Link prediction systems (e.g. recommender systems) typically use graph topology as one of their main sources of information. However, automorphisms and related properties of graphs beget inherent limits in predictability. We calculate hard upper bounds on how well graph topology alone enables link prediction for a wide variety of real-world graphs. We find that in the sparsest of these graphs the upper bounds are surprisingly low, thereby demonstrating that prediction systems on sparse graph data are inherently limited and require information in addition to the graph topology.