Given a function that classifies a data object as relevant or irrelevant, we consider the task of selecting k objects that best represent all relevant objects in the underlying database. This problem occurs naturally when analysts want to familiarize themselves with the relevant objects in a database using a small set of k exemplars. In this paper, we solve the problem of top-k representative queries on graph databases. While graph databases model a wide range of scientific data, solving the problem in the context of graphs presents us with unique challenges due to the inherent complexity of matching structures. Furthermore, top-k representative queries map to the classic Set Cover problem, making it NP-hard. To overcome these challenges, we develop a greedy approximation with theoretical guarantees on the quality of the answer set, noting that a better approximation is not feasible in polynomial time. To further optimize the quadratic computational cost of the greedy algorithm, we propose an index structure called NB-Index to index the \theta-neighborhoods of the database graphs by employing a novel combination of Lipschitz embedding and agglomerative clustering. Extensive experiments on real graph datasets validate the efficiency and effectiveness of the proposed techniques that achieve up to two orders of magnitude speed-up over state-of-the-art algorithms.