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Detecting and characterizing the community structure of complex network and social network is fundamental problem. Many of the proposed algorithm for detecting community based on modularity Q which fail to identify modules smaller than a scale community. In this paper, authors propose a new community detection algorithm based on genetic algorithm and modularity density (D value). We test our method on classical social networks whose community structure is already known and the results can be much easier compared with the method. Experiments show the capability of the method to successfully detect the community structure.