The persistence of the global climate system is critical for assuring the sustainability of the natural ecosystem. However, persistence at a network level has been rarely discussed. Here we develop a framework to analyze the time persistence of the yearly networks of climate and carbon flux, based on cross-correlations between sites, using daily data from China, the contiguous United States, and the Europe land region. Our framework for determining the persistence is based on analyzing the similarity between the network structures in different years. Our results reveal that the similarity of climate and carbon flux networks in different years are within the range of 0.57±0.07, implying that the climate and carbon flux in the Earth's climate system are generally persistent and in a steady state. We find a very small decay in similarity when the gap between years increases. Moreover, we find that the persistence of climate variables and carbon flux in the three regions decreases when considering only long range links. Analyzing the persistence and evolution of the climate and carbon flux networks, enhance our understanding of the spatial and temporal evolution of the global climate system.

Complex network; Climate network; Carbon flux; Persistence