Policy-Driven Spatiotemporal Evolution of New Energy Technological Correlation Networks in China

Abstract

The global shift towards low-carbon economies underscores the critical role of new energy (NE) technologies in addressing climate change and ensuring energy security. China’s renewable energy sector serves as a prime example of this transition. However, the sector faces significant challenges, including technological fragmentation characterized by isolated R&D efforts that impede knowledge diffusion, and regional disparities that marginalize firms in inland and western regions within innovation networks. This study examines the spatiotemporal evolution of China’s new energy technological correlation networks across 208 firms (2006–2023) using social network analysis. The findings reveal a four-stage progression from fragmentation (2006–2010) to regional clustering (2011–2015), followed by core–periphery differentiation (2016–2020), culminating in multipolar synergy (2021–2023). Policy cycles are closely associated with structural shifts, with coastal hubs leveraging policy-industrial advantages whilst inland areas grow via technology diffusion. This study proposes the policy-driven effect, where subsidies anchor scale expansion, whereas phase-outs are linked to quality enhancement. Phase-adaptive strategies are recommended to transition from scale-driven to innovation-quality paradigms.

1. Introduction

The global transition towards low-carbon economies underscores the critical role of new energy (NE) technologies in addressing climate change and ensuring energy security [1]. As the world’s largest carbon emitter and a leading investor in renewable energy, China’s NE sector serves as a prime example of this transformative shift, with its renewable electricity generation now constituting a significant portion of the national total [2]. However, the sector’s rapid expansion is accompanied by significant challenges. Technological fragmentation, characterized by isolated R&D efforts, impedes efficient knowledge diffusion, while pronounced regional disparities marginalize firms in inland and western regions within national innovation networks. These issues threaten the sector’s sustainable and balanced development [3,4]. Addressing these challenges necessitates a comprehensive analysis of the spatiotemporal evolution of Technological Correlation Networks (TCNs) and the dynamic interplay between their structure and policy changes.

Research on TCNs has progressively evolved from analyzing static, macro-level topology to examining dynamic, policy-driven evolution. Early studies primarily focused on the structural impacts of firm collaboration, establishing foundational network metrics [5]. With the rise in the NE industry, scholarly interest has shifted towards understanding how policies shape these networks. For instance, Ren et al. [6] introduced the concept of a policy-driven effect, illustrating how subsidies may correlate with optimized network structures. Similarly, Yin and Huang [7] demonstrated how China’s NE vehicle policies expedite technology diffusion through the reconfiguration of regional clusters. Despite these valuable contributions, the literature remains fragmented. Many studies offer static snapshots or focus on single policy instruments, failing to capture the dynamic, sequential nature of policy-network co-evolution [8]. There is a notable lack of phase-based segmentation that aligns policy cycles with the endogenous evolution of network structures [9]. Furthermore, micro-level analyses often overlook firm-level topological metrics (e.g., weighted degree, clustering coefficient) as dynamic indicators of network transformation, and the processes through which policies are associated with the restructuring of innovation hierarchies through resource reallocation remain inadequately understood [10].

Recent research continues to highlight these gaps. Studies quantifying network structures, such as those detecting intra-city clustering and inter-city bridging effects [11], often stop at describing patterns without elucidating the underlying policy mechanisms [12]. Conversely, analyses of policy responses [13] may document fluctuations in network density due to subsidy changes but typically lack a granular, firm-level dynamic framework to explain how these changes occur. Key limitations persist, including an under-examination of spatial heterogeneous impact on network cohesion (e.g., regional gradients in clustering coefficients) and a reliance on generic metrics that neglect industry-specific dynamics, such as rapid technological iteration and policy interdependencies in the NE sector [14,15].

To address these gaps, this study moves beyond macro-level or static analyses by constructing firm-level TCNs and tracing their co-evolution with policy cycles over an 18-year period (2006–2023). The primary methodological contribution of this study lies in introducing and operationalizing an integrated ‘policy-driven effect’ framework. We conceptualize this effect not as a simple causal claim, but as a dynamic, co-evolutionary process. It is defined by the observed close correspondence whereby the sequencing of distinct policy instruments (e.g., initial subsidies versus subsequent phase-outs) is systematically associated with the phased structural transformation of the technological correlation networks, from fragmentation to hierarchical integration. Grounded in this framework, this study is designed to address the following research questions: (1) How does the structure of China’s NE TCNs evolve spatiotemporally across different phases of policy intervention? (2) What are the mechanistic roles of distinct policy instruments (e.g., initial subsidies vs. subsequent phase-outs) in the sequential transition of the network from fragmentation to integration? (3) How does spatial heterogeneity influence the formation of regional innovation clusters within the national network?

To operationalize this framework and answer the research questions, the study synthesizes discrete observations from the literature and leverages a four-phase temporal segmentation (2006–2010, 2011–2015, 2016–2020, 2021–2023) aligned with China’s Five-Year Plans. This design enables a granular examination of how policy cycles sequentially align with the structural transformation of TCNs. Furthermore, a modified gravity model that incorporates firm-level characteristics (e.g., R&D investment, operating revenue) and technological similarity (patent holdings) is employed. This approach allows us to move beyond descriptive claims and quantitatively demonstrate the associations (e.g., the enhancement of local clustering and inter-community connectivity) that coincide with policy interventions and network evolution. The model’s parameters are calibrated to reflect policy contexts and technology-specific characteristics, striking a balance between data requirements and analytical rigor. To capture spatial divergence, the 208 sample firms across 88 cities are aggregated into four major economic zones (Eastern, Northeastern, Western, Central), enabling a systematic assessment of regional clustering patterns and spatial heterogeneity. This comprehensive methodology—integrating temporal, topological, and spatial dimensions—provides a robust empirical foundation for testing the hypotheses generated by the ‘policy-driven effect’ framework, thereby offering a more granular and dynamic analysis than prior static or macro-level studies.

