Expansion relevance which combines both relevance and diversity into a single function is resorted to a submodular optimization objective that can be solved by applying the classic cardinality constrained monotone submodular maximization. However, expansion relevance do not directly capture the dis-similarity over a pair of nodes. Existing submodular algorithms are sequential and not easy to take full advantage of the power of distributed cluster computing platform, such as Spark, to significantly improve the efficiency of algorithm. To tackle this issue, in this paper, a distance metric, which is defined by a sum function of personalized PageRank scores over the symmetry difference of neighbors of a pair of nodes, is first introduced to capture the pairwise dis-similarity over pairs of nodes. Then, the problem of diversified ranking on graphs is formulated as a max-sum k-dispersion problem with metrical edge weight. A polynomial time 2-approximate algorithm is proposed to solve the problem. Considering the computational independence of different pairs of nodes, a MapReduce algorithm is further developed to boost the efficiency of the process. Finally, extensive experiments are conducted on real network datasets to verify the effectiveness and efficiency of the proposed algorithm.