Graph representations of data are increasingly common. Such representations arise in a variety of applications, including computational biology, social network analysis, web applications, and many others. There has been much work in recent years on developing learning algorithms for such graph data; in particular, graph learning algorithms have been developed for both classification and regression on graphs. Here we consider graph learning problems in which the goal is not to predict labels of objects in a graph, but rather to rank the objects relative to one another; for example, one may want to rank genes in a biological network by relevance to a disease, or customers in a social network by their likelihood of being interested in a certain product. We develop algorithms for such problems of learning to rank on graphs. Our algorithms build on the graph regularization ideas developed in the context of other graph learning problems, and learn a ranking function in a reproducing kernel Hilbert space (RKHS) derived from the graph. This allows us to show attractive stability and generalization properties. Experiments on several graph ranking tasks in computational biology and in cheminformatics demonstrate the benefits of our framework.