Optimization of urban village public space vitality based on complex network

Urban villages, as products of rapid urbanization, are crucial for understanding urban spatial forms and social vitality. Optimizing the public space network within these areas can enhance the human environment. This study constructs a public space network for urban villages based on the topological relationships between public spaces and road systems. A vitality network is developed using a composite vitality index, gravitational model, and entropy power methods. The interaction between these two networks is analyzed through a coupling coordination degree model. The findings reveal: (1)The morphology network exhibits low-density loosening with local agglomeration at the overall level, characterized by limited connectivity and low structural stability, with their influence and intermediation capacities remain unaligned at the individual level; (2)The vitality networks exhibit similar dispersion-clustering patterns but higher structural stability at the overall level, with consistency between node influence and intermediation capacities at the individual level; (3)The coupling and coordination between the two networks is weak, particularly in MeiKuang Villages, where the disparity is most pronounced; (4)The morphology network positively correlates with individual vitality measures, suggesting that network structure influences node vitality. These results provide insights into optimizing public space layouts in urban villages, offering both theoretical and practical guidance for improving spatial configurations to enhance quality and social vitality.