The correlation evolution and formation mechanism of energy ecological efficiency in China: A spatial network approach

Enhancing energy ecological efficiency is critical for addressing climate change and advancing green, low-carbon economic development. This study utilizes an innovative Super Epsilon-based Measure (EBM) model alongside a gravity model to evaluate the energy ecological efficiency across 30 provincial-level regions in China from 2011 to 2021. This research fills a critical gap in the literature by combining efficiency assessments with complex network analysis, offering a novel perspective on the spatiotemporal evolution and distribution of energy efficiency. The findings reveal that: (1) China's energy ecological efficiency exhibited a fluctuating growth trend over the study period, with significant regional disparities characterized by the pattern “eastern region > central region > western region.” (2) Overall network density, network correlation, and the number of network relationships maintaining relatively stable growth, with a growth rate of 28.93 %, 27.51 % and 28.89 %, respectively. However, the efficiency network's overall connectivity remains low, with fewer correlation lines in the western and central regions and higher network density in the eastern coastal areas. (3) Quantitative analysis using the Quadratic Assignment Procedure (QAP) method identifies key factors influencing network formation, such as urban openness, industrialization level, environmental regulation, economic development, geographical proximity, population quality, and resource endowment. Notably, every 1 % increase in the industrial agglomeration level will have a negative impact of −0.248 % on the energy ecological efficiency network. This research fills a gap in understanding the structural and dynamic aspects of China's energy ecological efficiency, offering novel insights that can guide policymakers in formulating strategies to enhance sustainable development.