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Spatial outliers are the spatial objects whose nonspatial attribute values are quite different from those of their spatial neighbors. Identification of spatial outliers is an important task for data mining researchers and geographers. A number of algorithms have been developed to detect spatial anomalies in meteorological images, transportation systems, and contagious disease data. In this paper, we propose a set of graph-based algorithms to identify spatial outliers. Our method first constructs a graph based on k-nearest neighbor relationship in spatial domain, assigns the differences of nonspatial attribute as edge weights, and continuously cuts high-weight edges to identify isolated points or regions that are much dissimilar to their neighboring objects. The proposed algorithms have three major advantages compared with other existing spatial outlier detection methods: accurate in detecting both point and region outliers, capable of avoiding false outliers, and capable of computing the local outlierness of an object within subgraphs. We present time complexity of the algorithms, and show experiments conducted on US housing and Census data to demonstrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]