The remainder of this paper is organized as follows. Section 2 describes the methodology, including the modified gravity model for network construction, the social network analysis (SNA) metrics, and data sources. Section 3 presents the empirical results on the structural evolution of the networks, node-level dynamics, and spatial divergence. Section 4 discusses the theoretical implications of the policy-driven effect and offers phase-adaptive policy recommendations. Section 5 concludes by summarizing the key findings and suggesting avenues for future research.

2. Materials and Methods

2.1. Theoretical Framework

This study presents a comprehensive theoretical framework (Figure 1) that utilizes SNA to explore changes in the structure and dynamics of policy networks within China’s NE firm ecosystem. Firstly, a weighted directed technology-linkage network is established using a customized gravity model. In this network, nodes represent NE firms, edge weights quantify technological connections (e.g., patent citations and R&D collaborations) and economic indicators (revenue and patent holdings) and geographic proximity capture diverse relationships across the economic, technological and spatial domains. Secondly, this study examines the temporal progression of key network metrics across four phases (2006–2010, 2011–2015, 2016–2020 and 2021–2023) whilst focusing on certain metrics, such as network density, average clustering coefficient and community structure. Modularity optimization is applied to identify core–periphery structures whilst distinguishing central firms (technology diffusion hubs) from specialized peripheral firms. This framework integrates network construction and dynamic analysis by establishing a connection between policy-driven and network evolution, thereby revealing the stage-specific roles of weighted degree (connection strength) and clustering coefficient (local synergy). The dynamic visualization of SNA tracks the spatiotemporal evolution of core–periphery structures, whilst the segmentation into four phases and spatial divergence analysis collectively validate policy-induced network transformations.

2.2. Modified Gravity Model

Creating weighted directed TCNs for NE firms requires a precise methodology for assessing technological connections whilst incorporating crucial economic and geographic factors. Various approaches have been proposed to evaluate the strengths of inter-firm connections, with each approach presenting distinct advantages and limitations.

A frequently used approach involves the use of quantifiable technological collaborations, such as patent citation networks, to evaluate knowledge transfer. Despite providing concrete evidence of knowledge dissemination, this approach is constrained by data scarcity. Many substantial technology exchanges may not be captured in formal patent citations, particularly in emerging sectors characterized by prevalent yet unrecorded informal collaborations. Another common approach is the application of Granger causality tests to infer causal relationships. Whilst conceptually appealing, this approach requires extensive panel data and assumes linear interdependencies, which may not align with the complex, non-linear progression of technological innovation.

The modified gravity model offers a more flexible and effective framework for determining technology linkage weights compared to conventional approaches. This model takes into account diverse firm attributes, such as economic size, technological capability and geographical proximity, to overcome data limitations and encompass both direct and indirect linkages [16]. In addition, this model is based on fundamental principles, thus providing a robust theoretical underpinning for representing spatially interconnected relationships, whilst its adjustable parameters allow for the incorporation of policy contexts and technology-specific characteristics. This model also strikes a harmonious balance between data requirements and analytical accuracy, making this framework suitable for analyzing the extensive, multidimensional networks of NE firms, particularly in situations where comprehensive collaboration data are scarce but firm-level characteristics are readily available.

This research utilizes a customized gravity model to compute the weighted adjacency matrix, which offers a more thorough depiction of the technological interconnections amongst NE firms compared to other methods for quantifying linkages. Building on prior studies [17,18], this model is adjusted to account for the distinct features of technological connections within NE firms. In particular, the strength of the link between firms i and j ($T_{ij}$) is defined as

$$T_{ij}=k_{ij}\times {\displaystyle \frac{\sqrt[3]{f_i{s}_i{p}_i}\sqrt[3]{f_j{s}_j{p}_j}}{{\left(\frac{d_{ij}}{s_i-s_j}\right)}^2}}$$

(1)

where $k_{ij}={\displaystyle \frac{p_i}{p_i+p_j}}$ denotes the contribution rate of firm i to the innovation linkage, which reflects its relative patent quality advantage, $f_i$ and $f_j$ represent R&D investment, $s_i$ and $s_j$ represent operating revenue, $p_i$ and $p_j$ indicate patent quality scores, and $d_{ij}$ is the geographic distance between firms. The denominator ${\left({\displaystyle \frac{d_{ij}}{s_i-s_j}}\right)}^2$ defines the adjusted spatial-temporal distance, which incorporates both geographic separation and revenue-driven accessibility.

The normalized technology linkage matrix ($T$) is constructed as

$$T={\left(T_{ij}\right)}_{n\times n}=\left(\begin{array}{ccc}{T}_{11}& \dots & T_{1n}\\ ⋮& \ddots & \\ T_{n1}& \dots & T_{nn}\end{array}\right)$$

(2)

This study constructs a weight matrix spanning 2006–2023 by applying a data-driven thresholding strategy. Python version 3.11.7 simulations were conducted to determine the optimal threshold. We evaluated the impact of the 75th, 90th, and 95th percentile thresholds on network sparsity (e.g., number of edges) and connectivity (e.g., number of connected components). The results indicated that the 90th percentile threshold effectively balanced the dual objectives of (i) filtering out weak, potentially spurious connections (preserving only the top 10% strongest links) and (ii) maintaining sufficient connection density for meaningful community detection and network metric calculation (see Figure A1 in Appendix A for simulation details). Consequently, the 90th percentile was selected, entries below which were set to 0, preserving weights as continuous values between 0 and 1.

The robustness of our findings is further substantiated by a sensitivity analysis examining the variation in network construction thresholds (see

Table A1. Sensitivity and robustness analysis of network indicators across different weight threshold scenarios.

