关键词: 水资源与能源;复杂网络;关键节点;社团结构;

Abstract: Water and energy are two important types of resources in social and economic development.They depend on each other, restrict each other, and feed each other pressure.An in-depth analysis on the circulation characteristics of these two resources in the national economic system from a system perspective can provide an effective entry point for the efficient utilization and rational allocation of resources.Resource networks based on complex networks were built to explore the circulation characteristics of water and energy among different provinces and sectors in China, and key nodes in the resource networks were explored by searching network characteristics.The results show that:(1) Water and energy networks with provinces and sectors as nodes have complex network attributes, and the key nodes in the network were essential for resource regulation.(2) Compared with water and energy networks with provinces as nodes, networks with sectors as nodes had more significant small-world attribute, therefore, resource regulation from the perspective of key sectors would be more efficient than that from the perspective of provinces.(3) Economically developed provinces such as Jiangsu, Shandong, Guangdong, and Zhejiang had greater node strength in water and energy networks.The chemical product industry and metal smelting and rolling industry had large node strength and eigenvector centrality.The resource saving effects of the above provinces and sectors were most easily spread in the resource network.(4) Water and energy networks with provinces as nodes clustered into three and four communities respectively, the resource saving effect of the connecting nodes between communities, such as Jiangsu, Shaanxi, and Inner Mongolia, were easy to spread among communities.The water-energy networks constructed in this paper deepens the research on water and energy circulation characteristics from the perspective of trade, and provides decision-making basis for sustainable use of resources.

Key words: water-energy circulation; complex network; key nodes; community structure;