Introduction

In recent years, profound changes have taken place in the driving forces of global economic growth, the way of production and life, and the direction of scientific and technological development. Energy is the key to economic development. Clean and efficient use of energy is the foothold of green and low-carbon economic transformation1. As the world’s largest energy producer and consumer, China has made remarkable achievements in the innovation and development of energy technology. However, China’s energy security situation is still severe, facing problems such as overall low energy efficiency2. In addition, China’s total coal consumption is still in the increasing phase, the total carbon dioxide emission has not reached the peak. The improvement of energy use efficiency is still faced with large constraints on energy supply structure and ecological environment pressure3. How to improve energy utilization efficiency and optimize energy distribution is one of the major issues that China’s economy needs to overcome in order to achieve energy consumption reduction and green development from the stage of high-speed growth to the stage of high-quality development.

In 2019, the State Council of China issued the ‘Outline of the Yangtze River Delta Regional Integration Development Plan’, which stipulates that 27 cities in the provinces of Zhejiang, Jiangsu, Shanghai, and Anhui will constitute the core urban agglomeration of the Yangtze River Delta, exerting an influence on all cities within the broader region. Within this framework, the Yangtze River Delta region, characterized by its vibrant economic development, high level of openness, and robust innovation capacity, occupies a pivotal leadership position in promoting ‘regional integrated development’ and ‘high-quality economic development’ in China4. Nonetheless, the region is devoid of traditional energy resources and heavily reliant on energy imports from other provinces, with the total terminal energy demand accounting for approximately 17% of the nation’s total. Furthermore, the region exhibits a high proportion of fossil energy consumption, coupled with significant carbon emissions from the industrial sector. Consequently, the central region of the Yangtze River Delta continues to encounter numerous challenges in enhancing green total factor energy efficiency (GTFEE) and establishing a robust green circular economic system. Investigating GTFEE in the Yangtze River Delta is instrumental in further optimizing energy distribution and enhancing the efficiency of green energy utilization. Simultaneously, achieving low-carbon transformation and promoting integrated regional energy development holds profound significance within the international community.

Generally, the primary measurement indicators of energy encompass energy consumption5, energy intensity6, energy structure7, and energy efficiency8. Among these indicators, GTFEE takes into account diverse factors, including energy, labor, economy, and environment, embodying an “all-factor” characteristic that more accurately represents the interplay between economic development and energy utilization8. Recently, researchers have directed their attention towards identifying the pivotal factors influencing GTFEE2,3,9. Research on the urban scale and spatial correlation characteristics of GTFEE remains relatively scarce. Examining the spatial correlation characteristics of GTFEE among cities will assist governments in devising rational distributions of regional green and low-carbon energy sources, thereby optimizing the regional energy structure. Social Network Analysis (SNA) constitutes an efficacious approach for analyzing the correlation attributes of entities, particularly demonstrating potential in examining the correlation features between regions. At present, the SNA method has been widely used in the field of energy, for example, Xu et al.10 used the SNA method to analyze the associated characteristics of building energy performance gaps. Altuntas and Gök11 used the social network analysis method based on patent information to study wind energy technology. Patent documents were analyzed by applying social network analysis to identify the most influential and relevant technologies in the wind energy sector. However, limited research has been conducted on the evolutionary characteristics of the GTFEE spatial correlation network at the urban scale utilizing SNA.

GTFEE is an efficiency index that accounts for the mutual substitutability of production factors and structural alterations within the production process. It can be assessed through the development of a comprehensive evaluation index system alongside a radial DEA model12,13. Nevertheless, this methodology presents several issues, including the compensation of a high economic index value for a low environmental index value, disregard for the slack in input-output variables, and a tendency to overestimate the actual efficiency level14. Tone15 employed the SBM model, which incorporates undesirable outputs, to measure GTFEE. The results obtained from this method align more closely with the actual circumstances of GTFEE. Building on this foundation, an increasing number of scholars have extended the SBM model. Shi and Li3 applied the SBM-Malmquist-Luenberger index method to assess GTFEE in Chinese prefecture-level cities. Concurrently, Tong et al.16 further utilized the Super-SBM model to re-evaluate GTFEE. Xia and Gulinaer2, building upon prior research, constructed a non-radial, non-angular SBM-Undesirable model to assess GTFEE. Therefore, the Super-SBM model, which incorporates undesirable outputs, addresses the irrationalities inherent in the traditional DEA model that treats pollutant emissions as input variables17. This advancement holds profound significance for investigating changes in GTFEE.

