Accurately portraying the spatially linked network characteristics of digital infrastructure and exploring its energy-saving effects are highly valuable for enhancing the synergy in digital infrastructure development and expanding its network spillover effects on energy conservation. This paper uses panel data at the city level in China and employs a modified gravity model to calculate the centrality of digital infrastructure spatial correlation network nodes. Based on this, an econometric model is constructed, incorporating variables such as digital infrastructure spatial correlation network node centrality and urban green total factor energy efficiency. The model is used to analyze the effects and transmission paths of digital infrastructure network node centrality on urban green total factor energy efficiency. The analysis yields the following conclusions: (1) Digital infrastructure spatial correlation network node centrality significantly improves urban green total factor energy efficiency, with considerable variability due to city geographic location, city scale, and city attributes. (2) Nonlinear testing results indicate that as digital infrastructure construction advances, its impact on urban green total factor energy efficiency shifts from inhibitory to promotional. (3) The impact mechanism shows that digital infrastructure node centrality enhances urban green total factor energy efficiency through green technology innovation. Additionally, it promotes advanced industrial structures and reduces capital mismatch, further influencing energy efficiency. (4) Digital infrastructure node centrality not only boosts urban green total factor energy efficiency but also facilitates regional convergence, increasing the convergence rate from 0.094 to 0.170%. The findings of the research offer policy guidance for the government on advancing digital transformation initiatives and enhancing energy efficiency.
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