Multiplex dependence analysis of China's interprovincial virtual water based on an ecological network.

The interprovincial circulation of goods and services has formed virtual water flows between regions, which can redistribute water resources. Based on previous virtual water trade research, this study further explored the multiple dependencies of virtual water, i.e., direct, indirect, and complete dependence. This study examined the direct, indirect, and complete dependence of virtual water between provinces in China by constructing multilayer dependence networks and identified the key regions and paths of virtual water trade network. The results showed direct dependence was the densest and had the largest overall dependence degree, but indirect dependence was the most stable and orderly. Second, the dominant provinces were Guangxi, Hunan, Sichuan, Xinjiang, and Anhui, referred to as "core‒five‒region," and the flow relevant to them accounted for approximately 30% of the virtual water. The seven provinces of Shanxi, Zhejiang, Shandong, Hubei, Guangdong, Shaanxi, and Gansu depend both directly and indirectly on the "core‒five‒region." Shanxi and Zhejiang have close direct and indirect dependence, with more than one of the "core‒five‒region." Guangdong was the province with the most direct and indirect input of virtual water from the "core‒five‒region." The study provides a scientific basis for multiregional identification for the collaborative management of water resources in China from the perspective of dependence.