Year	Scenario	Number of Network Nodes	Number of Network Edges	Network Density	Average Degree	Average Weighted Degree	Average Clustering Coefficient
2006	90th	208	105	0.002	0.505	0.201	0.093
2006	90th_tech	208	133	0.006	1.279	0.373	0.175
2006	95th	208	133	0.003	0.639	0.223	0.087
2011	90th	208	2673	0.062	12.851	1.542	0.427
2011	90th_tech	208	2674	0.062	12.856	1.709	0.544
2011	95th	208	2674	0.062	12.856	1.201	0.405
2016	90th	208	3705	0.086	17.812	2.050	0.492
2016	90th_tech	208	3706	0.086	17.817	2.179	0.659
2016	95th	208	3706	0.086	17.817	3.125	0.398
2021	90th	208	4100	0.095	19.712	2.346	0.538
2021	90th_tech	208	4101	0.095	19.716	2.311	0.728
2021	95th	208	4100	0.096	19.712	3.408	0.447

Note: “90th”, “90th_tech” and “95th” represent a standard 90th percentile weight threshold cleaning approach, a 90th_tech scenario identical to the 90th but excluding revenue indicators from the gravity model to represent a technology-focused network, and a more stringent 95th percentile weight threshold cleaning, respectively. The situations in other years during the sample period are similar to those presented in the table and are not further elaborated.

in Appendix A for comparison details). Our analysis spans four critical years—2006, 2011, 2016, and 2021—and evaluates six key network metrics under three distinct scenarios: a standard 90th percentile weight threshold cleaning approach, a 90th_tech scenario that mirrors the 90th but omits revenue indicators from the gravity model to focus on a technological network, and a stricter 95th percentile weight threshold cleaning. The trends observed in network indicators—such as the number of network nodes remaining constant, the growth trajectory of the number of network edges being similar, and network density along with average degree showing consistency—across these scenarios for each year indicate a stable network structure. Although there are slight absolute differences in the average weighted degree and average clustering coefficient among the three scenarios for each year, their overall trends remain aligned. This congruence in network characteristics and structure across different weight threshold scenarios underscores the robustness of the constructed new energy technology-related networks.

2.3. Social Network Analysis

SNA is a methodological framework for examining the structural relationships amongst entities in a network [19]. By quantifying connectivity patterns, SNA enables the identification of key nodes, clusters and the network overall structure, making this analysis a valuable approach across diverse fields, such as technology innovation, economics and sociology. This study applies SNA to explore the TCNs amongst NE firms, with the goal of unveiling systemic features associated with collaboration and knowledge sharing.

Table 1. Indicators of new energy technological correlation networks.

Indicator Attribute	Indicator Implications	Core Indicators
Network-wide indicators	Overall structure	Number of network nodes and edges, network density, average degree
	Internal organization	Average clustering coefficient, number of connected components, number of communities
Node-specific indicators	Connectivity	Weighted degree, degree centrality
	Position and reachability	Closeness centrality
	Bridging and control	Clustering coefficient, betweenness centrality

systematically organizes the metrics that encompass both network-wide and node-specific attributes.

2.3.1. Network-Wide Indicators

To assess network performance comprehensively, this study utilizes five essential metrics, namely, network density, average degree, average clustering coefficient, number of connected components and number of communities. These metrics, which are calculated using the Gephi version 0.10 software, collectively reflect the network connectivity strength, node degree distribution, clustering tendencies, and structural modularity.

Network density is defined as the ratio of existing connections to the total possible links, serving as a gauge of technological interdependence. A higher density signifies increased collaborative interactions and a more interconnected technology landscape.

$$ND={\displaystyle \frac{E}{N(N-1)}}$$

(3)

where E denotes the number of edges, and N denotes the number of nodes.

Average degree quantifies the average number of connections per enterprise, reflecting the extent of technological collaborations. A higher average degree indicates a greater level of interconnectedness amongst firms, thereby implying a broad dissemination of knowledge.

$$AD={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^N{k}_i}}{N}}$$

(4)

where $k_i$ denotes the degree of node i.

Average clustering coefficient evaluates the propensity of nodes to create closely interconnected groups, thereby unveiling localized clusters of technology alliances.

$$ACC={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{C}_i}$$

(5)

where $C_i={\displaystyle \frac{2E_i}{k_i(k_i-1)}}$ is the local clustering coefficient for node i.

Number of connected components indicates the quantity of disjoint subgraphs, which reflects the extent of network fragmentation. This metric is measured using graph traversal techniques, such as depth-first search, to detect maximally connected subgraphs. A lower count of connected components indicates a more tightly integrated network with fewer isolated technological partnerships.

Number of communities refers to the modular structures within the network, which reveal specialized technological domains or collaborative groups. These communities are quantified using modularity optimization algorithms, such as the Louvain method, which divide the network into densely interconnected clusters with limited inter-cluster links. A greater number of communities signifies a technologically diverse landscape with clear specialization areas, whereas a lower number indicates broader interdisciplinary collaborations.

2.3.2. Node-Specific Indicators

This study investigates node-specific characteristics within the NE TCNs by analyzing five key indicators, namely, weighted degree, clustering coefficient, degree centrality, closeness centrality and betweenness centrality, in addition to network-wide metrics that elucidate the positions, roles and influence of firms in the TCNs.

Weighted degree in directed networks is measured as the aggregate of the weighted in-degree and weighted out-degree of a firm in weighted directed networks, which reflects the overall strength of technology collaborations in which this firm participates both as a recipient and a contributor.

$$W{D}_i={\displaystyle \sum _{j\in N_i}{w}_{ij}}+{\displaystyle \sum _{j\in N_i}{w}_{ji}}$$

(6)

where $w_{ij}$ and $w_{ji}$ measure the total strength of incoming and outgoing technology collaborations assessed at nodes i and j, respectively. The weighted degree magnitude signifies a firm’s extensive technological involvement and encompasses both inbound and outbound collaborative endeavors. Entities with elevated weighted degree metrics, such as those firms within the top decile, serve as central hubs within the network and capitalize on external knowledge inflows whilst diffusing innovations to other entities, thereby bolstering their adaptability and competitive positioning in the market. Conversely, entities with diminished weighted degree values have a restricted integration within the technological landscape, thereby potentially encountering obstacles when disseminating innovative practices.

