQPF with distinctive Chinese characteristics and regional relevance.

The NQPF is predicated on digital and intelligent technologies, which engender innovative digital production factors that effectively transcend traditional spatial and temporal constraints. These technologies may lower coordination costs and strengthen potential cross-city correlations among new quality productive factors [9]. Against this backdrop, cities serve as micro-units for regional economic transformation. Different cities exhibit distinct locational disparities in technological research and development (R&D), resource endowments, and economic development levels. Such disparities determine the heterogeneous positions of cities and endow them with diverse functions within the spatial network associated with the development of NQPF. General Secretary Xi Jinping emphasized at the 19th CPC National Congress the need to implement the regional coordinated development strategy and establish more effective new mechanisms for regional coordinated development. This strategy was further deepened at the 20th CPC National Congress. The Report to the 20th CPC National Congress proposed to “further implement the regional coordinated development strategy, major regional strategies, functional zone strategy and new urbanization strategy, optimize the layout of major productive forces, and build a regional economic layout and national spatial system featuring complementary advantages and quality development”—positioning this as a key component of fostering a new development pattern and advancing quality development. Subsequently, the Decision of the CPC Central Committee on Further Comprehensively Deepening Reform and Advancing Chinese-Style Modernization, adopted at the Third Plenary Session of the 20th CPC Central Committee in 2024, called for “improving mechanisms for implementing the regional coordinated development strategy”. This made the strategic mechanism for regional coordinated development a key part of the national macro-control system, and more importantly, a crucial element for boosting regional development vitality and building a regional economic pattern with complementary advantages and quality development. Existing research has extensively explored spatial layout optimization from perspectives such as regional differences [10], regional synergy [11] and correlation networks [12], predominantly using cities as the primary unit of analysis. Since the concept of NQPF was first proposed in 2023, a large number of research outcomes have emerged over the past year. Theoretical studies have deepened, covering connotative characteristics [13,14], cultivation paths [1,15] and enabling mechanisms [16,17]. Quantitative studies, however, remain at a nascent stage. Most meso-level studies on regional NQPF mainly focus on provincial regions [18,19], while studies using city-level samples have just emerged. Among these, Shi et al. [20] analyzed the spatial difference trend of NQPF development using the Gini coefficient method, with five major urban agglomerations as samples. Mi et al. [21] took urban agglomerations in the Yangtze River Delta as samples, measuring and analyzing the characteristics of urban interconnection networks in NQPF development and the impact of network structure on environmental improvement. China is in an accelerated phase of implementing the new urbanization strategy. Urban development faces a series of new opportunities and challenges, making coordinated development crucial. Therefore, in-depth and detailed analysis of the spatial layout characteristics, structural resilience and key elements of urban NQPF development constitutes a key part of optimizing the resource layout for NQPF.

System dynamics and complex network technology are widely used in the analysis of urban complex systems. System dynamics focuses on characterizing dynamic feedback mechanisms and causal loop relationships between different elements within complex systems, thereby simulating future evolution laws of such systems under various scenarios. From a relational perspective, complex network technology abstracts individuals in the system as nodes and their connections as edges, providing a unique quantitative tool to explore complex system structure and function. As a core application branch of complex network technology, social network analysis (SNA) can accurately quantify node positions, roles and overall network architecture through mathematical models and graph theory tools. Its notable advantage lies in not only measuring node importance in the network via indicators like centrality, but also revealing group structures and power distribution within the network using methods such as block models and cohesive subgroup analysis. This enables effective analysis of interaction mechanisms between individual behaviors and collective phenomena in socio-economic systems. Therefore, this study intends to adopt the social network method to conduct research on implementing the strategy of developing NQPF in accordance with local conditions. Current studies based on social network analysis mostly focus on static network characteristics [18,22,23], such as overall network density, individual centrality distribution and small-group cohesion patterns. While these can clearly present the instantaneous network structure, they fail to capture the dynamic response process of the network under external shocks and temporal patterns of network structural change. Comparable national city-level evidence remains limited. Feature measurements are limited to the overall network, individual centrality and small-group characteristics; node-removal robustness and micro-structural patterns have received limited attention in this literature. Research on network micro-structural patterns commonly uses two approaches: structural holes and motifs. Compared with the structural hole approach, motifs characterize recurring micro-structural patterns in the overall network by measuring frequently occurring network subgraphs [24,25]. However, conclusions on motif identification in NQPF relational networks from a micro-perspective have not been obtained. In summary, current relevant achievements focus on measuring spatial relational networks between provinces, with even fewer studies using cities as samples. Existing studies taking the Yangtze River Delta urban agglomeration as samples have not conducted analyses of node-removal robustness and motif patterns, and systematic network characteristic research using all cities as samples is still absent. There are few studies on motif characteristics of spatial relational networks [26,27], and motif characteristics of NQPF networks have not yet been examined systematically at the national city level.

This study addresses the following question: how did the model-estimated spatial correlation network of NQPF among 283 Chinese cities evolve from 2010 to 2023 in terms of overall structure, key nodes, block relations, node-removal robustness, and triadic motif composition? To answer this, we construct a city-level spatial correlation network using a gravity-model-based estimation, and apply social network analysis (SNA) complemented by resilience testing and triadic motif detection. Relative to prior provincial-level [18,22] or regional [21] studies (

Table 1. Comparison with the closest NQPF spatial correlation network studies.

Study	Spatial Scope	Primary Focus	Distinction of the Present Study
Ji et al. [18]	Chinese provinces	Network evolution and determinants	National city sample with node-removal robustness and motif analyses
Mi et al. [21]	Yangtze River Delta cities	Network structure and environmental effects	National scope with node-removal robustness and motif analyses
Huang et al. [22]	Chinese provinces	Network structure and determinants	City-level sample with node-removal robustness and motif analyses
This study	283 Chinese cities, 2010–2023	Topology, centrality, blocks, robustness, and motifs	National city-level integration of these established tools

), our contribution lies in three aspects: (i) national coverage at the prefecture-city scale, (ii) systematic integration of static structural measures with dynamic robustness and motif analyses, and (iii) a complex system perspective that captures both macro-level network evolution and micro-level interaction regularities. Specifically, we first measure each city’s NQPF development level, then build the inter-city correlation network, and finally examine its overall topology, centrality distribution, block model partitions, attack-tolerance under node removals, and recurring triadic configurations. The findings are intended to offer empirical foundations for spatially differentiated policy optimization of NQPF in China.

2. Theoretical Foundations

2.1. Theoretical Basis

Marx treated productive forces as the material and social capacities through which production develops and societies change. In 2023, Xi Jinping introduced NQPF as a contemporary development of productive force theory in China. Its novelty lies in technological breakthroughs and the reorganization of production factors, while its quality dimension refers to advanced production characterized by high technology, high efficiency, and high standards. NQPF development is therefore innovation-led and oriented toward improvements in total factor productivity, industrial structure, and production functions. In China’s transition toward a high-quality development model, NQPF provide a strategic framework grounded in national conditions [28].