In addition to the exploration of GTFEE measurement methods, the investigation of factors influencing GTFEE has garnered considerable attention. Firstly, economic development and energy efficiency exhibit a coordinated and synchronized relationship. Shifting the economic development paradigm leads to GTFEE enhancement18,19. Furthermore, green technology innovation contributes significantly to GTFEE improvement. This innovation effectively mitigates energy intensity20. Nonetheless, some scholars argue that the impact of innovation on energy efficiency can be hindered by technological bias, thus not invariably yielding positive outcomes21. Moreover, given the “market failure” resulting from resource and environmental externalities, the government implements a range of policies to regulate or encourage enterprises’ environmental conduct and green practices3,9. Hence, the influence of policy regulation on GTFEE cannot be overlooked. Additionally, the digital economy facilitates the rationalization and upgrading of the industrial structure, thereby enhancing GTFEE2. Yet, existing research predominantly focuses on the impact of individual factors on GTFEE, while the driving forces behind GTFEE network correlations remain underexplored.

In summary, the current research focuses more on analyzing the key factors affecting GTFEE, and there is a lack of research on the characteristics of urban scale and spatial association. Meanwhile, the existing research mainly focuses on the impact of a single factor on GTFEE, and does not comprehensively analyze the driving force of GTFEE network association. In addition, in terms of measurement methods, the traditional comprehensive evaluation index system and radial DEA model have some problems, such as high economic index value to compensate for low environmental index value, slack neglect of input-output variables, and easy overestimation of the true level.

In light of this, based on the production frontier theory, this study utilizes the urban agglomeration in the central region of the Yangtze River Delta, China, as a case study, with the objective of conducting a comprehensive assessment of GTFEE and its spatial correlation characteristics at the urban scale. This is achieved by incorporating a super-efficiency model that accounts for undesired outputs and employing the SNA method. Additionally, the quadratic assignment procedure (QAP) is employed to investigate the driving forces behind network correlation and to identify the key factors influencing these correlation characteristics. Thus, this study provides a scientific basis for understanding the city-scale spatial interaction mechanisms of GTFEE and for fostering regional energy integration.

This paper is divided into four parts. Section 2 gives a brief description of the research area, data sources, research methods and research framework. Section 3 analyzes the spatial and temporal pattern, spatial correlation network characteristics and driving factors of GTFEE in the central area of Yangtze River Delta. Finally, Sect. 4 gives the discussion, conclusion and policy recommendations.

Methodology

Study area and data source

The research objects of this study are the 27 cities involved in the urban agglomeration of the central area of the Yangtze River Delta. This paper uses ArcGIS software to draw the urban agglomeration of the central area of the Yangtze River Delta. (Fig. 1). The city base map presented is sourced from the standard vector map available on the website of the Standard Map Service of the Ministry of Natural Resources of China (http://211.159.153.75/). The review number downloaded from the map service website is GS(2020)3189. In order to better reflect the long-term spatiotemporal variation trend of GTFEE, and at the same time, QAP regression analysis requires sufficient data to support its results Therefore, in this paper, while ensuring the availability of data and minimizing missing values, the data of the central urban agglomeration of the Yangtze River Delta from 2006 to 2022 are selected for research. The pertinent data were obtained from the statistical yearbooks of each prefecture-level city spanning the years 2006 to 2023, with additional data sourced from the Statistical Bulletin of Social Development.

Fig. 1
figure 1

Study area (the standard map No. GS(2020)3189 downloaded from the standard map service website of the Ministry of Natural Resources of China is produced by ArcGIS software).

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Research framework

GTFEE represents a comprehensive index designed to quantify both economic benefits and environmental impacts. Building upon conventional total factor productivity analysis, GTFEE incorporates additional factors such as energy consumption and environmental pollution. This enables a more comprehensive assessment of the sustainability of economic activities.

Referring existing studies22,23, this study considers capital, labor, and energy as inputs, defines the gross regional product as the desired output, and identifies industrial sulfur dioxide emissions, smoke dust, and industrial wastewater as environmental discharge outputs. The Super-SBM model is used to assess GTFEE of the urban agglomeration in the central area of Yangtze River Delta. Subsequently, exploratory spatio-temporal data analysis is used to reveal the characteristics of spatio-temporal interaction. Then, social network analysis is used to investigate the spatial correlation network characteristics of GTFEE. Lastly, QAP model is used to analyze the driving force of network correlation and reveal the key factors that affect the correlation characteristics. The research framework is shown in Fig. 2.

