Food security strongly depends on how water resources available in a certain region contribute to determine the maximum amount of food that it can produce. Human societies often cope with water scarcity by importing food products from other regions. Thus, the international trade of food commodities is associated with a virtual transfer of water resources from production to consumption regions through a network of trade. Even though global food security increasingly relies on this trade, the spatiotemporal patterns of the virtual water network remain poorly investigated. It is unclear how these patterns are changing over time, whether there is an increase in the interconnectedness of the network, and at what rate the globalization of water resources is occurring. Here we use a rich database of international trade and reconstruct the virtual water network from 1986 through 2008. We find that the total flow has more than doubled, and the number of links has increased by 92% over this time period. The network has become more homogeneous but most of the flow concentrates in few links and hubs, while several countries exhibit only few (and weak) connections. 50% of the global fluxes are carried by 1.1% of the links, and on average 6–8% of the global population controls more than 50% of the net virtual water exports. The network is extremely dynamic and intermittent with only few permanent links, while each year many links are created and dismissed.
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 Food production is by far the largest form of societal water consumption and entails the most critical impacts of human societies on the water cycle [Baron et al., 2002; Falkenmark et al., 2004]. Water is a major factor controlling food security and in many regions around the world the limited availability of freshwater resources has historically constrained population growth. In the past few decades, however, the intensification of international trade has allowed some regions to sustain demographic growth beyond the limits posed by their local water budget [Allan, 1998; D'Odorico et al., 2010]. Over one billion people live in areas where human use of available water supplies has exceeded sustainable limits [National Intelligence Council, 2010]. Through the transport of food commodities from foreign countries these regions virtually import the water used for their production [Allan, 1998]. Known as “virtual water”, this water is virtually embedded – though not physically present – in all commodities, and is virtually transferred by trade from production to consumption regions [Allan, 1998; Hoekstra and Chapagain, 2008]. Thus, international trade is associated with a long-range transport of virtual water through a global network of virtual water flow [Suweis et al., 2011; Konar et al., 2011]. This network spans the globe, and connects a large portion of the global population, a phenomenon known as the “globalization of water” [Hoekstra and Chapagain, 2008].
 Virtual water trade has often been recognized for its ability to improve physical and economic access to food commodities in water scarce regions. By increasing food availability and lowering food prices, it may prevent water crises from degenerating into famine and water wars [Allan, 1998; Barnaby, 2009]. Moreover, virtual water trade allows for the support of larger global populations without engendering massive emigrations of people from water deficit to water excess areas. Thus, international food trade is often considered vital for global food security [e.g., Hanjra and Qureshi, 2010]. Virtual water transfers can be used for water solidarity toward regions affected by crop failures [Hoekstra and Chapagain, 2008]. However, there is evidence that connectivity of the virtual water trade network is currently driven by gross domestic product [Suweis et al., 2011] and social development status rather than water solidarity, thus increasing inequity in the access to water resources [Seekell et al., 2011]. Similarly, food trade is not necessarily driven by water scarcity. Moreover, it may reduce societal resilience to drought [D'Odorico et al., 2010] and enhance environmental degradation [e.g., Hoekstra and Chapagain, 2008].
 Despite their important role in determining global food security, the emerging global patterns of virtual water trade remain poorly understood. In particular, it is unclear how these patterns are changing over time. It has been estimated that the worldwide increase in food trade from 1961 to 2000 was around 400% [de Fraiture et al., 2007]. But how is the global redistribution of (virtual) water resources changing? Is this change due to an increase in the number of links and in the interconnectedness of the network or to an increase in the magnitude of fluxes through existing links? While we have a fairly good understanding of the topological and functional properties of the virtual water network [e.g., Suweis et al., 2011], it has not been determined (i) how its structure has evolved in the past few decades, (ii) how the global life support system has become increasingly dependent on the interconnected network of virtual water transfers, and (iii) at what rate the globalization of water is occurring. This paper addresses these questions by investigating the temporal evolution of the global virtual water network in the past few decades. Using a relatively rich global data base of international trade for the past two-to-three decades, we reconstruct the temporal evolution of the virtual water network, investigate the ongoing process of globalization of water resources, and improve our understanding of how the system has reached its existing configuration. To this end, we characterize the connectivity of the network calculating, for each country,i (i.e., node in the network), the number of export connections from that country (or “degree”, ki), and the sum of all the exporting fluxes from that node (or “strength”, si).
 Twenty three years (1986–2008) of detailed international trade data from FAOSTAT (http://faostat.fao.org/site/406/default.aspx) were used to reconstruct the global trade patterns of each food product reported by the FAOSTAT data base, including crops, crop-derived food commodities, and animal products. This trade data is reported in units of tonnes, heads or other appropriate units, depending on the type of product. For each product,m, and each year, t, trade was expressed by constructing a trade matrix, Tm(t), whereby the export of that crop from country i, to country j, is stored in the (i,j) element of the matrix. If no export occurs, that element is set equal to zero.
