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City cluster is an effective platform for encouraging regionally coordinated development. Coordinated reduction of carbon emissions within city cluster via the spatial association network between cities can help coordinate the regional carbon emission management, realize sustainable development, and assist China in achieving the carbon peaking and carbon neutrality goals. This paper applies the improved gravity model and social network analysis (SNA) to the study of spatial correlation of carbon emissions in city clusters and analyzes the structural characteristics of the spatial correlation network of carbon emissions in the the Yangtze River Delta (YRD) city cluster in China and its influencing factors. The results demonstrate that: 1) the spatial association of carbon emissions in the YRD city cluster exhibits a typical and complex multi-threaded network structure. The network association number and density show an upward trend, indicating closer spatial association between cities, but their values remain generally low. Meanwhile, the network hierarchy and network efficiency show a downward trend but remain high. 2) The spatial association network of carbon emissions in the YRD city cluster shows an obvious 'core-edge' distribution pattern. The network is centered around Shanghai, Suzhou and Wuxi, all of which play the role of 'bridges', while cities such as Zhoushan, Ma'anshan, Tongling and other cities characterized by the remote location, single transportation mode or lower economic level are positioned at the edge of the network. 3) Geographic proximity, varying levels of economic development, different industrial structures, degrees of urbanization, levels of technological innovation, energy intensities and environmental regulation are important influencing factors on the spatial association of within the YRD city cluster. Finally, policy implications are provided from four aspects: government macro-control and market mechanism guidance, structural characteristics of the 'core-edge' network, reconfiguration and optimization of the spatial layout of the YRD city cluster, and the application of advanced technologies. [ABSTRACT FROM AUTHOR]