Fig. 2
figure 2

Framework of research.

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Super-SBM model

In contrast to the traditional DEA model, the Super-SBM model, which accounts for undesired outputs, integrates relaxation variables within the objective function. The model assumes a monotonically linear relationship between inputs and outputs, that is, the relative efficiency of decision unit (DMU) is determined by linear programming techniques. Firstly, it addresses the issue of non-zero relaxations in input-output, and secondly, it resolves the problem of undesired outputs inherent in the production process15. Consequently, this study employs the Super-SBM model to assess the GTFEE of urban agglomerations in the central Yangtze River Delta region. The corresponding calculation formula is presented in Eq. (1).

$$\begin{array}{*{20}{c}} {\hbox{min} \rho =\frac{{\frac{1}{m}\sum\limits_{{h=1}}^{m} {(\overline {x} /{x_{hk}})} }}{{\frac{1}{{{r_1}+{r_2}}}(\sum\limits_{{l=1}}^{{{r_1}}} {\overline {{{e^d}}} /e_{{lk}}^{d}+\sum\limits_{{p=1}}^{{{r_2}}} {\overline {{{e^u}}} /e_{{pk}}^{u})} } }}} \\ {\left\{ {\begin{array}{*{20}{c}} {\overline {x} \geqslant \sum\limits_{{a=1, \ne k}}^{n} {{x_{ha}}{\lambda _a};\overline {{{e^d}}} \leqslant \sum\limits_{{a=1, \ne k}}^{n} {e_{{ha}}^{d}{\lambda _a};\overline {{{e^d}}} \geqslant \sum\limits_{{a=1, \ne k}}^{n} {e_{{pa}}^{d}{\lambda _a}} } } } \\ {\overline {x} \geqslant {x_k};\overline {{{e^d}}} \leqslant e_{{la}}^{d};\overline {{{e^u}}} \geqslant e_{{pk}}^{u}} \\ {{\lambda _h} \geqslant 0,h=1,2, \cdot \cdot \cdot ,m;a=1,2, \cdot \cdot \cdot ,n;a \ne 0} \\ {l=1,2, \cdot \cdot \cdot ,{r_1};p=1,2, \cdot \cdot \cdot ,{r_2}} \end{array}} \right.} \end{array}$$
(1)

Where, ρ is GTFEE value; m is the number of input factors; h represents the h-th input factor; x is the input factor; k is the k-th decision unit (DMU) based on the current efficiency; r1 and r2 are the number of expected and non-expected output factors, respectively; l and p are the l-th and p-th expected output and non-expected output factors respectively; n is the number of DMU. a is the a-th DMU; ed and eu represent expected and undesired output, respectively.

Social network analysis

GTFEE gravity model

Based on the study by Yin et al.24, a GTFEE gravity model is developed in this paper. Furthermore, the network nodes represent the GTFEE of each city, while the edges depict the connections among the GTFEE values of the cities. This model integrates information pertaining to economy, geographical distance, and energy efficiency. The gravity of GTFEE and the gravity coefficient are computed using Eqs. (2) and (3), respectively.

$${a_{ij}}={k_{ij}}\frac{{{X_i} \times {X_j}}}{{\gamma D_{{_{{ij}}}}^{b}}}$$
(2)
$${k_{ij}}=\frac{{{X_i}}}{{{X_i}+{X_j}}}$$
(3)

Where, aij is gravity of GTFEE between cities i and j; xi is the GTFEE of the i city; kij is the gravity coefficient of GTFEE from city i to j; Dij is the distance between cities i and j; b is the distance coefficient. b = 1 is set in this paper. γ represents the weight coefficient of geographical distance.

Overall network

The primary characteristics of the overall network structure encompass three indices: network correlation (NC), network density (ND), and network efficiency (NE), which are calculated using Eq. (4) to (6). These indices characterize the reachability among regions within the network, the strength of inter-regional relationships, and the degree of line redundancy in the network.

$${N_C}=1 - \frac{V}{{n(n - 1)/2}}$$
(4)
$${N_D}=\frac{W}{{n(n - 1)/2}}$$
(5)
$${N_E}=1 - \frac{S}{{\hbox{max} (S)}}$$
(6)

Where, n is the number of regions in the network; V is the number of unreachable point pairs in the network; W is the actual number of connections between nodes; S is the number of redundant lines; max(S) is the maximum number of possible redundant lines.