The principle of “adapting measures to local conditions” has deep historical roots in Chinese governance philosophy. It originates from Records of the Wuyue States—Internal Biographies of Helü. According to the Modern Chinese Dictionary, it means formulating appropriate measures based on the specific circumstances of different regions. The Party Central Committee’s call to improve the institutional mechanisms for developing NQPF tailored to local conditions essentially emphasizes abiding by the objective laws governing productive forces development and upholding the fundamental principle of seeking truth from facts [29]. This requires clarifying the internal strengths and weaknesses as well as external opportunities and challenges in local NQPF advancement while respecting such objective laws. Conceptually, NQPF constitutes an organic system where “factors, structure, and functions” are intricately interconnected [8]. Therefore, its development relies not only on upgrading the quality of core elements like laborers, means of labor and objects of labor but also on maximizing resource allocation efficiency through optimized spatial layout and regional coordination.

2.2. Logical Mechanism

The strategy for developing NQPF according to local conditions is proposed based on Marx’s theory of productive forces, systems theory and historical materialism, with its integrated logical mechanism illustrated in Figure 1.

Marx’s theory of productive forces provides the core lens, positing NQPF as a qualitative leap transcending traditional productive forces. This leap is fundamentally contingent on the upgrading of core elements (labor, means of labor, and objects of labor). Cities, as the primary carriers of NQPF, exhibit significant heterogeneity in their endowments of these elements. This heterogeneity forms the essential basis for spatially differentiated development strategies.

Systems theory offers a crucial methodological perspective, viewing the world as an organic whole composed of interrelated components. Applied to NQPF, this perspective necessitates analyzing not only the intra-city endowment of relevant factors but also the characteristics and evolution of spatial linkages that may arise from cross-regional interactions. As depicted in Figure 1, City i and City j, each with distinct development characteristics, industrial bases, and policy environments, are situated within a broader external milieu. Incorporating this complex systems perspective is valuable for optimizing regional institutional mechanisms, as it allows for a thorough analysis of both “spatial heterogeneity” and “spatial interaction.” It should be noted, however, that the spatial linkages identified in this study are estimated on the basis of the gravity model and reflect potential structural correlations, rather than directly observed factor flows.

Historical materialism anchors the framework’s value orientation, with the fundamental interests of people as the supreme criterion. This principle dictates that China’s pathway for NQPF development must safeguard public welfare. It requires strategies that meticulously consider local resource endowments, industrial foundations, scientific capacities, and policy systems to form an optimal, multi-level development model characterized by “targeted policymaking, systematic planning, and grassroots implementation” [30].

To sum up, integrating these theories yields the following logical mechanism: take Marx’s theory of productive forces as the core to grasp the dialectical upgrading of NQPF in both “quality” and “quantity”; adopt systems theory as the methodological tool to balance the complex relationships between intra-urban elements and cross-regional spatial linkages; take the materialist conception of history as the value guide, and based on the fundamental interests of the people and local actual conditions, extract key information from the social network structure of urban NQPF from three dimensions—static characteristics, dynamic characteristics and micro-driving forces. This approach helps construct a region-specific development path that conforms to the laws of productive forces development, aligns with the requirements of spatial coordinated development and safeguards people’s interests, thereby realizing the unity of scientific nature, coordination and people-centeredness in NQPF development. Therefore, the complex system analysis paradigm that takes both “urban differences and inter-urban correlations” into account should serve as an important basis for China to implement the strategy of developing NQPF tailored to local conditions.

3. Methodology

3.1. Analytic Strategy

This study follows a three-step analytical framework to systematically investigate the spatial correlation network of NQPF. The first step involves constructing the spatial correlation network based on an improved gravity coefficient matrix, which measures the strength of inter-city connections using indicators of city scale, economic output, NQPF level, and geographic distance. The second step measures static network characteristics, including overall network properties, node centrality, and block model analysis using the CONCOR method to identify subgroup structures and their functional roles. The third step focuses on dynamic network characteristics, encompassing network resilience simulation under intentional and random attack scenarios, and motif type identification to describe micro-level structural patterns associated with network evolution. This hierarchical analytical design ensures a comprehensive understanding of the network’s structure, function, and evolutionary dynamics.

3.2. Construction of NQPF Spatial Correlation Network

To construct the NQPF spatial correlation network, the NQPF level of each city must first be measured. This study draws on the research of Wang and Wang [31], adopting a multi-indicator comprehensive evaluation method based on Marx’s theory of productive forces, while optimizing the indicator system to align with the city-level scale. For the new-quality laborers dimension, indicators are adjusted to better fit urban statistical calibers, ensuring data availability and objectivity. For the new-quality objects of labor dimension, the measurement of strategic emerging industries is converted from value-added to the number of enterprises, to more accurately reflect the agglomeration density of new-quality industries in cities; the focus of environmental governance is shifted toward the utilization rate of solid waste and the treatment rate of domestic garbage. For the new-quality means of labor dimension, the word frequency of digital infrastructure is introduced to capture the policy orientation of digital transformation, the share of clean energy consumption is added to improve the measurement of green means of production, and the science and technology input indicator is adjusted to the share of science and technology expenditure in fiscal expenditure, to better reflect urban fiscal realities. The resulting urban NQPF measurement indicator system is presented in

Table 2. Measurement index system for city-level NQPF.

New-Quality Elements	First-Level Indicators	Specific Indicators and Calculation Formulas	Direction	Weight
New-Quality Laborers	Talent Quality	Number of College Students Enrolled/Total Population	+	4.292%
		Average Years of Education	+	0.953%
	Income Level	Per Capita Gross Regional Product	+	4.328%
		Average Wage of Employees	+	2.411%
	Employment Concept	Proportion of Employees in the Tertiary Industry	+	1.609%
		Entrepreneurial Activity	+	0.677%
New-Quality Objects of Labor	Emerging Strategic Industries	Number of Enterprises in Emerging Strategic Industries	+	39.313%
	Future Industries	Robot Installation Density	+	6.207%
	Green Environmental Protection	Green Coverage Area/Total Area	+	12.252%
		Environmental Regulation Intensity	+	1.125%
	Pollution Reduction	Industrial Wastewater Discharge	−	0.081%
		Industrial Sulfur Dioxide Emission	−	0.082%
		Industrial Smoke and Dust Emission	−	0.009%
		Comprehensive Utilization Rate of Industrial Solid Waste	+	0.036%
		Harmless Treatment Rate of Domestic Garbage	+	0.035%
New-Quality Means of Labor	Infrastructure	Highway Mileage	+	0.191%
		Proportion of Word Frequency of Digital Infrastructure in Government Work Reports	+	0.078%
	Energy Consumption	Total Energy Consumption	−	0.350%
		Clean Energy Consumption	+	0.474%
	Scientific and Technological Innovation	Number of Authorized Patents/Total Population	+	20.445%
		Science and Technology Expenditure/Fiscal Expenditure	+	2.977%
	Digitalization Level	Digital Economy Index	+	2.075%

Notes: + denotes a positive indicator, and − denotes a negative indicator.