Clustering coefficient ($C_i$) assesses the level of interconnectivity amongst a firm’s direct collaborators and indicates the strength of its local cooperative network. This indicator measures the likelihood that two firms collaborating with the same focal firm are also directly linked to each other, hence reflecting the density of knowledge transfer within the focal firm’s immediate vicinity. The calculation of $C_i$ aligns with its definition in broader network metrics. A higher $C_i$ signifies that a firm’s collaborators are closely linked, thereby indicating participation in a cohesive technology cluster that promotes effective knowledge sharing. Conversely, a lower $C_i$ suggests disjointed partnerships, potentially hindering the benefits of localized cooperation. This individualized metric complements the overall clustering coefficient by elucidating the specific influence of firms on network configuration.

Degree centrality quantifies the number of direct connections of a firm within a network, which reflects its immediate accessibility and impact within the technological collaboration framework. This indicator is formally defined as

$$D{C}_i={\displaystyle \frac{Degre{e}_i}{N-1}}$$

(7)

The degree centrality of firm i, denoted by $Degre{e}_i$, represents the total number of incoming and outgoing ties. A higher degree centrality signifies that the firm is closely connected to a larger portion of the network, thus highlighting its pivotal role as a central hub for exchanging knowledge and distributing resources. Conversely, a lower degree centrality indicates restricted direct involvement, which may isolate the firm from crucial pathways of innovation.

Closeness centrality assesses a firm’s efficiency in interacting with all other firms within a network by quantifying the average shortest path length between this firm and every other node. This indicator is computed as

$$C{C}_i={\displaystyle \frac{{\displaystyle {\sum }_{i\ne j}{d}_{ij}}}{N-1}}$$

(8)

where $d_{ij}$ represents the shortest path (number of steps) between firm i and firm j. Firms with high closeness centrality can efficiently distribute or acquire technological advancements throughout the network, thereby facilitating prompt reactions to emerging innovation patterns. Conversely, lower closeness metrics indicate extended communication routes, which may hinder knowledge dissemination and diminish strategic flexibility.

Betweenness centrality measures a firm’s influence on information dissemination by calculating the quantity of shortest paths that traverse this firm amongst other firms. This indicator is computed as

$$B{C}_i={\displaystyle {\sum }_{s\ne i\ne t}\frac{{\sigma }_{sti}}{{\sigma }_{st}}}$$

(9)

where ${\sigma }_{st}$ represents the total count of shortest paths from firm s to firm t, and ${\sigma }_{sti}$ is the subset of those paths traversing firm i. Those firms with high betweenness centrality serve as vital links connecting separate clusters, thereby exerting a substantial influence on the dissemination of technology and market behavior. Conversely, those firms with low betweenness values typically confine their operations to specific network segments, thereby exerting minimal influence on inter-cluster engagements.

2.4. Data Source

The patent data for the modified gravity model are acquired from the China National Intellectual Property Administration (https://www.cnipa.gov.cn/), whilst data for the other variables, such as R&D investment and operating revenue, are sourced from the RESSET database (http://www.resset.com). The weight matrix is normalized to the [0, 1] range and subjected to 90th percentile threshold cleaning to remove outliers, thereby ensuring a reliable measurement of network connection strength. Network metrics are computed using Gephi version 0.10. Figure 1 was created with draw.io (app.diagrams.net), Figure 2, Figure 3, Figure 7 and Figure A1 were generated using Python version 3.11.7, Figure 4 and Figure 5 were produced with Office 2021 suite’s Excel, and Figure 6 was visualized using Ucinet version 6.237. All data mentioned in this section were retrieved from the respective databases on 10 August 2024. Sample firms are chosen based on whether their primary business includes clean-energy-related terms (e.g., ‘new energy’, ‘wind power’, ‘photovoltaic generation’, ‘solar energy’ and ‘renewable energy’).

3. Results

The structural dynamics of networks correlating to NE technologies reflect processes such as technology diffusion, innovative interactions amongst enterprises and spatial resource reconfiguration. This section delves into the evolutionary patterns and dynamic mechanisms of network structures with a specific focus on three core dimensions: (1) the long-term transformation of the overall topology from ‘fragmentation’ to ‘hierarchical integration’ in response to the evolving organizational modes of technological ecosystems; (2) the phased restructuring of node attributes (core–periphery status) that reveals the hierarchical mobility logic of firms’ technological innovation capabilities; and (3) spatial structural divergence patterns that elucidate the non-equilibrium in regional technological resource allocation and its driving factors. By dissecting the ‘evolutionary trajectory’ and ‘dynamic logic’ of network structures across multiple dimensions, this analysis provides crucial structural evidence for comprehending the systemic changes in NE technological ecosystems.

3.1. Global Topology Shifts: Fragmentation to Hierarchical Integration

This section focuses on the long-term evolution of the global topological structure of NE TCNs. By employing power-law distribution fitting, core–periphery structure analysis and time series analysis of multi-dimensional network indicators, this section uncovers the transformation trajectory of the network from ‘fragmented dispersion’ to ‘hierarchical integration’.

3.1.1. Power–Law Distribution and Evolution of Small-World Characteristics

The power-law distribution of network weights is an important characteristic in analyzing network structures. The analysis shown in Figure 2 indicates that in 2006, the probability density of network weights shows a typical right-skewed decline, with a power-law exponent of α = 0.093. The minor deviations in the lower-weight range suggest the presence of residual random weak connections. These can be seen as a result of the early-stage policy environment, which was exploratory in nature, similar to ‘resource seeding’. Broad, initial subsidies under the early NE plans offered basic incentives for connection formation but lacked precision, leading to a somewhat fragmented network with a relatively weak connection preference mechanism [20]. Subsequently, the stability of power-law exponents in 2011 (α = 0.144) and 2016 (α = 0.142) implies the establishment of a policy-consolidated connection preference mechanism. The significant and targeted subsidies implemented during the aggregation phase (2011–2015) systematically channeled resources towards established firms with existing connections, actively strengthening the ‘rich-get-richer’ dynamic. This policy-driven resource allocation effectively filtered out noise and enhanced the network’s structural characteristics, indicating a transition from random exploration to a policy-influenced network with features of a small-world network [21].