Individual network

The key attributes of individual network structures comprise degree centrality (DC), closeness centrality (CC), and betweenness centrality (BC). These dimensions respectively quantify the number of direct connections for each node, the proximity of a node to all other nodes in the network, and the extent to which a node serves as a mediator within the network. The formulae for these calculations are presented in Eq. (7) to (9).

$$DC{\text{=}}\frac{{{L_m}}}{{2(P - 1)}}$$
(7)
$$CC_{m}^{{ - 1}}=\frac{{\sum\limits_{{n=1}}^{q} {{d_{mn}}} }}{{P - 1}}$$
(8)
$$BC{\text{=}}\frac{{2\sum\limits_{{n=1}}^{P} {\sum\limits_{{k=1}}^{P} {{h_{nk}}(m)/{h_{nk}}} } }}{{3{P^2} - 3P+2}}$$
(9)

Where, Lm is the number of connections with endpoint m; P is the number of cities in the network; q is the sum of all actual network connections; dmn is the shortest distance from m to n; hnk(m) is the number of times that city m appears in the shortcut associated with city n and k.

Clustering of networks

In this study, we employ the block model analysis method from Social Network Analysis (SNA) to perform cluster analysis on the network, as outlined by Yu et al.25. Utilizing the iterative correlation convergence method26, we categorize the GTFEE spatial correlation network into four blocks: the bidirectional overflow block, the net overflow block, the main benefit block, and the agent block. Furthermore, we investigate the spatial correlation and interaction mechanisms between GTFEE within the Yangtze River Delta urban agglomeration. The characteristics of each block are detailed in Table 1.

Table 1 Classification and characteristics of cities.
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Analysis of influencing factors

The formation of the GTFEE network is potentially influenced by a multitude of factors. The factors listed in Table 2 exert an indirect influence on the GTFEE network through their impact on green energy efficiency. These influencing factors are elaborated upon as follows.

  1. 1.

    Economic development level: On the one hand, some scholars argue that rapid economic growth often comes at the expense of a degraded living environment, thereby impeding the enhancement of green energy efficiency. However, other scholars posit that as economic growth occurs, people’s living standards and education levels improve, and this, in turn, significantly enhances environmental awareness among some individuals, thereby fostering the promotion of green transformation across various provinces2.

  2. 2.

    Industrial structure: The impact of various industries on GTFEE varies. Among these, the primary industry consumes relatively little energy and has a minimal impact on the ecological environment. The secondary industry, particularly heavy chemical and manufacturing industries, consumes significantly more energy during its development, especially in terms of power resources, exerting a greater impact on the ecological environment. As economy and society develop, the tertiary industry increasingly dominates, yet it relies less on energy, thus having a relatively minor impact. Nonetheless, the overall shift in industrial structure significantly influences the GTFEE level within a region27.

  3. 3.

    Green technology innovation: Green technology innovation has the potential to optimize energy consumption structures and enhance the utilization efficiency of diverse energy sources. Ultimately, the goal is to influence the overall level of green development by enhancing the capacity to manage undesirable outputs resulting from energy consumption18.

  4. 4.

    Green finance: The development of the Internet and the tightening of environmental regulations have indirectly facilitated the enhancement of regional total factor energy efficiency through green finance. Additionally, green finance stimulates innovation in green energy technologies. Furthermore, the ascendancy of the digital economy further augments the role of green finance in enhancing energy efficiency28.

  5. 5.

    Environmental regulation: Environmental regulation serves as an effective mechanism to mitigate pollution pressures on the ecological environment, while the reinforcement of such regulations facilitates the adoption of more efficient and environmentally friendly energy practices by enterprises27.

  6. 6.

    Level of digital economy: The digital economy exerts a significant influence on the balanced development of escalating energy demands and the low-carbon energy transition. The advancement of the digital economy can facilitate the acceleration of green energy utilization efficiency1,2.

  7. 7.

    Urbanization level: Urbanization results in population agglomeration, subsequently boosting the demand for energy consumption. Nonetheless, urbanization also accelerates the innovation and adoption of green technologies, thereby enhancing the efficiency of green energy utilization29.