 Conversion of the crop trade matrices to virtual water trade matrices, C(t), was accomplished by using the country-specific average water footprint,WCm, of each product, m, available from Mekonnen and Hoekstra  by crop FAOSTAT code. Only blue and green water consumptions were accounted for. Thus, the virtual water trade matrix was calculated as the sum, C(t) = ΣmWCm × Tm(t). Because virtual water moves through a weighted directed network, the matrix Cis non-symmetrical and two directed links can connect two nodes in two opposite directions. For countries not reported in the water footprint estimates byMekonnen and Hoekstra – due to either political change (example Czechoslovakia), or size (example: Turks and Caicos Islands) – the green and blue water footprint of the nearest neighbour by latitude and longitude was utilized. For islands or those countries with no close neighbour (i.e., with no neighbour within ±10° of latitude and longitude), the global average values of the green and blue water footprint of that crop type were used. Country-specific water footprint estimates existed for 309 crops and animal products traded. This analysis considers all of these major agricultural and animal products.
 Over the 23 years, food commodities were exchanged among 260 countries or other territories (network nodes). Due to the addition and loss of countries (e.g., those resulting from the splitting of the USSR or Yugoslavia), over the years of record not all 260 countries were extant and concurrently trading for all years. Countries with no reported trade are assumed to have zero trade; there were only few countries (≈10) every year for which no trade was reported, mainly small islands, small city-states, or – temporarily – countries emerging from the collapse of the USSR and Yugoslavia federations, or the splitting of other countries.
 For each country, i (i.e., node in the network), we calculated its degree, ki, which is the number of export connections that country has with the other nodes. The degree is calculated as the number of the non-zero elements in the trade matrix,C, in the i-th row (export connections) for the extant countries within a single year [Barrat et al., 2008]. Similarly, for each country, i, and year, the strength, si, is calculated as the sum of all the exporting fluxes from that node (i.e., as the row sum in the virtual water trade matrix), while the virtual water balance of import and export is expressed as the row sum (export) minus the column sum (import) in the virtual water trade matrix, C.
 In 1986 the global virtual water network included 205 active trading nodes (i.e., countries) connected by 8213 links. At the end of the period of record (2008) there were 232 active trading nodes connected by about 15,759 links (92% increase). The dissolution of the former Soviet Union in 1991 resulted in a net increase of 14 potential nodes, with the dissolution of Yugoslavia adding eventually another 5. The 2391 link increase from 1986 to 2008 associated with these nodes account for only a quarter of the total increase. Thus, in the past 23 years the number of links has dramatically increased, indicating that global food security currently relies on a more interconnected virtual water network. A similar increase in the number of connections can also be found when only major links are considered. In Figure 1 we show connections whose fluxes are larger than a threshold value, sT = 2.450 × 109 m3 y−1. In 1986 this “backbone network” (i.e., network with fluxes >sT) carried 50% of the total flows with only 1.1% of the links existing in the complete virtual water network. It is found that the total number of major links almost doubles (from 91 to 170) between 1986 and 2008. Interestingly, major changes have occurred in the patterns of the backbone network. In fact only 24 links in this network are permanent while 51 of the links that existed in 1986 disappeared by 2008; at the same time 162 new links emerged in the backbone network from 1986 and 2008. This suggests that the virtual water network has been very dynamic and most of its major links have changed in the course of the study period (1986–2008). In particular, new major trading countries have appeared: in 1986 Brazil, Argentina, Indonesia, and China had only few links to the rest of the world. By the mid 1990s Brazil and Argentina emerged as major “hubs” (i.e., highly connected nodes) in the virtual water network, and started playing an important role as virtual water exporters to Europe and China. Similarly, in recent years China, Indonesia, and other countries in Southeast Asia have become more connected to the rest of the world (see Figure 1d). While these new links were established, others disappeared or decreased in magnitude below the threshold used in this “backbone” analysis (sT = 2.450 × 109 m3 y−1); for example, major links between Russia and the rest of the world disappeared. Overall, the establishment of major trade relations between South America or South-east Asia and other regions around the world was not paralleled by a comparable increase in connectivity in African countries, which remain only marginally affected by the globalization of freshwater resources. This marginalization of the African continent may reflect its limited access to the global economy furthering evidence that virtual water trade may be more driven by social development than water or food solidarity [Seekell et al., 2011].
