Toward dual carbon targets: Spatial correlation on comprehensive carbon emission index in urban agglomerations based on a new evaluation model

China is confronted with substantial pressure to mitigate its carbon emissions. Urban agglomerations assume a pivotal role in the attainment of carbon peaking and carbon neutrality. This study constructed a carbon emission evaluation model from the perspectives of total quantity, intensity, efficiency, population, and land. A modified gravity model and social network analysis method was used to analyze the spatial correlation characteristics of six urban agglomerations, clarified their carbon emission spillover effects, and explored their influencing factors using the quadratic assignment procedure method. The results are as follows. (1) The carbon emission correlations in the Yangtze River Delta, Pearl River Delta, and Chengdu-Chongqing urban agglomerations increased, while Beijing-Tianjin-Hebei, Central Plains, and Middle Reaches of Yangtze River urban agglomerations decreased. (2) From a macro perspective, the Yangtze River Delta and Pearl River Delta urban agglomerations were at the core of the network, and the "bridging" role of the Middle Reaches of Yangtze River urban agglomeration was evident. From a micro perspective, the cities in the middle of urban agglomerations were more likely to become network cores. (3) Spillover effects between plates were present in the correlation network, with a gradual balance between the reception and spillover relationships. Most urban agglomerations exhibited an uneven distribution of community correlation capacity. (4) Geographic adjacency and urbanization level significantly promoted carbon emission correlation, although the direction and magnitude of other factors' influence varied. The findings contribute to the implementation of low-carbon planning, carbon reduction strategies and regional sustainable development.