  8. 8.

    Spatial proximity: Due to the fact that GTFEE among neighboring cities can mutually influence each other, particularly in the realms of resource sharing, technological collaboration, and industrial relocation, spatial proximity relationships may consequently impact GTFEE levels.

Table 2 Explanation and description of variables.
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In QAP regression analysis, the researcher will assume that the data is in the form of a symmetric square matrix and there is interdependence ‌between the variables. Given the potential for multicollinearity among the selected variables in this study, the QAP model does not necessitate the assumption of variable independence34, the QAP model can be directly used for analysis. Consequently, the QAP model, as outlined in Eq. (10), is employed to investigate the driving forces behind the network correlation of various factors.

$$Y=\beta X+\varepsilon$$
(10)

Where, Y is the intensity matrix of GTFEE spatial correlation between cities; X is the vector matrix composed of various influencing factors.

Experiments and results

Spatiotemporal evolution of GTFEE

Figure 3 illustrates the overall trend of GTFEE changes in 27 cities located in the central region of China’s Yangtze River Delta over the period from 2006 to 2022. As depicted in Fig. 3, GTFEE exhibited a rapid increase during the period from 2006 to 2012. During the years 2013–2014, GTFEE underwent a slight decrease. From 2014 onwards, GTFEE has consistently increased. Nevertheless, starting in 2016, GTFEE in the central region of the Yangtze River Delta has demonstrated a fluctuating upward trajectory. Overall, the trend of GTFEE in these cities is on an upward path, suggesting that the green energy efficiency of the urban agglomeration in the central region of the Yangtze River Delta is continuously enhancing, and green and low-carbon development is progressing in a systematic manner.

Fig. 3
figure 3

Change trend of GTFEE in central area of Yangtze River Delta.

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To delve deeper into the spatio-temporal distribution patterns of GTFEE in the central region of the Yangtze River Delta from 2006 to 2022, the present study categorizes the GTFEE of the urban agglomeration into four levels. The results are presented in Fig. 4. Generally, GTFEE exhibits an upward trend from 2006 to 2022. Nonetheless, notable disparities in GTFEE are observed among cities. During the initial phase, the spatial distribution of GTFEE was characterized by higher values in the north and south, and lower values in the center. From 2012 onwards, there has been a significant increase in GTFEE in the central region of the Yangtze River Delta, particularly in the core cities of the urban agglomeration. This surge is attributed to the policy environment in the Yangtze River Delta region. In 2018, the GTFEE of the urban agglomeration remained relatively stable. Nonetheless, GTFEE in the eastern coastal cities exhibited a continuous improvement, indicating a gradual expansion towards surrounding cities. By 2022, GTFEE had developed a distinct spatial pattern characterized by urban agglomeration. The agglomeration effect was particularly evident in the northeast, and the area of high GTFEE concentration in the east expanded progressively.

Fig. 4
figure 4

GTFEE of prefecture-level Yangtze River Delta urban agglomeration (the standard map No. GS(2020)3189 downloaded from the standard map service website of the Ministry of Natural Resources of China is produced by ArcGIS software).

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Spatial correlation network characteristics of GTFEE

Evolution of network

In this study, the natural breakpoint method is employed to stratify the correlation network into four distinct levels, namely, the core network, basic network, conventional network, and edge network, based on the magnitude of correlation strength. Figure 5 illustrates the spatial distribution of the GTFEE association network within the central region of the Yangtze River Delta. The core and basic networks are predominantly concentrated in the northern section of the central Yangtze River Delta region. Between 2006 and 2022, there has been no noteworthy alteration in the prominent position of GTFEE in the northern part of the central Yangtze River Delta region. Furthermore, since 2018, the quantity of core networks has started to rise, and the significance of GTFEE in the northern region has become increasingly evident.

Fig. 5
figure 5

Spatial pattern of GTFEE correlation network of the cities in 2006, 2012, 2018 and 2022.

