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Most of local outlier detection methods proposed in the literature make use of k nearest neighbors. These methods suffer from a drawback that the detected results are sensitive to the parameter k. In this paper, a novel graph composed of two rounds of minimum spanning tree (MST) is presented. In terms of the two-round-MST based graph, we propose a graph-cut method to detect the local outliers. The experimental results on both synthetic and real datasets demonstrate that, compared with k nearest neighbors related local outlier detection methods, the proposed method can produce more robust results.