Study on the Water-Energy-Food-Ecosystem system in the Upper Yellow River based on complex network analysis

The upper reaches of the Yellow River serve as a crucial water conservation area and ecological barrier for the basin. The structural differences in the Water-Energy-Food-Ecosystem (WEFE) system and the mechanisms of key nodes directly influence the efficiency of regional resource allocation, as well as ecological protection and high-quality development in the basin. However, existing WEFE system studies predominantly focus on holistic evaluations, making it difficult to reveal internal structural differences and the mechanisms of key nodes. This study integrates complex network theory and Copula functions to identify key nodes through joint centrality, combined with betweenness centrality to characterize functional role differences among nodes. It quantitatively analyzes the interconnected patterns of the WEFE system in the upper Yellow River from a structural perspective. The results show that the WEFE system in the upper Yellow River exhibits significant spatial disparities. At a correlation threshold of 0.6, the network modularity index reaches 0.274, indicating high structural stability. The energy subsystem demonstrates the strongest internal connectivity (0.81), while food and ecosystem subsystems show relatively high coupling (0.55). In contrast, the correlation between energy and food systems is the weakest (0.25), reflecting insufficient coordination. The network structure identifies two major functional zones: the water-energy module and the food-ecosystem module. Key nodes in the water-energy module exhibit high joint centrality but low betweenness centrality, playing a core role in local resource regulation. Key nodes in the food-ecosystem module possess both high joint centrality and betweenness centrality, serving as critical bridges for cross-system resource flows. This study provides a scientific basis for the coordinated governance of multi-resource systems and high-quality development in the upper Yellow River Basin.