Quantifying the sustainability of water use systems: Calculating the balance between network efficiency and resilience

In ecological network theory, network efficiency and resilience are two essential but complementary attributes of the network structure, and a balance between these factors is critical for an ecosystem's long-term sustainability. Our paper introduces this method and related concepts into water use systems to provide a new angle for sustainability quantification. In this paper, we investigate the meanings of network efficiency and resilience in the context of sustainable development of water use systems, and define sustainable systems based on the optimal balance between network efficiency and resilience. With the consideration of complex artificial characteristics of water use, we propose an optimal water use network and quantify its flows. By ascendency calculation, the balanced network structure can be determined. We then use the four sub-basins of China's Haihe River as a case study to illustrate how the optimal network can be constructed and how the optimal balance for each scenario can be calculated. The results show that the optimal balance for the sub-basins has ascendency values ranging from 0.5970 to 0.7161. By analyzing the contribution of each water use activity to network's balance structure, the location of the optimal balance in water use systems can be better understood. This research represents the first attempt to explore the balance between a network structure's efficiency and resilience as a way to quantify the sustainability of water use systems, and builds a foundation for future studies on the assessment, regulation, and management of water resources.