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Identification of outliers can lead to the discovery of unexpected, interesting, and useful knowledge. Existing methods are designed for detecting spatial outliers in multidimensional geometric data sets, where a distance metric is available. In this paper, we focus on detecting spatial outliers in graph structured data sets. We define statistical tests, analyze the statistical foundation underlying our approach, design several fast algorithms to detect spatial outliers, and provide a cost model for outlier detection procedures. In addition, we provide experimental results from the application of our algorithms on a Minneapolis-St.Paul(Twin Cities) traffic dataset to show their effectiveness and usefulness.