Many real-world data sets are structured as graphs, and as such, machine learning on graphs has been an active area of research in the academic community for many years. One popular machine learning task on graphs is link prediction, which involves the prediction of missing relationships/edges between the nodes in the graph. For instance, in a social network we may use link prediction to power a friendship recommendation system, or in the case of biological network data, we might use link prediction to infer possible relationships between drugs, proteins, and diseases. 2,10 However, despite its popularity, previous work on link prediction generally focuses only on one particular problem setting: it generally assumes that link prediction is to be performed on a single large graph and that this graph is relatively complete, i.e., that at least 50 percent of true edges are observed during training. 3,9

In this work, we consider the more challenging setting of few-shot link prediction, where the goal is to perform link prediction on multiple graphs that contain only a small fraction of their true, underlying edges. This task is inspired by applications where we have access to multiple graphs from a single domain but where each of these individual graphs contains only a small fraction of the true, underlying edges. For example, in the biological setting, high-throughput interactomics offers the possibility to estimate thousands of biological interaction networks from different tissues, cell types, and organisms; however, these estimated relationships can be noisy and sparse, and we need learning algorithms that can leverage information across these multiple graphs in order to overcome this sparsity.16 Similarly, in the e-commerce and social network settings, link prediction can often have a large impact in cases where we must quickly make predictions on sparsely-estimated graphs, such as when a service has been recently deployed to a new locale. In other words, link prediction for a new sparse graph can benefit from transferring knowledge from other, possibly more dense, graphs assuming there is exploitable shared structure.