| In recent decades,fresh water resources have become increasingly scarce around the world due to climate change,ecological damage and increased demand,with many regions facing extreme water scarcity pressures and water resources becoming a major ongoing concern for countries around the world.Water stress in a region is not only related to the amount of local water reserves,but also to the virtual water implicit in trade,where some water-scarce regions can relieve water stress by importing water-consuming products through the supply chain rather than producing them locally.The introduction of the virtual water concept avoids the limitations of traditional water use and availability-based water research questions and provides a new perspective on addressing the global water crisis.While there is an urgent need to address the security of water supply in areas where water is scarce,it is also particularly important to describe the economic losses caused by the inability to meet production needs due to water scarcity,i.e.the risk of water scarcity.This study first quantifies the initial water scarcity risk in each country,assesses the global virtual water scarcity risk(VWSR)transfer relationship between 1994 and 2016 based on a global multiregional input-output model,and explores the cross-regional impacts and evolutionary patterns of VWSR along international supply chains.Then,a series of global VWSR transfer network models are constructed through complex network theory,and modal analysis is applied to explore the local patterns of VWSR risk transfer among multiple countries with functional roles and their contributions to network evolution.The main conclusions obtained from the study are as follows:(1)In terms of the overall structural characteristics of the network,the countries involved in global VWSR transfers as well as the volume of transfers increased and stabilised year by year during the period 1994-2016.As a result of the financial crisis in 2008,there was a small decline in the number of countries involved in VWSR transfers,followed by a slow increase and stabilisation.All VWSR transfer networks exhibit small-world characteristics over the period examined,meaning that VWSRs only require a small number of steps to transfer,even between countries where no direct risk transfer takes place.Based on the network structural entropy indicator,the VWSR transfer network is disordered,with an uneven distribution of degrees,strengths and mesas of countries,a finding that is verified in the network microstructure characterisation.(2)In the network microstructure characterisation,it was found that the incoming degree and incoming intensity of the economies varied relatively little during the period under examination,while the outgoing degree distribution and outgoing intensity distribution were very heterogeneous.A very small number of countries,including the USA,China and Germany,were the main sources of VWSR,and in 2016,for example,their VWSR exports were close to 90% of the total risky exports.The US ranked firmly in first place for initial water scarcity risk and VWSR exports during the period examined.China’s initial water scarcity risk WPL and VWSR exports trended up significantly during the examination period,and as of2016,were similar to the US,which was in first place.Countries such as Japan,China and the UK act as ’intermediaries’ in the VWSR transfer network,through which VWSR can be transferred from the exporting country to the importing country,even though there is no direct risk transfer relationship between the two countries.(3)The motif analysis of the VWSR transfer network found that the proportion of motifs M12,M4 and M7 was significantly higher than the other motifs during the period under examination,indicating that these three types of motifs were the main motifs of interaction among countries.The highest proportion of these three types of local motifs,motif M12,is consistent with the global structure in which a small number of VWSR exporters transfer risk to multiple economies around the world.The weighted network motif analysis indicates that motif M5 has the highest carrying capacity index of all significant motifs.This reveals that despite its low participation in the VWSR transfer process,motif M5 is not negligible in terms of its influence and is a local mode with an important functional role in the global VWSR transfer network.Identifying the functional players in local interaction patterns in a motif perspective,the US,China,Japan,India and Germany were among the global VWSR transfer network during 1994-2016 countries that play a major functional output role in the global VWSR transfer network during 1994-2016,which is consistent with the results revealed by microstructural features.Motif M12 reveals that the interaction pattern of these countries is a unidirectional export of VWSR to two economies that are not directly related.The countries with a functional input role,as reflected in motif M4,are predominantly located in the African region,which duplicates and overlaps with the results of the microstructural features.In contrast to the microstructural characterisation results,motif M7 reveals that the countries of India and South Africa are the main functional intermediaries in the VWSR transfer network.The motif analysis provides richer and more diverse information for exploring the role of economies in the network.This study provides a quantitative assessment of the economic losses caused by water supply deficits in economies across the globe during 1994-2016 from a systematic perspective,as well as the transfer relationships of this loss before the economies(VWSR); a series of VWSR transfer network models are constructed based on complex network theory,and the evolutionary mechanisms of the structural characteristics of the networks are explored,filling a research.On the other hand,it is a breakthrough from the previous studies that only focused on the development of VWSR.This study considers the interaction patterns among multiple countries and explores the structural features of functional motifs,including dynamic evolutionary trends and their role in the evolution of VWSR networks,beyond the limitations of previous studies which only focus on the linkages between country pairs.This study can improve understanding of the impact of local structural features on the formation of VWSR transfer network relationships and the mechanisms at play,and help governments to adjust trade policies to mitigate the cascading effects of VWSR propagation along international supply chains in order to avoid irreversible economic losses. |