Circulation Characteristic Analysis of Implied Water Flow Based on a Complex Network: A Case Study for Beijing, China

Water and energy are two indispensable resources in national economic production. Water is circulated among economic sectors through products or services; however, indirect water consumption calculated by the input–output method fails to reflect the implied water utilised during energy consumption. This study combined the ecological input–output method with a complex network model to analyse the embodied energy intensity (EEI) and the implied water intensity of embodied energy (IWIEE), and then constructed and analysed the implied water circulation network (IWCN) of 40 sectors in 2007, 2010, and 2012 in Beijing. The results indicate that the energy consumption of all of the sectors is mainly embodied in the transfer of the external provinces of China, and the variation trend of the implied water intensity of the embodied energy is consistent with the embodied energy intensity. The implied water circulation networks had small-world characteristics, indicating that water-saving effects in key sectors can quickly spread to other sectors. However, this may also result in a corresponding negative impact if water shortages occur in these sectors, due to the same spreading effect. The node strength, eigenvector centrality, key edge, and key indirect water flow path were selected as indicators to measure key sectors. Finally, water-saving measures and suggestions were proposed according to the complex network characteristics.