 When all links in the network are considered, we find that the average degree of the nodes has increased by about 70% in the study period (1986–2008), which indicates an increase in the number of active trade relations among countries. Most of the increase in average degree, 〈k〉, took place between 1990 and 2001, while 〈k〉 remained constant in the years before and after this interval. Interestingly, because the standard deviation of k increased much less than the mean (Figure 2a) the coefficient of variation (not shown) overall decreased, suggesting the occurrence of a homogenization of the network. This point is also stressed by the degree distribution which became more uniform in the course of the study period (Figure 2, inset). In other words, the distribution of the number of connections among nodes is becoming more uniform. The total strength of the network (i.e., the sum of the strength of its nodes) more than doubled between 1986 and 2008, and the standard deviation of the nodal strengths increased at a similar rate.
 Overall, both the total strength and the average degree of the network increased during the study period, but not always at the same rate (Figure 2). We can recognize three phases: (i) before 1990 the number of connections increased from 8213 to 8648. This increase is explained by a concurrent growth in the number of trading countries (from 205 to 217), while the average degree of the nodes remained constant; (ii) between 1991 and 2001 both strength and average degree increased, only partly due to the introduction of new nodes and trade reporting from former soviet states. In this period the growth rate of 〈k〉 was greater than that of the total strength resulting in a decrease in the average virtual water flux per link, due to the initial activation of new trade relations with relatively low strength; (iii) after 2001 both the average degree and the number of links remained almost constant (on average 15,480 ± 290 links), while the increase in virtual water trade (i.e., in the network's strength) was due to a 21% increase in the flow rate through existing links.
 Of all the 8213 links existing in 1986, only 3964 have remained active for all years in the interval 1986–2008. The fact that only a relatively small fraction of links is permanent indicates that the virtual water network is very dynamic and its growth in time does not occur by simply adding new links to an existing network because some of them disappear, while others are created or rewired. This extremely variable character of the temporal evolution of the virtual water network is also shown by Figure 3a, which provides a frequency plot of the duration (in number of years) of each link. Only a small fraction (≈20%) of the connections that existed in 1986–2008 has remained active throughout this 23-year period (permanent links). As noted, most of the network is made of ephemeral links, which remain active only for few years. If the network was growing in number of connections by adding at a constant rate new links to an initial configuration, the frequency plot inFigure 3awould exhibit a different shape, with a uniform distribution of the number of connections (the average increase rate of the number of links) across all durations. However, the exponential-like shape on the left-hand side of the distribution indicates the existence of a very intermittent behaviour with the continuous activation and dismissal of links. Interestingly, a similar behaviour is also found in the backbone network, i.e. when only the links with high strength are retained (Figure 3a, inset). This result suggests that the backbone structure of the virtual water network is also very dynamic, with only few connections (24) remaining active throughout the 23-year period. Thus, the intermittency of the network is induced not only by the on-off behaviour of the small links in the network but is rather the signature of its strong plasticity, i.e., of its ability to change structurally and functionally in time. It is unclear what the drivers of this plastic behaviour are.
 Important information on the network structure is obtained by plotting for each node, i, the total strength, si, (i.e., sum of the export fluxes) versus the degree (see Figure 3b, corresponding to the year 2008). The strength increases with the degree following a relation which is well represented by a power-law,s ≈ kq. Interestingly, the scaling exponent is much larger than one (q ≈ 2.78 in 2008), indicating that the average strength of the connections, si/ki, strongly increases with k: countries with a relatively large number of trade partners (i.e., large k values) tend to develop stronger connections in terms of average virtual water volume transported by each link; in contrast, relatively isolated countries (i.e., with low k values) have on average weaker connections. Thus, virtual water fluxes are strongly clustered with few highly connected countries dominating the global trade. The increase observed in the scaling exponent, q, of the s-k relation (Figure 3b, inset) suggests that the network has been evolving in time toward a configuration dominated (in terms of their share in the global virtual water trade) by fewer and fewer major exporters.
 The tendency (or lack of thereof) of nodes to connect with nodes having similar properties is a key characteristic of a network [Boccaletti et al., 2006]. When this tendency is observed, the network is said to exhibit an “assortative behaviour.” In contrast, when the nodes prefer to establish connections with nodes having disparate attributes, the network is called “disassortative”. These different behaviours have a strong impact on the network topology and their assessment is a first simple way to infer the community structure of the network. The parameter typically used to evaluate assortative or disassortative behaviours is the average degree of the nodes directly connected to a given node
Where k,i is the degree of node i, D(i) is the set of nearest neighbors of node, i, that import from i. Therefore, knn,i is the average degree of the nearest neighbors of the i-th node. We denote withknn the average degree of the nearest neighbours for nodes of degree k. It is possible to demonstrate that for a random uncorrelated network knn does not depend on k [Barrat et al., 2008]. Differently, in the case of assortative (disassortative) networks knn is an increasing (decreasing) function of k.
