Link prediction via linear optimization

Link prediction is an elemental challenge in network science, which has already found applications in guiding laboratorial experiments, digging out drug targets, recommending friends in social networks, probing mechanisms in network evolution, and so on. With a simple assumption that the likelihood of the existence of a link between two nodes can be unfolded by a linear summation of neighboring nodes' contributions, we obtain the analytical solution of the optimal likelihood matrix, which shows remarkably better performance in predicting missing links than the state-of-the-art algorithms for not only simple networks, but also weighted and directed networks. To our surprise, even some degenerated local similarity indices from the solution outperform well-known local indices, which largely refines our knowledge, for example, the direct count of the number of 3-hop paths between two nodes more accurately predicts missing links than the number of 2-hop paths (i.e., the number of common neighbors), while in the previous studies, as indicated by the local path index and Katz index, the statistics on longer paths are always considered to be complementary to but less important than those on shorter paths.