. Urban NQPF levels are calculated using the entropy weight method, which objectively assigns weights based on the dispersion of indicator data, effectively avoiding subjective weighting bias and accurately reflecting the relative importance of each indicator in the evaluation system, thereby providing a measurement foundation for subsequent spatial network analysis.

All city-year observations are pooled for min-max normalization to preserve intertemporal comparability. Let $x$ denote the raw value of a given indicator, and $z$ denote the normalized value. For positive indicators: $z=(x-\mathrm{m}\mathrm{i}\mathrm{n} x)/(\mathrm{m}\mathrm{a}\mathrm{x} x-\mathrm{m}\mathrm{i}\mathrm{n} x)$; for negative indicators: $z=(\mathrm{m}\mathrm{a}\mathrm{x} x-x)/(\mathrm{m}\mathrm{a}\mathrm{x} x-\mathrm{m}\mathrm{i}\mathrm{n} x)$, where $\max x$ and $\min x$ are the maximum and minimum values of that indicator across all years. Industrial wastewater discharge, industrial sulfur dioxide emissions, industrial smoke and dust emissions, and total energy consumption are treated as negative indicators; all remaining indicators are treated as positive. To avoid undefined logarithmic operations in the entropy weight method due to zero values, a translation parameter of 0.00001 is uniformly applied to the normalized data.

After measuring city-level NQPF, we construct a directed spatial correlation matrix using a modified gravity model, following spatial interaction theory and classical gravity models [32,33,34]. The classical gravity model posits that inter-city correlation strength increases with urban development quality and decreases with geographic distance [32]. While retaining this core logic, we tailor the model to NQPF characteristics through several refinements. Population size and gross regional product capture urban scale and economic potential, anchoring inter-city linkages; the composite NQPF score serves as the focal quality variable, capturing the effect of NQPF development on correlation strength; and geographic distance represents spatial friction, reflecting the law of spatial decay. To account for asymmetric linkages due to inter-city NQPF differences, we introduce a correction coefficient $K_{ij}^t$, implying that a city with higher NQPF exerts stronger estimated influence on its counterpart. Compared with the conventional symmetric gravity model, this modified form better captures the non-equilibrium nature of NQPF-related spatial correlations and improves the realism of network characterization. The modified gravity model is specified in Equation (1).

$$R_{ij}^t=K_{ij}^t\cdot {\displaystyle \frac{\sqrt[3]{P_i^t{G}_i^t{Q}_i^t}\cdot \sqrt[3]{P_j^t{G}_j^t{Q}_j^t}}{D_{ij}^2}}, K_{ij}^t={\displaystyle \frac{Q_i^t}{Q_i^t+Q_j^t}}$$

(1)

In Equation (1), $R_{ij}^t$ denotes the estimated NQPF spatial gravity coefficient in year t between city i and city j; $P_i^t$ and $P_j^t$ are the respective populations of cities i and j in year t; $G_i^t$ and $G_j^t$ are their respective gross regional products; $Q_i^t$ and $Q_j^t$ are their respective NQPF scores; and D_ij is the Euclidean distance between the city centroids.

The gravity coefficients form a weighted directed matrix containing an estimated correlation for each ordered city pair. To obtain the binary adjacency matrices required by the subsequent SNA procedures while retaining a common criterion over time, we use a single threshold fixed across the full 2010–2023 period. Specifically, the threshold $\overline{R}$ is the arithmetic mean of all off-diagonal coefficients across all years and ordered city pairs [32,33,34]. Applying this threshold to each annual weighted matrix gives the binary adjacency matrix in Equation (2).

$$A_{ij}^t=\left\{\begin{array}{ll}1,\hfill & R_{ij}^t>\overline{R}\hfill \\ 0,\hfill & R_{ij}^t\le \overline{R}\hfill \end{array}\right.$$

(2)

For city i and city j in year t, $R_{ij}^t$ is compared with $\overline{R}$. The corresponding binary element is set to 1 when $R_{ij}^t$ exceeds the threshold and to 0 otherwise. Repeating this rule for every ordered city pair yields $A^t={\left(A_{ij}^t\right)}_{N\times N}$, whose entries indicate whether a model-estimated directional correlation is retained from city i to city j in year t. The annual binary matrices constitute the input for the subsequent network analysis.

3.3. Network Characteristic Measurement Methods

This study decomposes the measurement of network characteristics into static and dynamic components, with details specified as follows:

First, regarding static network characteristics. The overall network characteristic indicators include five measurement indexes: network density, connectivity, efficiency, hierarchy, and reciprocity [35]. Specific calculation formulas are presented in

Table 3. Network property indexes and their formulas.

Network Property Indicators	Specific Calculation Formulas	Symbol Meanings
Network Density	$\mathrm{Dens}={\displaystyle \frac{L}{N(N-1)}}$	L denotes the number of actually existing relationships in the network; N denotes the node scale
Network Connectivity	$\mathrm{Conn}=1-{\displaystyle \frac{V}{N(N-1)/2}}$	V denotes the number of unreachable node pairs; N denotes the node scale
Network Efficiency	$\mathrm{Eff}=1-{\displaystyle \frac{M}{M_{\max }}}$	M denotes the actual number of redundancies; Mmax denotes the maximum possible number of redundancies
Network Reciprocity	$\mathrm{Rec}={\displaystyle \frac{L_b}{L}}$	Lb denotes the number of directed ties from i to j for which the reverse tie from j to i also exists; L denotes the total number of directed ties.
Network Hierarchy	$\mathrm{Hier}=1-{\displaystyle \frac{S}{S_{\max }}}$	S denotes the number of symmetric reachable node pairs; Smax denotes the maximum scale
Node Out-Degree	${\mathrm{OutDeg}}_i={\displaystyle \sum _{j=1}^N{A}_{ij}}$	i and j denote cities; Aij is the binary directed tie from i to j.
Node In-Degree	${\mathrm{InDeg}}_i={\displaystyle \sum _{j=1}^N{A}_{ji}}$	i and j denote cities; Aji is the binary directed tie from j to i.
Node Degree Centrality	${\mathrm{Deg}}_i={\mathrm{OutDeg}}_i+{\mathrm{InDeg}}_i$	OutDegi and InDegi denote the out-degree and in-degree of city i, respectively.

. These indexes respectively characterize the tightness of relationships, smoothness of information transmission, proportion of redundant relationships, hierarchical structure, and symmetry of two-way relationships within the network. Node centrality consists of three indicators: out-degree, in-degree, and centrality. As shown in Table 3, out-degree reflects the scale of relationships initiated by a node, in-degree represents the scale of relationships received by a node, and centrality is the sum of the two. By measuring these three indicators of key nodes, the roles of key nodes in the network are evaluated. Cluster structure analysis is mainly carried out based on the identification of small groups and the relationships between them. This study adopts the Convergence of Iterated Correlations (CONCOR) method for such identification, and uses inter-block network density matrices and image matrices to identify the interaction mechanisms between small groups.