Figures 3c and 3d show knn,ifor the years 1986 and 2008. A few aspects clearly emerge from this figure. Firstly, despite the existence of a remarkable dispersion in the behaviour of single nodes, overall the network exhibits a disassortative behaviour throughout the 1986–2008 period: countries with a low degree (i.e., connected to only few other nodes) tend to trade with high-degree countries. Conversely, high-degree countries exhibit on average a lower degree of nearest neighbours,knn. In fact, because high degree countries trade with nearly all the other nodes (i.e., their degree, k, is close to the number of nodes, N), the average degree of their nearest neighbours, knn, tends to 〈k〉. Secondly, the general increase of knn from 1986 to 2008 (Figures 3c and 3d) is a result of the increase in the number of links in the network - i.e., of food trade partnerships. However, the shape of the average curve representing the dependence ofknn on khas changed. While in the mid 1980's it displayed a well-defined decay, in recent years the curve is almost constant for low values ofk and then it bends down for larger values of k. This signifies that mid-degree countries tend to increase their exports to mid-degree countries, while for low degree countriesknn remains almost unchanged despite the big increase in the average degree, 〈k〉, of the network. This fact suggests that low degree countries have remained excluded from the increase in network connectedness that has occurred in the past two decades. These results indicate that there is a (temporally consistent) tendency to homogenization of the network, and that low degree nations only marginally participate to global virtual water trade.
 However, while overall network connectedness has increased, only 3964 links remained active the entire time, with 11954 links being activated only once during the 23 year period (Figure 4a). The average duration of those singly activated links was only 5.5 years. Limiting the analysis to the last 10 years of the study period resulted in 10538 links being activated only once with a similarly low mean duration of 3.38 years. This again indicates the continued dynamic nature of the network with the majority of the links possessing limited durations (Figure 4a) while being continually activated and deactivated.
 To relate changes in virtual water flows to the global population growth, we analyzed the temporal evolution of the average virtual water flux per capita, i.e. where ptot(t) is the total world's population at time t. We observe (Figure 4b) that before 1993 the average flux per capita remained almost constant, with values around 235 m3/cap/y. After 1993 it increased until it reached 420–425 m3/cap/y in 2007, indicating an increased reliance on virtual water flows. These results suggest that before 1993 the increase in total virtual water flux, ∑isi, can be explained by a proportional increase in population. Conversely, in the following years the total flux grows in time at a rate larger than population growth. This behaviour could reflect an increase in the living standards of some societies (particularly in the developing world), which are adopting a more water-demanding diet, or an increase in the number of people who have access to virtual water trade [e.g.,Hanjra and Qureshi, 2010].
 However, despite the trend existing in per capita export (Figure 4b), we have found that the population fraction controlling 50% the net virtual water resources placed on the global trade market (i.e., 50% of the net virtual water exports) remains almost constant (6–8%) throughout the 1986–2008 period. Data for 1997–2007 show that the three major net virtual water exporters (Brazil, Argentina, and USA) accounted for 5.7% of the global population and contributed to about 40% of the global net exports; altogether, with 8.8% of the global population the top five net exporters (Brazil, Argentina, USA, Canada, and Australia) controlled on average 56% of the net exports, with no substantial variations from year to year.
4. Discussion and Conclusions
 The view emerging from these results is that the virtual water network is extremely dynamic. Over the past few decades both the number of links and the virtual water volumes exchanged through those links have increased. The network has grown first (1990–2001) by establishing new links and then by increasing the fluxes through existing links (2002–present). The addition of new links increases the homogeneity of the network with a more uniform distribution of the number of export links per node. However, this increase in homogeneity does not entail a more uniform distribution of fluxes among countries. Low degree countries are connected to the rest of the world by fewer and weaker links than high degree countries. This difference between marginalized and well connected countries appears to have increased over time. Moreover, despite the dramatic growth in the number of links observed in the study period, low degree countries appear to be connected always to low-mid degree nodes with no substantial changes between 1986 and 2008. This suggests that these countries have remained for most part excluded (marginalized) from the globalization of water resources.
 Virtual water fluxes remain very concentrated: for example, in 1986 half of the global virtual water fluxes were carried by 1.1% of the links; over 50% of the global net exports are contributed by 5 countries and controlled by 6–8% of the global population. Interestingly, despite the observed increase in number of links, nodal strengths, and global population, there is no evidence of changes in the concentration of net export fluxes.
 Overall, both weak and strong connections have been changing intermittently. Several new links have been established only for a short duration and then dismissed. Quite surprisingly, the network is not growing by simply adding new links to an initial set of connections. Old connections have disappeared and new ones have been established. While some of these new links are due to political change (e.g., dissolution of USSR, and Yugoslavia), the majority of these new connections are amongst the prior existing nodes of the network. The network has a very simple permanent backbone structure and even the pattern of major trade relations has dramatically changed in the period of study with an increase in importance of Argentina, Brazil, China, and Indonesia as major players in the virtual water trade.
 The Editor thanks Alberto Montanari and an anonymous reviewer for their assistance in evaluating this paper.