Spatial association network structure of eco-efficiency and its influencing factors: Evidence from the Beijing-Tianjin-Hebei region in China

•Evaluated the static and dynamic urban eco-efficiency of the Beijing-Tianjin-Hebei region in China.•Described the spatial association network characteristics of the urban eco-efficiency.•Analyzed the impact of influencing factors on the spatial association network.•Suggestions for strengthening the spatial association of urban eco-efficiency. This paper uses the DEA-Malmquist model to measure the static and dynamic ecological efficiency of city and describes its spatial distribution characteristics. Then, we use social network analysis and the quadratic assignment procedure to analyze the spatial association network characteristics of ecological efficiency and its influencing factors. The results show that urban eco-efficiency is close being effective according to the DEA method but does not fully. The ecological total factor productivity of the city is increasing. The spatial distribution of technical progress is consistent with total factor productivity, which shows that the former is the main reason for the progress of the latter. The ecological efficiency spatial association network structure is obvious and shows the characteristics of multithreading and complexity. The changing trends of network density and associated relationships remain consistent. In general, there is an upward trend of volatility. Network connectedness, network hierarchy, and network efficiency show that the spatial association of ecological efficiency is inseparable. The overall network structure has better correlation and stability, but there are strict ecological efficiency spatial association network structural characteristics between cities. The analysis of individual network characteristics shows that the connection between cities is getting closer, but the spatial association needs strengthening. The correlation coefficients of green level, industrial structure, government financial support, and fixed asset investment are significantly positive, while the influence of economic level and opening up on the ecological efficiency spatial network are not significant.