Diversified ranking on graphs is a fundamental mining task and has a variety of high-impact applications. There are two important open questions here. The first challenge is the measure - how to quantify the goodness of a given top-k ranking list that captures both the relevance and the diversity? The second challenge lies in the algorithmic aspect - how to find an optimal, or near-optimal, top-k ranking list that maximizes the measure we defined in a scalable way? In this paper, we address these challenges from an optimization point of view. Firstly, we propose a goodness measure for a given top-k ranking list. The proposed goodness measure intuitively captures both (a) the relevance between each individual node in the ranking list and the query; and (b) the diversity among different nodes in the ranking list. Moreover, we propose a scalable algorithm (linear wrt the size of the graph) that generates a provably near-optimal solution. The experimental evaluations on real graphs demonstrate its effectiveness and efficiency.