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This paper presents a new clustering algorithm named ANGEL, capable of satisfying various clustering requirements in data mining applications. As a hybrid method that employs discrete-degree and density-attractor, the proposed algorithm identifies the main structure of clusters without including the edge of clusters and, then, implements the DBSCAN algorithm to detect the arbitrary edge of the main structure of clusters. Experiment results indicate that the new algorithm accurately recognizes the entire cluster, and efficiently solves the problem of indentation for cluster. Simulation results reveal that the proposed new clustering algorithm performs better than some existing well-known approaches such as the K-means, DBSCAN, CLIQUE and GDH methods. Additionally, the proposed algorithm performs very fast and produces much smaller errors than the K-means, DBSCAN, CLIQUE and GDH approaches in most the cases examined herein.