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In this paper I have proposed a novel algorithm AGMA (Automatic Graph Mining Algorithm). AGMA automatically classifies a weighted social network graph into appropriate number of clusters which does not require user involvement. AGMA uses the linked pattern and the link weight as the clustering criterion based on which the classification of nodes is done. The algorithm is able to find out communities in disconnected graphs. The final section of the paper demonstrates the applicability of AGMA with examples in identifying social communities in artificial as well as in the real world examples like Gahuku-Gama Subtribes Network and 9/11 terrorist network. The signed social networks also lie in the applicability domain of this algorithm.