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This paper proposes a new social network classification method by comparing statistics of their centralities and clustering coefficients. Specifically, the proposed method uses the statistics of Degree Centralities and clustering coefficients of networks as a classification criterion. A theoretical justification to this method is also given. In relation to the widely held belief that a social network graph is solely defined by its degree distribution, the novelty of this paper consists in revealing the strong dependence of social networks on Degree Centralities and clustering coefficients, and in using them as minimal information to classify social networks. In addition, experimental classification demonstrates a very good performance of the proposed method on real social network data, and validates the hypothesis that Degree Centralities and clustering coefficients are the only two viable independent properties of a social network.