Spatial correlation network characteristics and influencing factors of urban ecological vulnerability in the Yellow River Basin, China.

Investigating the characteristics and formation mechanisms of the spatial association network of ecological vulnerability in the Yellow River Basin is of great significance for identifying regional ecological risk transmission pathways and promoting coordinated governance. We constructed an evaluation index system for ecological vulnerability based on the sensitivity-resilience-pressure model, calculated the ecological vulnerability index for the Yellow River Basin from 2013 to 2024 using the entropy method, and employed social network analysis and exponential random graph models to explore the characteristics and influencing factors of the spatial association network of ecological vulnerability. The results showed that ecological vulnerability in the Yellow River Basin exhibited a spatial pattern of low in the west and high in the east. The average connectivity of the ecological vulnerability network was 1, with an average hierarchy of 0.01, indicating a highly connected and flat-structured network. The capi-tals of the related provinces and their surrounding cities demonstrated strong inward attraction and outward radiation within the network. Apart from node attributes such as economic development level and population density significantly facilitating network formation, endogenous structural variables like reciprocity were also significant, indicating that inter-city ecological vulnerability associations were influenced not only by exogenous factors but also by notable endogenous dependencies. Moreover, the network was significantly affected by geographical adjacency and administrative subordination relationships. These findings provide empirical support for formulating regional ecological governance strategies from a network collaboration perspective.