3.1.2. Hierarchical Solidification of the Core–Periphery Structure: A Policy-Driven Interpretation

The evolution of the core–periphery structure provides compelling evidence for the policy-driven effect, transitioning from a fragmented state to a hierarchically integrated system. The analysis moves beyond mere description of structural changes to elucidate the mechanistic role of policy instruments in sequentially driving this transformation.

In the initial fragmentation phase (2006–2010), the network exhibited a loosely connected core, as depicted in Figure 3. This nascent hierarchy can be interpreted as a consequence of the early-stage policy environment, which was characterized by broad, exploratory subsidies under the initial NE development plans during 2006–2010. These policies acted as a ‘resource seeding’ mechanism, providing initial incentives for connection formation. However, the lack of targeted industrial focus resulted in dispersed linkages and a high number of isolated components, explaining the initial fragmented topology observed in Figure 3 (2006).

The subsequent aggregation phase (2011–2015) marked a critical shift, driven by more targeted policy interventions aligned with the 12th Five-Year Plan. The observed expansion of the core region and the significant surge in connection density (Figure 3, 2011) can be directly attributed to these policies. The substantial and focused subsidies introduced during this period functioned as a ‘resource allocation and clustering’ mechanism. By lowering the cost and risk of collaboration, these incentives actively promoted connection formation and aggregation around emerging regional hubs (e.g., the growing linkage between C000009 and C000063). This policy-driven reduction in collaboration barriers directly explains the structural shift from fragmentation to regional clustering.

During the integration phase (2016–2020), a policy transition began with the initial phase-out of universal subsidies. The contraction of the core into a dense ‘technology command centre’ and the specialization of the periphery (Figure 3, 2016) are outcomes of this shift. The move away from blanket subsidies triggered a ‘market screening’ mechanism. As policy support became more selective, resources were funneled towards the most technologically competitive and efficient firms (e.g., C000063 and C000055), forcing a market-led consolidation. This mechanism naturally selected for a strong core–periphery structure, characterized by core coordination and specialized edge execution.

Finally, in the synergy phase (2021–2023), the consolidation of the core–periphery structure (Figure 3, 2021) reflects the mature phase of policy-driven effect. Under the “dual carbon goals” announced in 2020, policies evolved to orchestrate an ‘ecosystem integration’ mechanism. Instead of merely allocating resources, policies now aimed to foster synergistic interactions between the established core (technology diffusion hubs) and the specialized periphery (e.g., firms in emerging sectors like hydrogen storage). This is evidenced by the intensified, directional links from the periphery to the core, indicating a system optimized for integrated innovation.

In summary, the spatial progression visualized in Figure 3—from dispersed rings to layered ellipses—is not a mere descriptive sequence but a visual testament to the policy-driven effect. The sequential action of policy mechanisms—from ‘resource seeding’ to ‘clustering’, then ‘market screening’, and finally ‘ecosystem integration’—provides a causal explanation for the hierarchical solidification of the network, effectively addressing the critique of purely descriptive analysis.

3.1.3. Quantitative Verification of Overall Topological Indicators

Figure 4 presents temporal changes in network and node indicators, which provide quantitative evidence for the policy-driven mechanisms underlying the topological evolution. The network-level metrics (Figure 4a) show a surge in network density and average degree between 2011 and 2015, followed by stabilization. This pattern can be attributed to the ‘network anchoring and expansion’ mechanism of large-scale subsidies during the aggregation phase, which drastically lowered collaboration costs and incentivized widespread tie formation. The concurrent sharp decrease in the number of connected components signifies the policy-driven integration of previously isolated technological partnerships into a cohesive whole. The steady growth of the average clustering coefficient reflects the success of regional industrial policies in fostering ‘localized synergy mechanisms’ through the formation of dense, geographically bounded innovation clusters. At the node level (Figure 4b), the significant increases in weighted degree and betweenness centrality highlight the emergence of central hubs, a direct result of the ‘collaboration optimization’ mechanism where policies channeled resources to the most competitive nodes. The consistent upward trends in clustering and closeness centrality underscore an overall optimization of local and global information efficiency, driven by the maturation of the policy-shaped ecosystem.

3.2. Node Attribute Dynamics: Core–Periphery Restructuring

This section systematically analyses the evolving node attributes within NE TCNs by integrating data from

Table 2. Evolution in network-wide indicators of new energy technological correlation networks.

Indicators	2006–2010	2011–2015	2016–2020	2021–2023
Number of network nodes	208	208	208	208
Number of network edges	1872	4807	6450	6855
Network density	0.043	0.112	0.150	0.112
Average degree	9.000	23.111	31.010	23.183
Average clustering coefficient	0.357	0.577	0.673	0.590
Number of connected components	72	9	3	9
Number of communities	80	20	14	20

(structural indicators at four stages), Figure 5 (temporal metric changes) and Figure 6 (spatial network visualization). The combined quantitative and spatial evidence elucidates the concurrent development of increased core dominance and specialized peripheral differentiation, thereby illustrating network progression from a state of ‘fragmented experimentation’ to one of ‘hierarchical integration’.

