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This paper presents an automatic point matching algorithm for establishing accurate match correspondences in two or more images. The proposed algorithm utilizes a group of feature points to explore their geometrical relationship in a graph arrangement. The algorithm starts with a set of matches (including outliers) between the two images. A set of nondirectional graphs is then generated for each feature and its K nearest matches (chosen from the initial set). Using the angular distances between edges that connect a feature point to its K nearest neighbors in the graph, the algorithm finds a graph in the second image that is similar to the first graph. In the case of a graph including outliers, the algorithm removes such outliers (one by one, according to their strength) from the graph and re-evaluates the angles until the two graphs are matched or discarded. This is a simple intuitive and robust algorithm that is inspired by a previous work. Experimental results demonstrate the superior performance of this algorithm under various conditions, such as rigid and nonrigid transformations, ambiguity due to partial occlusions or match correspondence multiplicity, scale, and larger view variation.