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(The standard map No. GS(2020)3189 downloaded from the standard map service website of the Ministry of Natural Resources of China is produced by ArcGIS software)

Overall characteristics of the network

Table 3 presents an overview of the characteristics of the GTFEE spatial correlation network. As evident from Table 3, the GTFEE network correlation for the urban agglomeration in the central Yangtze River Delta region is 1, suggesting a strong interconnection among nodes and the presence of a spatial spillover effect. In comparison to the years 2006, 2012, and 2018, the network density in 2022 has notably increased, indicating a closer connection in green energy utilization between cities. An increasing number of cities are becoming interdependent and mutually influenced in their green energy consumption. This trend is attributed to the recent optimization of industrial structures, the acceleration of green and low-carbon industrial transformations, and the promotion of green and clean energy utilization. Nonetheless, from 2006 to 2022, a declining trend in network efficiency has been observed. Concurrently, the value of network density remains relatively low. This further indicates that, despite the continually strengthening correlation between cities, there is a need to enhance the efficiency of green energy use and strengthen the conversion and utilization of green energy across regions.

Table 3 Overall characteristics of GTFEE Spatial correlation networks.
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Individual characteristics of the network

Table 4 presents the results of the individual centrality indices for the GTFEE spatial correlation networks. In this study, we analyze the status and function of the urban network based on degree centrality (DC), closeness centrality (CC), and betweenness centrality (BC). As evident from Table 4, the DC values for Changzhou, Shanghai, Wuxi, Hangzhou, and Nanjing are notably higher, suggesting that these cities exhibit significant achievements in green and low-carbon transformation and maintain strong connections with their adjacent regions. The lower DC values observed for Anqing, Chizhou, Chuzhou, and Yancheng imply weaker connections with other cities in the network.

In terms of CC values, Changzhou, Shanghai, Wuxi, Hangzhou, and Nanjing exhibit consistently high scores, indicating their ability to swiftly connect with other regions in the network, serving as pivotal nodes within the network, and facilitating the dissemination of green energy initiatives. Hangzhou and Wuxi, with high BC values, emerge as key hubs for the production and utilization of green energy. The BC values for Chuzhou, Yancheng, Chizhou, and other cities approach zero, suggesting that cities with smaller populations and scales exert minimal influence on the GTFEE of other cities. The comprehensive analysis reveals that GTFEE is primarily associated with capital cities and major industrial hubs, exemplified by Hangzhou, Nanjing, Wuxi, and Shanghai. However, the impact of smaller cities on network connectivity is comparatively limited.

From the perspective of evolution characteristics, the core cities show the characteristics of stability and diffusion from 2006 to 2022. Shanghai and Wuxi have always been in a dominant position, and at the same time, the sub-core has matured, for example, the DC values of Nanjing and Changzhou have also begun to rise. In addition, the differentiation trend of network hierarchy is significant, and the provincial capital cities or large industrial cities always maintain high connectivity, while the DC value of Chizhou decreases, and the BC value of Chuzhou is always close to 0, indicating that small cities are always at the edge of the network. Meanwhile, the period from 2012 to 2018 is a turning point, with Suzhou starting to decline from the absolute core and Hangzhou gradually becoming the key node of green energy transmission.

Table 4 Individual centrality index of GTFEE Spatial correlation network.
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Clustering characteristics of the network

Figure 6 illustrates the clustering patterns of the GTFEE spatial correlation network spanning from 2006 to 2022. As illustrated in Fig. 6, over time, there is an increase in the number of cities within the bidirectional overflow block and the main benefit block, indicating frequent energy exchanges among cities and mutual influences on GTFEE. Among these cities, Zhoushan, Ningbo, Jinhua, Wenzhou, and Taizhou consistently belong to the bidirectional overflow block, suggesting that they not only satisfy their own green energy demands but also contribute to the energy supply of other cities. Anqing, Chizhou, Xuancheng, Maanshan, Wuhu, Hefei, and Tongling have consistently been classified within the main benefit block. Notably, traditional resource-based cities, including Chizhou, Xuancheng, and Maanshan, require external green technology assistance to enhance their GTFEE levels. Other cities exhibit a continuous transition from the net overflow block to the bidirectional overflow block. These cities demonstrate a higher level of development and exert considerable external influence.

From 2006 to 2022, the mobility of green energy among regions has persistently existed. Furthermore, over time, the concept of net overflow regions has gradually diminished, while the mobility of resources and information amongst cities has consistently augmented. This observation further implies that, amidst the process of national integration, the frequency of factor flows between cities within the central region of the Yangtze River Delta has intensified, the circulation of energy sources has escalated, and consequently, the efficiency of green energy utilization has enhanced.