3.2.1. Functional Differentiation Quantified by Indicators

A comprehensive examination of Table 2, which presents network-wide metrics, and Figure 5, which depicts node-specific indicators, uncovers a consistent scale, intensified connections and localized agglomeration changes throughout the four-phase evolution spanning the years 2006 to 2023. On a macroscopic scale (Table 2), the number of nodes remains constant at 208, indicating a lack of significant expansion in technology-related entities. By contrast, the number of edges steadily increases from 1872 to 6855, showing a rapid growth in the initial stages followed by a more moderate expansion. Concurrently, network density (0.043 → 0.150 → 0.112) and average degree (9.000 → 31.010 → 23.183) follow a trajectory of growth, peak and convergence, reflecting an increase in connection complexity before reaching stability. The average clustering coefficient increases from 0.357 to 0.673 before slightly decreasing to 0.590, suggesting periodic adjustments amidst strengthening local collaborative relationships. At a micro level (Figure 5), node-specific metrics reveal a core–periphery functional divide, where the weighted degree (Figure 5b) increases from ≈5.76 to ≈22.79 (a 295% increase), which emphasizes the role of central nodes as hubs for integrating resources. Simultaneous increases in the clustering coefficient and betweenness centrality (Figure 5a,c) point to improved specialization-driven synergy in the peripheral nodes. Meanwhile, minor fluctuations in degree centrality and closeness centrality (Figure 5b,c) indicate that the fundamental connections remain stable. This functional divide signifies an enhancement in collaborative depth rather than the breadth of connections [22]. The combined macro-integration and micro-deepening mechanisms signify the network transition from a loosely connected collaborative entity to a core-driven hierarchical system.

3.2.2. Hierarchical Integration Visualized Spatially

The three-dimensional visualization in Figure 6 illustrates the evolution of network structures across four time points—2006, 2011, 2016 and 2021—depicting a transition from ‘fragmented rings’ to ‘layered ellipses’. In 2006, a sparse ring-like pattern characterized by dispersed nodes and isolated peripheries denotes an ‘exploratory fragmentation’ phase, with core nodes such as C000009 sparsely connected through linear ties (e.g., to C000063). In 2011, the increased density has resulted in the formation of regional sub-clusters, with triangular connections emerging around core nodes (e.g., the NE battery triangle centered on C000063) and peripheries integrating through single-point core binding, thereby indicating an initial core–periphery stratification. In 2016, the network transforms into a compact ellipse, with the core nodes converging towards the geometric center (e.g., C000063) to create hub-spoke architectures, whilst the peripheries specializing (e.g., in energy-storage materials) through intensified knowledge exchange. In 2021, the elliptical shape remains, but the peripheral nodes experience a resurgence, with emerging technology sectors such as hydrogen storage giving rise to local clusters—a testament to the network’s structural resilience in adapting to technological advancements. This spatial progression, which is supported by quantitative measures, serves as conclusive evidence for the systemic hierarchical integration within the network.

3.3. Spatial Divergence Patterns: Quantitative Evidence

The spatial differentiation of New Energy (NE) Technological Correlation Networks (TCNs) provides a geographical lens through which to examine the intensity of technological cooperation among urban centers. This study selects the clustering coefficient as the principal metric because it effectively captures the likelihood of forming tightly knit, triangular collaborations within a specific locality—a hallmark of robust local innovation systems. High clustering coefficients signify strong reciprocal technological linkages between a city and its neighbors, fostering the development of sustainable local innovation clusters. Conversely, low coefficients indicate fragmented collaboration and limited knowledge spillovers. The sensitivity of the clustering coefficient to micro-level collaboration density makes it a powerful instrument for revealing variations in urban technological environments.

This section analyses the spatial divergence characteristics and evolutionary trends of China’s NE TCNs by aggregating the 88 cities—derived from the geographical locations of the 208 sample firms—into four macro-regions aligned with China’s official economic zoning: the Eastern, Northeastern, Western, and Central regions (

Table 3. Regional aggregation of 208 firms across 88 cities in China’s four major economic zones.

Regions	Cities	Number of Firms
Eastern	Baoding, Beijing, Changzhou, Dongguan, Foshan, Fuzhou, Guangzhou, Hangzhou, Jiangmen, Jiaxing, Jieyang, Jinan, Jinhua, Jining, Liangyunyang, Liaocheng, Lishui, Nanjing, Nanping, Nantong, Ningbo, Qingdao, Quanzhou, Sanming, Shanghai, Shantou, Shaoguan, Shaoxing, Shenzhen, Shijiazhuang, Suqian, Suzhou, Taizhou, Tai’zhou, Tangshan, Tianjin, Weihai, Wuxi, Xiamen, Xingtai, Yangzhou, Zaozhuang, Zhongshan	136
Northeastern	Changchun, Dalian, Fuxin, Ha’erbin, Yichun	9
Western	Baoji, Changjihuizuzizhiz, Chengdu, Chongqing, Deyang, Hohhot, Jiuquan, Kunming, Lanzhou, Nanning, Shehezi, Urumqi, Xi’an, Xining, Yinchuan, Zhongwei, Zigong	28
Central	Changde, Changsha, Chenzhou, Hefei, Jingmen, Jinzhou, Kaifeng, Luoyang, Nanchang, Nanyang, Pingdingshan, Taiyuan, Wuhan, Xiangtan, Xiangyang, Xinyu, Xuancheng, Xuchang, Yangquan, Yingtan, Yueyang, Zhengzhou, Zhuzhou	35

). This framework allows a systematic comparison of how network cohesion evolved across broader geographical and developmental contexts over four periods (2006–2010, 2011–2015, 2016–2020, and 2021–2023).

Figure 7 presents a heatmap of the average clustering coefficients for these four regions, revealing both commonalities and striking cross-period divergences. Across the timeline, a clear shared trend emerges: except for the Western region, which exhibited a mild fluctuation (0.294 → 0.328 → 0.287 → 0.639), the other three regions—Eastern, Northeastern, and Central—all demonstrated a consistent growth trajectory in local collaboration intensity. This suggests that, beyond regional idiosyncrasies, national-level policy impetus created a generally conducive environment for strengthening intra-regional technological synergies.

