In ranking, one is given examples of order rela- tionships among objects, and the goal is to learn from these examples a real-valued ranking func- tion that induces a ranking or ordering over the object space. We consider the problem of learn- ing such a ranking function when the data is rep- resented as a graph, in which vertices correspond to objects and edges encode similarities between objects. Building on recent developments in reg- ularization theory for graphs and corresponding Laplacian-based methods for classification, we develop an algorithmic framework for learning ranking functions on graph data. We provide generalization guarantees for our algorithms via recent results based on the notion of algorithmic stability, and give experimental evidence of the potential benefits of our framework.