Fig. 6
figure 6

Spatial pattern of GTFEE correlation network of the cities in 2006, 2012, 2018 and 2022.

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Driving force analysis

The results of the QAP regression analysis are presented in Table 5. A stronger network correlation strength of a city is associated with a greater impact of GTFEE on the surrounding area, thus increasing the likelihood of it contributing to the collective utilization of regional green energy. In 2006, the industrial structure and urbanization level exerted a significant negative influence. However, over time, the impact of industrial structure and urbanization level on GTFEE correlation strength gradually diminished and became nonsignificant. Green finance exhibited a significant positive effect solely in 2018. In the long term, the industrial structure, urbanization level, and green finance may cease to be the primary determinants within the network.

The impact of the digital economy on GTFEE correlation strength was not statistically significant. However, by 2022, it had evolved into a significant positive effect, primarily attributed to China’s initial proposal in 2019 to vigorously develop the digital economy, which exhibited a lag in its developmental impact. During the period from 2006 to 2018, the impact of the digital economy was not significant; however, its influence has been progressively increasing.

The influence of green technology innovation from 2006 to 2022 has been significantly positive. Over time, the impact of green technology innovation on the strength of GTFEE correlation has progressively intensified. This indicates that China’s emphasis on innovation has been on the rise, positioning innovation as the primary driver of productivity, thereby establishing green technology innovation as a pivotal determinant of network correlation intensity.

Environmental regulation has had a significant positive impact between 2018 and 2022, and its influence has been progressively increasing. In recent years, China has consistently prioritized green and ecological development, accompanied by the reinforcement of ecological supervision across multiple domains. This, in turn, has facilitated the adoption and enhanced efficiency of green energy.

The influence of spatial proximity on the strength of GTFEE correlation is significantly positive, suggesting that neighboring cities may exhibit mutual influences in terms of resource sharing, technical cooperation, and industrial transfer, among others. Consequently, spatial proximity emerges as a crucial determinant of GTFEE network correlation strength.

Table 5 Results of QAP regression.
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Discussion and conclusion

Discussion

Utilizing the Super-SBM model, which accounts for unexpected outputs, alongside the SNA method, this study thoroughly examines the disparities and interconnections of GTFEE within urban agglomerations in the central Yangtze River Delta region, thereby offering a more holistic perspective on regional energy coordination and development. In contrast to conventional research that primarily emphasizes the examination of variations in energy consumption, energy intensity, and energy structure, GTFEE provides a more comprehensive reflection of the interplay between the economy and the environment, enabling a more thorough assessment of the sustainability of economic activities.

Research on energy use efficiency has progressively garnered the attention of scholars; however, the majority of studies have been limited to examining the impact of a single factor on overall energy use efficiency9,22,35. Regional division and attribution analysis have been overlooked34. Employing a block-based community partitioning approach, this study delves deeply into the dynamic transfer mechanism. Concurrently, by integrating major social and economic indicators, this study identifies the key drivers influencing network connectivity strength, thus offering a significant reference for policy formulation and regional cooperation in promoting green energy efficiency.

The coordinated development of energy integration across cities is crucial for achieving adjustments in urban energy structures and enhancing energy efficiency. Our findings indicate that solely relying on individual cities to enhance green energy use efficiency, while neglecting spatial correlation effects, may hinder the rapid allocation and transfer of green technologies and resources. This aligns with the notion of accelerating regional energy integration and reducing regional disparities in green total factor energy efficiency, as proposed by Feng et al.36. Furthermore, echoing the research conducted by Feng et al.36 on the national green energy use efficiency network, a notable imbalance is observed in the GTFEE correlation network within the central region of the Yangtze River Delta. This imbalance may precipitate a future ‘Matthew effect’, whereby the intensification of urbanization and innovation capacity could exacerbate the concentration of high-efficiency green energy use areas in select advantageous cities.

From the perspective of network complexity, the correlation between the overall scale and density of GTFEE networks within the central urban agglomeration of the Yangtze River Delta is on the rise. This may be attributed to cities’ heightened focus on energy structure adjustment and green development, coupled with the progressive refinement of regional energy integration systems, which has augmented the regional significance of GTFEE.