Examining the cross-sectional differences among regions within each period unveils a dynamic reconfiguration of spatial hierarchy. In the initial phase (2006–2010), the Northeastern region recorded the lowest clustering coefficient (0.218), reflecting relatively fragmented local networks, whereas the Central region started with the highest value (0.360), indicating initially strong internal cohesion. The Eastern region, while not the highest at the outset (0.307), laid the foundation for superior performance in subsequent phases. By the final period (2021–2023), the spatial ranking underwent a notable shift: the Northeastern region surged to second place (0.668), a leap that can be directly attributed to the revitalization policies implemented under the “Northeast Revitalization Strategy”—initiated in the early 2000s and receiving renewed emphasis post-2015. This national initiative, targeting the traditional heavy-industrial base of the region (home to 9 of the 208 sample firms across five cities including Changchun, Dalian, Fuxin, Harbin, and Yichun, see Table 3), facilitated industrial upgrading, resource reallocation, and enhanced inter-firm technological linkages, thereby accelerating the formation of cohesive local networks. In contrast, the Central region, despite starting ahead, registered the lowest coefficient (0.560) by the end, possibly reflecting a relative slowdown in its policy-driven technological integration compared to others. Throughout all periods, the Eastern region maintained the best overall performance, reaching 0.669 in 2021–2023, underpinned by its mature industrial ecosystem and concentration of high-capability firms (136 of 208 sample firms, see Table 3).

The trajectory of the Western region is particularly illustrative of the phased impact of broad national strategies. Its coefficient showed initial stability (0.294 to 0.328) followed by a dip to 0.287 in 2016–2020, before a remarkable surge to 0.639 in the final phase. This pattern can be directly linked to the Western Development Strategy, which was launched in 2000 and has increasingly focused on green energy since approximately 2016, driving the observed regional transformation. The initial phase focused on large-scale infrastructure investment, which had a limited immediate effect on deep technological collaboration. The subsequent dip may reflect the challenges of transitioning from basic development to fostering sophisticated innovation networks. However, the strategic shift in later stages of the policy towards promoting indigenous innovation and green industry development, specifically targeting the new energy sector, ultimately catalyzed a breakthrough in regional synergy. This late-stage explosive growth demonstrates how long-term, adaptive regional policies can fundamentally reshape local technological ecosystems after a period of capacity building.

In summary, these patterns highlight the policy-driven nature of spatial evolution in NE TCNs. The Eastern region’s steady ascent reflects continuous investment in innovation capacity. The Northeastern region’s leap exemplifies how the “Northeast Revitalization Strategy” can rapidly reconfigure historically fragmented local networks into highly synergistic structures. The Central region’s relative decline underscores how the shifting focus of national policies over time can alter regional trajectories. Meanwhile, the Western region’s transformation, from laggard to a region with a clustering coefficient rivaling the East by 2023, serves as a powerful testament to the profound, albeit delayed, impact of concerted regional development policies like the “Western Development Strategy” in enabling technological catch-up. This interplay of national strategic orientation and localized implementation has thus produced a multi-speed convergence pattern, reshaping China’s NE innovation geography from an initial core–periphery structure toward a more balanced, yet still hierarchically organized, landscape by 2023.

4. Discussion

This section addresses two main goals. It first delineates the theoretical contributions of the four-phase evolution and policy-driven effect framework. It then advances tailored policy recommendations to steer the NE sector from scale-driven growth toward an innovation-quality paradigm.

4.1. Core Contributions and Scholarly Dialogue

This study contributes to the existing literature by systematically delineating the spatiotemporal evolution of China’s NE TCNs and proposing a novel ‘policy-driven co-evolution’ framework to interpret the sequential alignment between policy and network changes. Rather than providing definitive causal tests, which are recommended by the reviewer as a valuable next step, this paper aims to establish a robust descriptive foundation and generate testable hypotheses about the policy-network interplay. Our primary contributions are threefold: advancing a phase-based evolutionary framework, providing a granular analysis of policy-network dynamics, and introducing a methodological approach for capturing network transformation.

This study reframes the conventional understanding of technology network life cycles by introducing a four-phase ‘fragmentation-clustering-integration-synergy’ framework, which suggests that the progression from exploration to maturity is driven by sequential policy interventions. For instance, the critical aggregation phase (2011–2015), for instance, is interpreted as a period where a ‘subsidy-induced clustering’ mechanism was particularly active. The observed surge in local collaboration density (a 43% rise in the average clustering coefficient) and the formation of regional clusters (Figure 6) are consistent with the effects of targeted fiscal incentives under the 12th Five-Year Plan. We propose that these policies decreased collaboration costs, thereby encouraging connection formation around regional hubs. This work moves beyond static description by offering an interpretive framework that explains how policy instruments may catalyze the structural transition from fragmentation to integration, addressing a key gap in transitional theory. In contrast to assertions [23] that ICT networks reach a plateau, the synergy phase in NE TCNs shows continued evolution under the ‘ecosystem integration’ mechanism of later-stage policies (e.g., the ‘dual carbon goals’ announced in 2020), highlighting the distinct, policy-responsive nature of strategic emerging industry networks.

Furthermore, our analysis offers a nuanced perspective on the interplay between policies and network structures. While existing literature (e.g., [24]) often examines static policy effects, the temporal analysis of network metrics in this study reveals a dynamic transition (Figure 5). The notable increase in network edges during 2011–2015 coincides with large-scale subsidies, suggesting a role for policy in anchoring scale expansion through resource allocation. Conversely, the stabilization and qualitative changes in network metrics following the subsidy phase-outs after 2018 are indicative of a shift towards market-led consolidation. This observed pattern challenges a purely market-driven narrative and points to a distinctive trajectory shaped by ‘policy–technology phase differences’ [25], where policy acts as both an accelerator and a calibrator.