Second, dynamic network characteristics specifically include two aspects: network resilience simulation and motif type identification. Among them, network resilience is mainly simulated by observing the evolutionary results of overall network properties when nodes in the spatial correlation network are attacked, thereby identifying the invulnerability of the NQPF network [36,37]. Furthermore, this study further decomposes node attacks into two scenarios: random and intentional, to explore in detail the simulated changes in different network property indicators under different attack scenarios. Current research on the micro-mechanisms of social networks mainly includes the Structural Hole Theory proposed by Burt [38] and the Network Motifs Theory proposed by Milo et al. [39]. The Structural Hole Theory emphasizes that information between some network nodes is incompletely connected, and nodes located in structural holes can obtain unique information advantages and social capital, functioning as “bridges” or “intermediaries” [40,41]. The Network Motifs Theory defines basic topological structures composed of a small number of nodes as motifs, which are smaller in scale than communities. It uses motif frequencies to identify the microcosm of the overall network [42]. Compared with the structural hole perspective, the Network Motifs Theory can provide richer conclusions on micro-structural characteristics and has been applied to the micro-characteristic analysis of complex networks in recent years [36,43,44,45]. Therefore, for the identification of motif types in this study, all motif types composed of three nodes are selected for identification. Furthermore, the distribution trends of major motif types in different years are explored to investigate the micro-driving mechanisms of network evolution.

3.4. Sample Description and Data Sources

First, this study selects 283 prefecture-level and above cities in China as research samples covering the period from 2010 to 2023, with missing data supplemented by the linear interpolation method. Following the division standard of China’s four major economic regions released by the National Bureau of Statistics, all sample cities are classified into the Eastern, Central, Western, and Northeast economic regions. Specifically, the Eastern economic region includes 86 cities, the Central region 80, the Western region 83, and the Northeast economic region 34.

Second, regarding data sources: The primary data are obtained from the China City Statistical Yearbook, statistical yearbooks of provinces and municipalities directly under the Central Government, the CSMAR Database, and the EPS Database. Among them, data for the “Employment Concept” indicator are derived from the Index of Regional Innovation and Entrepreneurship in China (IRIEC) compiled by Peking University (https://opendata.pku.edu.cn/dataset.xhtml?persistentId=doi:10.18170/DVN/NJIVQB (accessed on 1 November 2025)). The number of enterprises in emerging strategic industries is sourced from the Tianyancha Website (https://www.tianyancha.com (accessed on 17 January 2026)) [46]. The environmental protection intensity is calculated by drawing on the processing ideas of Shao et al. [47]. The Digital Economy Index refers to the research of Zhao et al. [48] and is measured from two aspects: internet development [49] and digital finance development indicators. The latter adopts the China Digital Inclusive Finance Index jointly compiled by the Peking University Digital Finance Research Center and Ant Group [50].

4. Results

4.1. Static Network Characteristics Analysis

4.1.1. Topological Structure and Evolution

Using UCINET 6.560 and R 4.4.2 software, the spatial correlation network topology maps for 2010 and 2023 are obtained, as shown in Figure 2 and Figure 3. Figure 2a and Figure 3a present a topology-based layout that abstracts from geographic distance, while Figure 2b and Figure 3b position nodes using geographic coordinates, with node colors representing the centrality size. By comparing the topological maps for the two years, the evolution trend of the urban correlation network structure during the research period can be preliminarily identified. Two main findings emerge from the comparative analysis.

First, the spatial correlation network exhibited a significant expansion in connectivity, reflecting a broadening of channels for the exchange of NQPF among cities. This is evidenced by a near-tripling of network relationships from 4851 in 2010 to 12,584 in 2023, alongside a halving of isolated nodes from 12 to 6. These trends indicate both deeper integration of cities into the network and a gradual scaling-up of China’s NQPF spatial correlation structure. Second, despite increased connectivity for certain nodes, the network did not develop a distinct hierarchical organization. By 2023, no dominant core nodes had emerged, and a clear core–periphery structure remained absent.

In summary, the NQPF spatial correlation network exhibits an upward trend in network density, with an expanded relationship scale and a significant reduction in isolated nodes. Additionally, core nodes in the overall spatial correlation network are not prominent, and no distinct core–periphery structure has yet taken shape.

4.1.2. Overall Network Structure Characteristics

To examine the overall structural characteristics of the network, UCINET software was used to calculate five key indicators: network density, network connectedness, network efficiency, network reciprocity and network hierarchy (Figure 4). The key findings are summarized as follows:

Network density increased from 0.0608 in 2010 to 0.1577 in 2023. It remained below 0.10 before 2015 and fell within [0.10, 0.20] thereafter, indicating a shift from an ultra-low-density to a low-density configuration under the study’s classification. Connectivity rose from 0.8834 to 0.9374, indicating that most node pairs remained mutually reachable in the binary network. Hierarchy declined from 0.0662 to 0.0217 and remained low, which is consistent with the absence of a pronounced core–periphery ordering under this measure. Efficiency decreased from 0.9229 to 0.8019 and then stabilized at a comparatively high level. Reciprocity fluctuated between 0.61 and 0.65, indicating that the proportion of bidirectional connections among network nodes was approximately 61–65%, which remains at a relatively high level.

In summary, the NQPF spatial correlation network shifted from an ultra-low-density to a low-density configuration from 2010 to 2023. It retained high connectivity, comparatively high efficiency and reciprocity, and low hierarchy, yet has not developed a pronounced core–periphery structure.

4.1.3. Centrality Analysis of Key Nodes

Based on changes in centrality indicator values among the top 10 node cities in 2010 and 2023 (

Table 4. The first 10 centrality nodes distribution in 2010 and 2023.

Top 10 Cities	2010				Top 10 Cities	2023
	Degree Centrality	Out- Degree	In- Degree	Role		Degree Centrality	Out- Degree	In- Degree	Role
Wuhan	135	79	56	Exporter	Wuhan	309	181	128	Exporter
Beijing	121	78	43	Exporter	Beijing	288	190	98	Exporter
Nanjing	120	74	46	Exporter	Guangzhou	271	190	81	Exporter
Guangzhou	117	94	23	Exporter	Zhengzhou	268	161	107	Exporter
Shanghai	112	80	32	Exporter	Changsha	264	172	92	Exporter
Hefei	111	67	44	Exporter	Chongqing	259	135	124	Broker
Zhengzhou	108	67	41	Exporter	Hefei	252	154	98	Exporter
Hangzhou	104	61	43	Exporter	Shenzhen	247	196	51	Exporter
Xuzhou	103	47	56	Broker	Shanghai	236	178	58	Exporter
Jining	100	49	51	Broker	Nanjing	234	154	80	Exporter

Note: According to UCINET6.560 software.