The results of community division, utilizing the block model, further elucidate the spatial correlation mechanism of GTFEE. Cities within different blocks demonstrate distinct characteristics and functions in relation to GTFEE. For instance, cities within the bidirectional overflow block enhance the efficiency of green energy utilization by facilitating resource sharing. Cities within the net overflow block exert a significant influence on other regions. Cities within the main benefit block require access to resources from other blocks and technological innovation to enhance the efficiency of green energy utilization. Meanwhile, over time, the net overflow block gradually dissipated, and the circulation of resources and information between cities steadily increased. This indicates that, amidst the process of national integration, the frequency of inter-city factor flows in the central region of the Yangtze River Delta has steadily risen, leading to enhanced energy utilization and circulation, and subsequently improved efficiency of green energy use.

Finally, this study demonstrates that green technology innovation, environmental regulation, and spatial proximity exert significant positive influences on the strength of GTFEE network connections. This finding further corroborates the research conducted by Yao et al.20 and Shi and Li3 from a spatial perspective. Concurrently, this study confirms the positive impact of the digital economy on GTFEE from a spatial dimension, thereby reinforcing the research conclusions of Xia and Gulinaer2, which were derived using a panel regression model. In conclusion, this study offers valuable insights for the formulation and implementation of joint carbon emission reduction policies across cities in the future.

In addition, there are still some shortcomings in this study. First of all, the region involved in this study is limited to the central urban agglomeration of the Yangtze River Delta, which has a good level of economic development. The research conclusions may not be applicable to the regions with a large gap with the economic development level of the region. Therefore, future research can compare and explore the differences in temporal and spatial changes of GTFEE at different levels of development by region. Secondly, QAP regression is mainly used to analyze network data, and its results are easily affected by the complexity of network structure. In the driver analysis, if the network structure is complex, the use of QAP method may bring bias to the results. Based on this, future research can further optimize the research methods of driving factors, so that the reliability and robustness of the results can be continuously improved.

Conclusion

  1. 1.

    The overall GTFEE of urban agglomerations in the central region of the Yangtze River Delta exhibits a decreasing trend, with agglomeration observed in both high-efficiency and low-efficiency cities. The urban agglomeration located in the northern section of the central Yangtze River Delta region holds a pivotal role within the GTFEE spatial correlation network. Furthermore, the rise in network density coupled with the decline in efficiency indicates substantial potential for coordinated energy development among cities.

  2. 2.

    In the individual network analysis, cities exhibiting strong associations with GTFEE are predominantly provincial capitals or major industrial hubs, exemplified by Hangzhou, Nanjing, Wuxi, and Shanghai. Nonetheless, the impact of smaller cities on the network’s correlation is relatively minimal. The growing number of cities participating and the gradual diminution of the net overflow block within the bidirectional overflow network community indicate an intensifying interdependence and influence of GTFEE among urban centers.

  3. 3.

    The driving force analysis revealed that green technology innovation, environmental regulations, and spatial proximity exert significant positive influences on the connectivity strength of the GTFEE network. Furthermore, the accelerated growth of the digital economy in recent years has resulted in a sustained significant correlation impact of this factor on the GTFEE network.

Policy suggestions

To achieve regional coordinated energy development in the central Yangtze River Delta region, this paper proposes the following suggestions.

  1. 1.

    Develop tailored energy development policies based on the variations in carbon emission efficiency among urban industries. Provincial capitals and major cities, exemplified by Hangzhou, Nanjing, Wuxi, and Shanghai, should allocate more resources to green energy investment, whereas smaller and medium-sized cities must enhance their environmental regulatory oversight.

  2. 2.

    Leverage the pivotal roles of core cities in fostering green technological innovation and enhancing energy efficiency, and institute regional cooperation frameworks to assist peripheral cities in optimizing their green energy utilization.

  3. 3.

    Based on the level of urban centrality, devise differentiated energy utilization strategies to facilitate technological innovation and knowledge exchange. Highly centralized urban areas should adopt cutting-edge technologies to enhance the overall efficiency of green energy utilization. Less centralized urban centers are collaborating with highly centralized ones to optimize the efficiency of green energy consumption.

  4. 4.

    In light of the multifaceted influences of green technological innovation, environmental regulations, green finance, and the digital economy on the holistic development of regional green energy, governmental entities ought to foster the growth of high-tech enterprises, facilitate the transition of foreign trade towards clean energy sources, achieve a balance between urbanization and environmental sustainability, promote cleaner production practices within heavy industries, and implement more stringent environmental protection standards.