To effectively and expeditiously address emission reduction, a comprehensive understanding of the current status of carbon intensity and the spatial interactions of carbon intensity in China is necessary. This paper utilizes GIS technology, the Moran Index, and combines traditional Markov chain, spatial Markov chain, and social network analysis (SNA) methods to investigate various features of carbon intensity at the provincial level in China. The study yields the following findings: (1) The center of China’s carbon intensity has shifted towards the northwest, whereas the center of economic development has moved towards the south. This indicates a significant spatial divergence in China’s low-carbon development level. (2) The distribution pattern of carbon emission intensity in China is dominated by the proximity of high carbon emission intensity provinces to other high carbon emission intensity provinces and low carbon emission intensity provinces to other low carbon emission intensity provinces. (3) Carbon emission intensity exhibits significant spatial spillover effects, with positive spillover effects being more pronounced in regions with low carbon emission intensity. (4) The trend toward the development of China’s overall carbon intensity is positive, but the spatial connectivity network of carbon intensity demonstrates a tendency to be entrenched, and leading provinces in low-carbon development have yet to fully realize their positive driving role.