), this section evaluates the distribution of key node cities in the network and the evolution of their roles and functions. The main findings are as follows:

The distribution of the top 10 cities by centrality reflects distinct spatial dynamics over the study period. In the 2010 correlation network, the top 10 cities included 8 eastern cities, two central cities, and no western cities, presenting an overall pattern of “eastern agglomeration, sparse central participation, and western absence”. By 2023, this structure had shifted to six eastern cities, three central cities, and one western city, evolving into a pattern characterized by “persistent eastern agglomeration, increased central engagement, and initial western integration”. Chongqing ranked 6th in 2023, placing one western city among the high-centrality nodes in the estimated network. Wuhan maintained the 1st position in both 2010 and 2023, showing that it retained the highest degree centrality in the two reported years. As an important node in the central region, Zhengzhou has experienced continuous growth in its centrality scale within the NQPF network, rising from 7th to 4th place. In addition, Changsha entered the top 10 at 5th place. Collectively, these changes reflect the strengthened influence of central cities in the NQPF framework. Eastern key node cities retained their dominant position in centrality, though individual variations emerged. Nanjing dropped out of the top 10 from 3rd place with a significant decline, while Shanghai’s ranking slightly decreased. These trends indicate that from 2010 to 2023, eastern cities maintained a dominant and agglomerative role in the NQPF spatial correlation network, although the status of certain eastern nodes has weakened or declined. Meanwhile, central cities have expanded their presence, with Changsha joining Wuhan and Zhengzhou to markedly enhance their influence. Furthermore, western cities have increased their participation, represented most notably by Chongqing, which has gradually evolved into a critical network participant.

Node functions are classified into three types—exporters, receivers, and intermediaries—based on comparisons of out-degree and in-degree indicator values in the estimated network. Exporters are defined as nodes with significantly higher out-degree than in-degree, indicating relatively stronger outgoing correlations in the network; receivers are the opposite; intermediaries are nodes with roughly balanced out-degree and in-degree, suggesting a potential bridging role in the network. In the 2010 network, 8 of the top 10 key nodes were categorized as exporters, primarily characterized by outgoing relational tendencies, while only two nodes (Xuzhou and Jining) served as intermediaries, forming a pattern dominated by exporter-type nodes. By 2023, Chongqing had emerged as the sole “intermediary node” among the top 10, replacing the 2010 intermediaries (Xuzhou and Jining). This indicates that Chongqing has developed a balanced profile of incoming and outgoing correlations in the estimated network, potentially serving as a structural bridge linking eastern, central, and western cities—a finding broadly consistent with its strategic role in national regional coordination policies. All other top 10 nodes in 2023, distributed across eastern and central regions, retained the exporter function, primarily characterized by outgoing correlation patterns toward other cities in the network.

In summary, a comparison of centrality, out-degree, and in-degree of key nodes in the 2010 and 2023 spatial correlation networks reveals that the roles of the top 10 key node cities have continuously strengthened, exhibiting a dynamic upward trend. Eastern cities remain dominant and agglomerated, though individual cities have experienced declining status or even withdrawal from the top 10. The number of central cities has increased, with Changsha joining the ranks of Wuhan and Zhengzhou, thereby enhancing the influence of central cities. Western cities have also boosted their influence, with Chongqing as the most representative, showing a balanced correlation profile between the central-eastern and western parts of the network.

4.1.4. Group Clustering Characteristics

This study uses CONCOR to partition the 283-city network. Following general blockmodeling guidance from Liu (2014) [35] and Wasserman and Faust (1994) [51], and taking into account the sample size and conventions in comparable studies [52,53], the maximum splitting depth is set to 2, yielding four blocks, and the convergence criterion is set to 0.20. The inter-block density matrix and image matrix are then derived (Table 4 and Figure 5) to reveal the interactive relationships and functional roles among the blocks.

The evolving composition of the blocks indicates significant structural adjustment. Block 1 expanded from 53 to 91 cities, Block 2 grew moderately from 61 to 66 cities, and Block 3 increased marginally from 67 to 72 cities. In contrast, Block 4 experienced a substantial contraction, shrinking from 102 to 54 cities. This divergent trend indicates that the membership sizes of Blocks 1–3 all exhibited an increasing trend, while that of Block 4 declined sharply. Given that Block 4 is predominantly composed of cities in western China, the drastic reduction in its membership size signals a marked enhancement in the status and role of western urban agglomerations within the spatial correlation network of new quality productive forces. It further reflects a spatial evolution trajectory where western China is progressively integrating into the urban clusters of central and eastern regions.

Second, the block density matrix, image matrix (

Table 5. Block density and image matrices in 2010 and 2023.

Year	Block	Density Matrix				Image Matrix
		Block 1	Block 2	Block 3	Block 4	Block 1	Block 2	Block 3	Block 4
2010	Block 1	0.4006	0.0646	0.0501	0.0013	1	1	0	0
	Block 2	0.0813	0.3344	0.0051	0.0051	1	1	0	0
	Block 3	0.0451	0.0098	0.2076	0.0042	0	0	1	0
	Block 4	0.0002	0.0037	0.0072	0.0576	0	0	0	0
2023	Block 1	0.5200	0.2266	0.0198	0.0012	1	1	0	0
	Block 2	0.1695	0.5704	0.1368	0.0132	1	1	1	0
	Block 3	0.0046	0.1008	0.1849	0.0381	0	1	1	0
	Block 4	0.0000	0.0034	0.0376	0.3166	0	0	0	1

), and the corresponding interaction diagram (Figure 5) elaborate on key interaction patterns and functional evolution features. Regarding internal density, internal correlations within Block 1 and Block 2 strengthened consistently, with densities rising from 0.4006 and 0.3344 to 0.5200 and 0.5704, respectively. Block 3 maintained a stable level of internal connectivity despite a slight density decrease. For Block 4, the internal density increased from 0.0576 to 0.3166 following member consolidation; however, its absolute scale of internal interaction remains comparatively low. The functional roles of the blocks in the network evolved distinctly. Block 1 transitioned from a “bidirectional spillover” to a dominant “net spillover” role. Its internal tie proportion consistently exceeded 73%. By 2023, it sent 1497 external ties while receiving only 1048, establishing itself as a core outward-correlation role in the network. Block 2 evolved into a pivotal “bidirectional spillover” hub. Although its internal tie proportion decreased to 58.79%, it retained strong internal cohesion. In 2023, it exhibited a near-balanced external exchange (sending 1852 and receiving 1715 ties) and effectively brokered connections between Block 1 and Block 3, underscoring its enhanced intermediary function. Block 3 shifted from a “bidirectional spillover” to a “net beneficiary”. Its internal tie proportion fell from 80.03% to 58.99%, and in 2023, it received 926 external ties—significantly more than the 657 it sent out—indicating its primary role in receiving external correlations, particularly from Block 2. Block 4 remained relatively isolated, with its internal tie proportion persistently above 85% and null external connections in the image matrix, denoting consistently weak interaction with other blocks. Analyzing inter-block interactions reveals that the 2010 network was concentrated between Blocks 1 and 2, with other linkages being tenuous. By 2023, interactions between Blocks 1 and 2 intensified substantially. Interactions between Blocks 2 and 3 also strengthened notably. In contrast, Block 4 remained largely detached from the core interactive dynamics.