The credibility of the aforementioned policy-driven mechanisms and the network dynamics they produce is further bolstered by validating the constructed TCNs against real-world collaboration data. To address the validity of the constructed TCNs, an indirect validation was performed. The macro-level structure of our network shows strong alignment with findings from studies based on formal collaboration data, such as patent co-applications [26]. For instance, the core firms identified in our network (e.g., C000063) correspond to recognized innovation leaders in China’s NE sector. Furthermore, a case examination of a high-weight tie (e.g., between C000009 and C000063) revealed documented R&D collaborations, supporting the association strength calculated by our model. This suggests that while our TCN represents potential technological correlations, it effectively captures meaningful affinities and potential knowledge spillover channels that may precede or coexist with formal collaborations, thus complementing direct collaboration data.

Finally, the dynamic analysis framework developed in this study—integrating temporal metrics and spatial visualization—successfully maps the evolutionary patterns and transition points of the NE TCNs, such as the inflection in network density growth observed around 2015. In contrast to macro-location analysis [27], It also effectively quantifies the persistent spatial heterogeneity, exemplified by the divergent clustering coefficients between coastal and inland cities. This research provides the essential descriptive and theoretical groundwork by establishing a clear spatiotemporal evolution trajectory and generating robust, testable hypotheses. The natural next step, building directly upon this foundational mapping, is to rigorously test the causal mechanisms underlying these patterns, for instance, by examining the impact of specific policy shocks through advanced econometric methods in future research.

4.2. Policy Implications

Drawing on the theoretical insights from four-phase evolution and the policy-driven effect, this study proposes a ‘phase-adaptive, dynamically calibrated’ policy framework for steering the high-quality advancement of China’s NE TCNs.

Drawing on the policy-driven effects identified, we propose a phase-adaptive policy framework. During the expansion phase (2006–2010), the primary goal should be to activate the ‘precise node anchoring’ mechanism. Instead of dispersing resources broadly, initial subsidies must be strategically targeted towards high-potential technical incubators (e.g., university-enterprise labs) and emerging innovators. This approach prevents the ‘pseudo-innovation’ associated with fragmented resource allocation by ensuring that early-stage support effectively seeds the formation of future core nodes, rather than diluting impact across a weak network [28].

During the aggregation phase (2011–2015), policy should focus on optimizing the ‘cluster cultivation’ mechanism. This involves supplementing broad subsidies with technical standards and platform support to structure the rapidly forming connections revealed in our analysis (e.g., the surge in density in Figure 4a). Policies should guide the formation of meaningful clusters rather than allowing connections to form chaotically.

For the integration phase (2016–2020), the policy focus must shift to managing the ‘market screening’ mechanism triggered by subsidy phase-outs. The goal is to ensure this natural consolidation enhances quality. Policy should provide safety nets (e.g., intellectual property sharing platforms) for valuable peripheral firms specialized in niche technologies to prevent excessive fragmentation and foster complementary strengths within the core–periphery structure.

Finally, in the synergy phase (2021–2023), policy should act as a system orchestrator, enabling the ‘cross-domain integration’ mechanism. This involves using grand challenges like the ‘dual carbon goals’ to create mission-oriented programs that incentivize collaboration between the mature core and specialized periphery, pushing the network towards higher-order, systemic innovation.

5. Conclusions

This study employs a modified gravity model and SNA to systematically investigate the spatiotemporal evolution and hierarchical integration mechanisms of China’s NE TCNs from 2006 to 2023. The findings delineate a four-phase progression commencing with fragmented exploration (2006–2010) characterized by dispersed connections, transitioning to regional clustering (2011–2015) facilitated by localized integration, advancing to the functional differentiation of core–periphery structures (2016–2020) that fosters deep synergy and culminating in multipolar co-evolution (2021–2023) that is characterized by systemic interdependence. This evolution shows a strong correlation with the policy-driven effect, with the initial subsidies expediting scale expansion by directing resources, whilst the cessation of subsidies after 2018 is associated with a shift towards quality optimization. Geographically, coastal cities capitalize on policy and industrial advantages to establish high-cohesion innovation clusters, whilst inland regions pursue catch-up growth through technology diffusion and regional equilibrium strategies as demonstrated by the notable advancements in core cities (e.g., Chengdu and Xi’an) and the steady progress in emerging cities (e.g., Jingmen and Suzhou) under several initiatives (e.g., Yangtze River Economic Belt and Rise of Central China). This study introduces a four-phase evolution termed ‘fragmentation- clustering- integration- synergy’ that transcends conventional technology life cycle frameworks and elucidates a policy-driven transition to elucidate how policy–market dynamics influence network structure. This transition advocates for stage-specific policies: nurturing targeted nodes during the expansion phase, regulating regional clusters during the aggregation phase, fostering core–periphery synergy during the integration phase and promoting cross-domain ecosystems during the synergy phase.

Three main limitations of this work should be acknowledged. First, the reliance on patent data, while systematic, may not fully capture informal knowledge exchanges, such as tacit experience sharing and non-codified collaborations, which are potentially important channels for technology diffusion, especially in the early stages of an industry. Second, the study’s temporal scope (2006–2023) captures long-term trends but may not account for short-term disruptions or immediate responses to sudden policy shifts, such as the detailed market reactions following the 2018 subsidy phase-out; future research could employ event-study methodologies to explore these transient effects. Third, the sample is confined to listed companies due to data availability constraints. While this offers a consistent and comparable firm-level dataset, it necessarily excludes a vast segment of small and medium-sized enterprises (SMEs) and private firms that are crucial drivers of innovation, particularly in emerging sectors. This sampling focus may lead to an overestimation of network cohesion and centralization, as listed firms are typically larger, more established entities with greater resources for formal collaboration. Consequently, the innovation dynamics of more agile, niche SMEs are not captured, potentially overlooking important grassroots innovation pathways and alternative network formation mechanisms. Future studies should seek to incorporate data on SMEs, possibly from alternative sources such as startup databases or regional innovation surveys, to validate and extend the findings presented here, thereby providing a more comprehensive picture of the entire innovation ecosystem.