Analysis of Agricultural Water Security Based on Network Invulnerability: A Case Study in China's Virtual Water Trade Networks

Abstract “Invulnerability” of complex network was firstly introduced to virtual water (VW) research, aiming to broaden the scope of studies on water use and management. Beginning with the construction of China's virtual water trade networks (VWTNs) of major grain crops, Node Degree ( K ) and Betweenness Centrality ( B ) are employed to evaluate and rank the importance of China's 31 regions. Regions with high values for both indicators are identified as playing pivotal roles in the VWTNs: Jiangsu (ranking 1st for both K and B ), Hubei (2nd for K , 3rd for B ), Henan (3rd for K , 6th for B ), Hebei (4th for K , 4th for B ), Hunan (4th for K , 5th for B ). Using this ranking to simulate the invulnerability of VWTNs under random and intentional attacks. The results reveal a rapid decrease in both Network Efficiency ( E ) and Maximum Connectivity ( C ) under intentional attack. In comparison to seven random attacks, E falls below 0.1 and C drops below 0.5 after only three intentional attacks, and the network completely collapsed after 10 intentional attacks. This highlights the VWTN's vulnerability in maintaining food supply and agricultural water security when key regions are subjected to man‐made destruction, such as military blockades or occupations. Future work should include integrating climate change models, crops yield models, and water resource allocation models to protect the key areas. Furthermore, interdisciplinary approaches are crucial for overcoming the limitations of VW research and these findings will provide valuable insights to enhance the optimal regulation of VWTNs.