Abstract: As a critical component supporting carbon neutrality, terrestrial carbon sinks play a vital role in assessing regional net carbon emissions. Using provincial panel data from China between 2011 and 2022, this study applied a modified gravity model and social network analysis to examine the spatial correlation structure and influencing factors of provincial carbon emissions, and proposed differentiated response strategies and policy recommendations. The findings revealed that the spatial correlation network of carbon emissions across Chinese provinces exhibited a distinct "core-periphery" structure, with core nodes dynamically shifting from the eastern region to the central and western areas. The spatial correlations clustered into four major plates: two-way spillover, net benefit, net spillover, and brokerage. Provinces exhibited differentiated connectivity functions within the network. The evolution of this network followed a two-stage trajectory. From 2011 to 2019, the correlation center of gravity migrated northward from the Yangtze River Delta to the Beijing-Tianjin-Hebei region and North China. In 2020, under the combined influence of the COVID-19 pandemic and the "dual carbon" goals, network density declined sharply while hierarchical intensity increased, positioning carbon sink-rich provinces as new cores and enhancing overall network efficiency. Geographical proximity exerted a consistently negative attenuating effect on the spatial correlation of carbon emissions. The impacts of industrial structure, marketization, economic development, and environmental regulation were both phased and nonlinear. Provincial carbon network status was primarily driven by in-degree centrality, with various factors exhibiting distinct nonlinear effects on in-degree and out-degree centrality. Out-degree centrality, however, demonstrated strong path dependency. Therefore, it is necessary to strengthen the spatial regulation and trading mechanisms of terrestrial carbon sinks, differentially enhance inter-provincial carbon flow efficiency, precisely manage the industrial structure threshold while coordinating market regulation, establish an emission reduction evaluation system centered on degree centrality, and promote the transition of provincial carbon emission reduction from scale control to structural optimization.