To trade or not to trade: Link prediction in the virtual water network

In the international trade network, links express the (temporary) presence of a commercial exchange of goods between any two countries. Given the dynamical behaviour of the trade network, where links are created and dismissed every year, predicting the link activation/deactivation is an open research question. Through the international trade network of agricultural goods, water resources are ‘virtually’ transferred from the country of production to the country of consumption. We propose a novel methodology for link prediction applied to the network of virtual water trade. Starting from the assumption of having links between any two countries, we estimate the associated virtual water flows by means of a gravity-law model using country and link characteristics as drivers. We consider the links with estimated flows higher than 1000 m3/year as active links, while the others as non-active links. Flows traded along estimated active links are then re-estimated using a similar but differently-calibrated gravity-law model. We were able to correctly model 84% of the existing links and 93% of the non-existing links in year 2011. It is worth to note that the predicted active links carry 99% of the global virtual water flow; hence, missed links are mainly those where a minimum volume of virtual water is exchanged. Results indicate that, over the period from 1986 to 2011, population, geographical distances between countries, and agricultural efficiency (through fertilizers use) are the major factors driving the link activation and deactivation. As opposed to other (network-based) models for link prediction, the proposed method is able to reconstruct the network architecture without any prior knowledge of the network topology, using only the nodes and links attributes; it thus represents a general method that can be applied to other networks such as food or value trade networks.