Abstract
Against the backdrop of tightening water constraints and deepening interregional energy trade, energy production, processing, and consumption are continuously reshaping the spatial allocation of embodied water resources via commodity flows. Previous studies have mainly focused on aggregate virtual water accounting or provincial-scale transfers, yet limited attention has been paid to city-scale dominant corridors and core controlling nodes in energy-sector virtual water networks. Using the Yellow River Basin as a case study, this paper integrates a multi-regional input-output model, complex network analysis, and an attack model to construct a network-based analysis framework for the energy-sector virtual water transfer system across 61 prefecture-level cities in 2017. The network displays a pronounced hub-and-corridor structure, with outflows dominated by Lanzhou, inflows dominated by Lanzhou is the largest virtual water outflow city, with an export volume of 27.18 million m3, accounting for 46.01% of the total outflows, while Luoyang is the largest virtual water inflow city, receiving 21.27 million m3 and accounting for 36.00% of the total inflows. The Lanzhou-Luoyang corridor carries about 12.23 million m3 of virtual water, accounting for about 45% of Lanzhou’s total outflow and 57.5% of Luoyang’s total inflow, indicating that the strongest supply-demand linkage in the network is concentrated in a single core corridor. Centrality metrics further identify Luoyang as the leading topological hub, ranking first in degree centrality, betweenness centrality, closeness centrality, eigenvector centrality, and PageRank, while Qingdao, Weihai, Yantai, Chengdu, and Zhengzhou form important secondary nodes in different metrics. These findings indicate that the energy-sector virtual water network in the Yellow River Basin is characterized by hub concentration and dominant-corridor dependence. The framework can help identify key exporting cities, key importing cities, and dominant corridors, thereby supporting basin-level coordination of energy security and water ecological security.