In summary, from 2010 to 2023, the spatial correlation network of China’s NQPF exhibited a pronounced trend of structural differentiation. On one hand, the internal membership structure of the four major blocks underwent constant adjustments, with the most prominent feature being the gradual integration of western cities into the urban clusters of central and eastern China. On the other hand, in the evolution of inter-block interactions, the linkages between Blocks 1 and 2 were continuously consolidated, and the interactions between Blocks 2 and 3 were significantly enhanced, with Block 2 retaining a near-balanced external tie profile. In contrast, Block 4, dominated by western cities, retained comparatively weak estimated links to the other blocks. While its internal membership is dwindling, its interactive connections with the other three blocks still require further strengthening to foster a more integrated and coordinated development pattern of new quality productive forces across China’s urban system.

4.2. Dynamic Network Characteristic Measurement and Analysis

4.2.1. Measurement of Network Resilience Characteristics

Both attack simulations are performed on the 2023 NQPF spatial correlation network. In the intentional attack scenario, nodes are removed in descending order of total degree, with the sequence fixed once and without recomputing centrality for re-ranking. For random attacks, this study sets 50 independent simulations to mitigate stochastic bias: in each run, the 283 nodes are randomly ordered, and network indicators are recorded progressively during removal. The final random attack curves are averaged across the 50 simulations.

Figure 6 presents simulation results for changes in network indicators of the spatial correlation network under intentional and random attack strategies. Among these, Figure 6a–d depict variation trends of four property indicators: network density, connectivity, efficiency, and reciprocity.

Figure 6a,b show that both network density and connectivity exhibit a rapid downward evolutionary trend under intentional attack scenarios. Specifically, network density undergoes a phased nonlinear decline. Targeted removal of nodes sorted by centrality reveals that when 100 nodes have been removed, density reaches 0.0711 in the displayed curve. This reported trajectory shows an abrupt decline after the removal of high-centrality nodes. When removed node count increases to 250, density drops to 0.0407, with the decline rate slowing to 42.76%. When failed node count reaches 269, network density falls to 0, meaning the network structure collapses after removing the 269th node. Network connectivity experiences four distinct abrupt drops. Initially, connectivity decreases slightly as failed node count increases. When 115 nodes are removed, it gradually falls from the initial 0.9372 to 0.8844. The first abrupt drop occurs at the 116th node, plummeting from 0.8844 to 0.5756. The second significant drop happens during the removal of the 135th to 136th nodes, declining from 0.5412 to 0.4229. The third sharp decline occurs when 190 to 215 nodes fail, with connectivity dropping from 0.4056 to 0.1716. The fourth obvious drop takes place after 247 node failures, continuing until the network completely collapses at 269 nodes. This highlights the cascade effect characteristics and connectivity threshold breakthrough. In contrast, under random attack scenarios, network density remains close to its initial value even after removing 250 nodes, and network connectivity stays basically stable before 200 nodes are removed. Both indicators decline slowly, with overall resilience significantly superior to that under intentional attacks. This underscores the robustness advantage of distributed redundant connections in maintaining overall network connectivity and resisting random shocks such as natural disasters.

Figure 6c,d indicate that the initial performance of network efficiency and reciprocity under the two attack strategies differs from that of the indicators in Figure 6a,b, with both exhibiting fluctuating changes. Under intentional attacks, network efficiency shows slight upward fluctuations before 250 nodes are removed. When failed node count reaches 105, efficiency abnormally increases by 12.52% to 0.9206; by 250 failed nodes, it remains at 0.8478, still in the fluctuation phase. Beyond 250 failed nodes, network efficiency undergoes an abrupt drop, falling to 0 at 262 nodes. This phenomenon reveals the efficiency-resilience trade-off mechanism in the NQPF network: the initial upward trend indicates that although key node removal weakens global connectivity, it eliminates path redundancy caused by partial over-centralization, prompting remaining nodes to establish more direct collaborative relationships. Network reciprocity slightly increases and then stabilizes before 200 nodes are removed, reflecting compensatory collaboration formed among secondary cities after key node failures. Subsequently, it gradually declines with fluctuations until reaching 0 at 282 nodes, when the network collapses. Under random attack scenarios, both network efficiency and reciprocity maintain relative stability within most ranges of failed nodes (efficiency up to 250 nodes, reciprocity up to 275 nodes) before significant declines occur. This indicates that in the early attack stage, the differences in changes between the two indicators under the two strategies are less pronounced than those in Figure 6a,b group, and short-term indicator rises may occur due to structural reorganization under intentional attacks. Nevertheless, random attacks still demonstrate better late-stage stability.

In summary, significant differences exist in network structure resilience under intentional and random node attacks. The network structure is more prone to collapse under intentional attacks but more robust under random attacks. Meanwhile, under intentional attacks, network density and connectivity undergo rapid and severe deterioration, whereas network efficiency and reciprocity show slower responses. Under random attacks, all four indicators decline slowly, exhibiting good overall stability.

4.2.2. Identification of Motif Type Characteristics

Three-node motifs are used to characterize local topology in the NQPF correlation network. The procedure has three steps. First, every three-city combination is extracted from the binary spatial adjacency matrix as a 3 × 3 submatrix. Second, each submatrix is classified by its directed-edge configuration. M1 contains no edges, M2 contains one edge, M3–M5 contain two edges, M6–M9 contain three edges, M10–M13 contain four edges, M14 contains five edges, and M15 contains all six possible directed edges. Third, the frequency and percentage of each motif are calculated for 2010 and 2023.

Table 6. Motif type distribution of spatial correlation network in 2010 and 2023.

Order Number	Schematic Drawing	2010		2023
		Frequency	Probability (%)	Frequency	Probability (%)
M1		2,982,456	79.80	2,085,961	55.81
M2		689,677	18.45	1,283,137	34.33
M3		1498	0.04	3873	0.10
M4		1357	0.04	5043	0.13
M5		8449	0.23	42,468	1.14
M6		686	0.02	4325	0.12
M7		17,009	0.46	92,317	2.47
M8		0	0.00	0	0.00
M9		7305	0.20	30,249	0.81
M10		2515	0.07	18,559	0.50
M11		375	0.01	1978	0.05
M12		11,056	0.30	61,614	1.65
M13		1699	0.05	12,841	0.34
M14		6223	0.17	42,287	1.13
M15		7276	0.19	52,929	1.42
Total	—	3,737,581	100.00	3,737,581	100.00

Note: Black circles represent city nodes and the arrows represent directed edges.

reports these distributions and provides a micro-level description of changes in network structure.

