Network identification and key influencing factor analysis of low-carbon economy synergy efficiency in Chinese cities: an interpretable machine learning approach

Against the background of China’s dual-carbon strategy, improving the synergy efficiency of urban low-carbon economies is essential for achieving sustainable economic and social development. This study investigates the spatial association network of low-carbon economy synergy efficiency across 271 prefecture-level cities in China from 2008 to 2022 and further examines the factors associated with cities’ embeddedness in this network. A super-efficiency slacks-based measure (SBM) model incorporating undesirable outputs is employed to measure urban low-carbon economy synergy efficiency. A modified gravity model and social network analysis are then used to identify the spatial association structure among cities, while interpretable machine learning is applied to examine the predictive importance, contribution directions, nonlinear associations, and joint predictive characteristics of key influencing factors. The results show that: (1) low-carbon economy synergy efficiency generally increased during the study period. High-efficiency areas were mainly concentrated in urban agglomerations along the eastern coast, while western regions exhibited relatively low levels. (2) The intercity synergy network became increasingly complex and stable, with an overall increase in association strength within the model-implied network and a more balanced network structure, although a distinct hierarchical pattern had not yet emerged. (3) Eastern cities occupied core positions in the network and demonstrated strong relational connectivity and high network centrality, whereas most central and western cities were located at the network periphery and had relatively weak connections. (4) Cities could be classified into net beneficiaries, such as Beijing and Shanghai, brokers, such as Yunnan, and net spillover regions. (5) The interpretable machine learning results indicate that higher levels of consumer market size, employment agglomeration, investment in science and education, foreign direct investment, and financial development generally correspond to higher model-predicted network embeddedness. By contrast, higher values of government intervention, the urbanization rate, and industrial structure more often correspond to lower predicted values and exhibit clear nonlinear and stage-specific characteristics. These machine learning results reflect predictive relationships under the given sample and model conditions and should not be directly interpreted as causal effects in the strict sense. To promote coordinated low-carbon development, policymakers should implement locally tailored low-carbon strategies, establish cross-regional coordination mechanisms, and strengthen network linkages and coordination between core cities and other cities. These findings provide practical implications for advancing sustainable urban development and achieving China’s carbon-neutrality target.