Reducing carbon emissions from the logistics industry is beneficial for controlling environmental pollution and achieving sustainable development. To improve the carbon emission efficiency of the logistics industry (LCEY) for sustainable development, we propose social network analysis for LCEY evaluation and improvement. We established an evaluation index system for LCEY, measured it with the Super-SBM model considering unexpected output, created its spatial correlation matrix using a modified gravity model, and analyzed its spatial network characteristics with social network analysis. Taking 16 cities in Anhui Province as examples, this study demonstrates the implementation process of the method in detail. The results show that the average value of LCEY in 16 cities in Anhui Province increased from 0.3851 in 2012 to 0.7371 in 2021, showing a steady upward trend. The network efficiency decreased from 0.7619 in 2012 to 0.6857, indicating that the spatial spillover effect is significant, the spatial network relationship is gradually enhanced, and the network tightness must be improved. The characteristics of the spatial network are unbalanced; therefore, improving the structure of the benefit-spillover relationship is crucial. Hence, we propose countermeasures and suggestions to improve the LCEY to provide theoretical and methodological support for the research and management of the LCEY.