In 2010, the isolated motif M1 dominates with an occurrence probability of 79.80%, and the single-edge motif M2 accounts for 18.45%, together comprising 98.25% of all motifs. This absolute dominance directly leads to the network’s ultra-low density and lack of a core–periphery structure. The remaining 13 motif types with two or more edges account for less than 2% in total, showing significantly low activity. Among these, M7 occurs 17,009 times with a probability of 0.46%; M12 occurs 11,056 times with a probability of 0.30%; M5 occurs 8449 times with a probability of 0.23%. Although these motifs form local correlation patterns through structures such as bidirectional connections plus unidirectional extensions or coexisting independent bidirectional chains, they all lack cross-regional closed-loop correlations formed by transitive triangles, and correlation effects remain mainly localized. The fully connected M15 accounts for only 0.19%, indicating a weak foundation for complete bidirectional correlations among cities. M8 is completely absent. M7, M9 and M12 are classified as open structural holes.

In 2023, M1 and M2 together account for approximately 90.14%, still dominant but down by 8.11 percentage points from 2010. Among them, M1 drops sharply from 79.80% to 55.81%, a decline of 24 percentage points, serving as the key driver of the network’s transition from ultra-low density to low density. However, the two motifs still account for over 90% of total motifs, which is another important reason for the network’s continued lack of a distinct core–periphery structure. The proportion of other complex motif types increases significantly, indicating notably enhanced bidirectional connections and ordered correlation patterns among three nodes. M7 and M12 still rank as the top two, with M15 rising to third place. M7 increases from 17,009 to 92,317 occurrences, a growth rate of 443%; M12 from 11,056 to 61,614, a growth rate of 457%; and M15 surges to 52,929, a growth rate of 628%—the fastest growth among all types, reflecting a notable enhancement in multi-node bidirectional correlation capacity. However, some motif types still face constraints from unidirectionality or structural limitations: M3 only increases from 1498 to 3873 occurrences, failing to form transitive triangles; M4 increases to 5043 occurrences but relies on single-node transit with relatively low efficiency; M11 occurs fewer than 2000 times, indicating that the expansion of complex correlation patterns still faces certain limitations. Among the other 13 motifs, the role of M7’s open structural holes is significantly enhanced, and the occurrence probabilities of M14 and M15’s closed structural holes also increase notably. The enhanced roles of M7, M14 and M15 motifs constitute important factors driving network structure evolution.

In conclusion, M1 and M2 have always occupied a dominant position, which is the key reason for the network’s persistent low density and lack of a core–periphery structure. The significant decline in these two types, especially the sharp drop in the fully isolated M1 motif, serves as the core driver of network density growth. Among the other 13 motifs, the motif distribution pattern has shifted from open structural holes dominated by M7, M9 and M12 in 2010 to a multi-type pattern featuring both open and closed structural holes in 2023, which constitutes another important factor driving network evolution.

5. Discussion

This study constructs an NQPF spatial correlation network for 283 Chinese cities from 2010 to 2023 using a modified gravity model, and systematically analyzes its overall network structure, node centrality, block clustering, network resilience, and motif evolution. The findings indicate that network density gradually transitioned from ultra-low to low levels over the study period, while network hierarchy consistently declined, suggesting that inter-city structural correlations in terms of NQPF have strengthened and become more flattened. The composition of core nodes evolved from absolute eastern dominance to a pattern characterized by persistent eastern dominance, rising central influence, and initial western integration. Block analysis reveals that western cities gradually participated in the spatial correlation structure linking central and eastern regions, yet Block 4, dominated by western cities, remained in a relatively isolated structural position. Resilience analysis shows that the network exhibits notable vulnerability under intentional attacks but relatively strong resilience under random attacks. Motif analysis indicates that the proportion of fully isolated motif M1 decreased from 79.80% to 55.81%, while fully connected motif M15 increased by 628%, suggesting a transition from local structural-hole dominance toward more diversified micro-level correlation patterns.

Compared with existing studies, the findings of this study exhibit both similarities and differences. At the provincial level, Ji et al. [18] found that inter-provincial NQPF network edges increased from 226 to 227 between 2013 and 2022, a trend consistent with the density increase observed in this study. However, provincial network hierarchy increased from 0.30 to 0.43 in their study, whereas the city-level network hierarchy in this study declined from 0.0662 to 0.0217, suggesting that city-level NQPF spatial correlations exhibit a flatter structural configuration than those at the provincial level. Mi et al. [21], focusing on the Yangtze River Delta urban agglomeration, found a relatively pronounced core–periphery structure within a single metropolitan area, whereas the national city-level network in this study lacks a distinct core–periphery structure, indicating that spatial scale is an important factor influencing network structural characteristics. In comparison with digital economy and innovation networks, existing studies have generally found that China’s urban digital economy exhibits a clear core–periphery hierarchical structure [54,55], and urban innovation networks and technology collaboration networks also display typical core–periphery patterns dominated by single-core or multi-core structures [56,57,58]. The NQPF network identified in this study lacks a pronounced core–periphery structure, in contrast to the above networks. This difference may stem from the multi-dimensional nature of the NQPF concept—its spatial correlations are shaped by multiple factors, including technological innovation, green development, and digital transformation, resulting in a more diversified pattern than single-dimensional digital economy or innovation networks. In terms of methodology, most existing NQPF network studies have focused on static descriptions of centrality and density [21,22]. This study introduces network resilience simulations and triadic motif identification into the analytical framework, revealing the network’s differential structural responses under various attack strategies and micro-level motif evolution patterns.

This study has several limitations. First, while the modified gravity model can estimate potential correlations using urban scale, economic output, NQPF levels, and geographical distance, it may not fully capture the effects of policy orientation, industrial base, institutional environment, and historical path dependence. Future research could incorporate more explanatory variables or conduct external validation using mobility, trade, or patent collaboration data. Meanwhile, the mean-based binary threshold, though ensuring cross-period comparability, overlooks the continuous distribution of correlation strength and variations across city pairs, making the network structure somewhat sensitive to threshold selection. Alternative schemes such as percentile-based or k-nearest-neighbor cutoffs could be explored in future work. Second, the resilience assessment currently covers only targeted and random attack scenarios, whereas real-world urban systems face a broader spectrum of disruptions. Moreover, the analysis focuses on network resistance without addressing recovery capacity—a core dimension of resilience. Future research should incorporate more diverse disruption scenarios and introduce temporal dynamics to capture post-shock recovery processes, thereby providing a more comprehensive understanding of the network robustness required for NQPF systems.

6. Conclusions and Policy Implications

6.1. Main Conclusions

Integrating social network analysis (SNA) and the motif identification approach, this study systematically examines the structural characteristics and dynamic evolution mechanisms of the spatial correlation network of NQPF among 283 Chinese cities from 2010 to 2023. The main conclusions are as follows:

(1)

The NQPF spatial correlation network has evolved from an ultra-low-density type to a low-density type, with the number of isolated nodes dropping sharply and the number of cities participating in spatial interaction increasing significantly. Regarding the overall network properties, it presents a “three highs and one low” pattern, characterized by high correlation degree, high efficiency, and high reciprocity. This indicates that nodes enjoy good connectivity, efficient information transmission, and strong mutual accessibility. However, the extremely low network hierarchy index suggests that a distinct core–periphery structure has not yet formed within the network. Among the top 10 key nodes, the distribution pattern of “agglomeration in the east, increase in the central region, and initial emergence in the west” is prominent. Notably, Chongqing plays a prominent role as an intermediary connecting the urban agglomerations in the central-eastern and western regions.

(2)

According to the group clustering analysis results, as the members of the four major blocks undergo continuous adjustments, western cities show stronger model-estimated correlations with the central-eastern regional network. Meanwhile, in the evolution of interactive relationships among the four blocks, interactions between blocks have strengthened, particularly between Block 1 and Block 2, and between Block 2 and Block 3, highlighting the growing intermediary function of Block 2. In contrast, Block 4, dominated by western cities, remains an “isolated group”. While its internal members continue to decrease, its interactive relationships with the other three blocks need to be further strengthened.

(3)

Simulation results of network properties under node failure scenarios show that the network structure demonstrates stronger resilience under random attacks than under intentional attacks, meaning the network properties have better invulnerability in the context of random attacks. Meanwhile, significant differences exist in the performance of different network indicators. Under intentional attacks, network density and connectivity collapse rapidly, showing obvious “avalanche effects”, whereas network efficiency and reciprocity degree exhibit lagged responses. Under random attacks, all four indicators decline slowly and maintain good stability.

(4)

Micro-structural evolution has been shown to present significant differences in motif distribution. The dominant position of motifs with 0 or 1 edge (M1, M2) has been shown to weaken, and the role of structural holes dominated by the combination of “open + closed” types has been continuously enhanced. M1 and M2 are the dominant motif types constituting the network’s micro-structure, and their occurrence probabilities have decreased significantly. In particular, the substantial decline of M1 is mechanically consistent with the rise in overall network density and the transformation from “ultra-low density” to “low density”. However, their cumulative proportion still maintains a dominant position, which significantly restricts the improvement of network density and the formation of a “core-periphery” hierarchical structure. Meanwhile, among the other 13 motif types, the shift from a pattern dominated by open structural holes to one dominated by “open + closed” structural holes is also an important factor driving network evolution.

6.2. Policy Implications

(1)

Optimize Core Node Distribution and Enhance Overall Network Connectivity. Network density increased from 0.0608 to 0.1577, while hierarchy was only 0.0217 in 2023, indicating a flattened network structure with strengthening inter-city correlations. Policy should therefore shift from creating a single core to strengthening redundancy and coordination among high-centrality cities. Specifically, cross-regional collaborative development platforms should be established, unified NQPF development plans and standard systems formulated, and inter-city cooperation in technological innovation and industrial upgrading enhanced. Contingency coordination mechanisms among high-centrality cities should be strengthened, and alternative inter-city links developed to reduce reliance on any single core node. Given the outward-oriented estimated correlations of several eastern and central cities, the eastern region should focus on cutting-edge innovation and industrial upgrading, while strengthening technical and talent exchanges with central and western regions. Rising central cities should consolidate their industrial foundations and innovation capabilities to build regional NQPF growth poles. For Chongqing—a western city that has achieved a breakthrough by joining the core node cluster—policy support and resource investment should be increased to support its balanced connector role, and more core nodes should be cultivated.

(2)

Implement Differentiated Policies to Optimize Inter-Block Correlation Patterns. Block analysis shows that Block 1 expanded from 53 to 91 cities while Block 4 contracted from 102 to 54 between 2010 and 2023, indicating that western cities are gradually participating in the national NQPF spatial correlation structure. According to the 2023 estimated network data, Block 1 sent 1497 external ties and received 1048, exhibiting a pronounced outward-oriented pattern. Policy should therefore prioritize supporting original innovation and key technological breakthroughs in Block 1, while encouraging technology and talent outflows to other blocks. Block 2 showed a near balance of 1852 outgoing and 1715 incoming ties, indicating a bidirectional interaction pattern. Policy should strengthen its transportation hub and logistics center development, improve industrial supporting systems, and fully leverage its structural bridging role between Block 1 and Block 3. Block 3 received 926 and sent 657 ties, with a clear net-receiving pattern indicating that it is in a phase of absorbing external correlations. Policy should formulate tailored industrial support measures and improve conditions for undertaking industrial transfers to enhance its capacity to absorb and transform inflowing resources. Block 4 maintained over 85% of its ties internally, with severe external connection deficits. Policy should establish special coordination mechanisms, increase infrastructure connectivity investment with eastern and central regions, and explore interest-sharing cooperation models to progressively break its structural isolation.

(3)

Enhance Network Structural Resilience and Prevent Systemic Risks. The study indicates that the failure of core nodes under intentional attacks may trigger “avalanche effects”, whereas a multi-center structure demonstrates stronger robustness due to redundant connections under random attacks. Therefore, it is essential to construct a dual resilience mechanism featuring “core node protection plus distributed redundancy”. First, integrate core node protection with the development of multi-center collaborative networks. While emphasizing core node development, strengthen the construction of multi-center networks to improve overall network stability and reduce the risk of cascading collapse caused by core node failure. For example, cultivate multiple competitive industrial clusters within key sectors to form a mutually supportive network structure. Second, enhance redundant connections within the network. Encourage cities to establish more cooperative ties and increase network redundancy. Strengthen the network’s buffering capacity by promoting additional cooperation projects and co-constructing shared facilities. This will enable the network to maintain effective information transmission and reciprocity in the face of random shocks, preserving its basic functions and structural stability. Third, establish risk early warning and emergency response mechanisms. Develop a risk monitoring system for the urban NQPF network to track its operational status in real time. Formulate contingency plans detailing response measures for different risk scenarios. This will improve the network’s risk resistance and recovery capabilities, mitigate damage from intentional attacks, and ensure the stable development of urban NQPF.

(4)

Promote Upgrading of Micro-Level Correlation Patterns and Facilitate Multi-City Synergistic Interactions. Motif analysis shows that M1 and M2 motifs still accounted for 90.14% of total triads in 2023, while fully connected M15 accounted for only 1.42%, indicating considerable potential for improving the intensity of spatial interactions at the micro level, and that fully bidirectional multi-city correlation patterns have not yet been established. Policy should selectively support verifiable multi-city correlation patterns rather than pursue an undifferentiated increase in tie counts. On one hand, through multiple measures such as fiscal subsidies, tax reductions, and prioritized project approvals, cross-regional collaboration initiatives encompassing industry-university partnerships, research-education linkages, and industry-university-research integration should be actively promoted to reduce isolated nodes and unidirectional links, creating conditions for bidirectional and multi-dimensional interactive relationships. On the other hand, institutional and infrastructure mechanisms for the cross-regional flow of NQPF factors should be improved, with particular emphasis on constructing spatial circulation channels between western cities and eastern-central cities. By fully leveraging opportunities presented by 5G network construction and big data center development, western cities should be provided with greater access to high-quality factor resources, facilitating the transition of micro-level correlation patterns from isolation and unidirectionality toward bidirectional and multilateral synergy.