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As the assessment standards of the community structure, in this paper, it unfolds the process of modularity. Firstly, it describes the original authority definition of Newman in detail, and popularizes to all kinds of different types networks. With the discovery of overlap feature, the modularity integrates the characteristic property of belonging factor, including extensions on Newman's modularity and the non-fuzzy modularity based on node contribution. Next, some new novel definitions are represented; LC modularity proves the defects of Newman modularity and provides a better choice with density and cohesion, and local modularity shows a way to community in large scale network. And then, the comparisons of the various definitions demonstrate their advantages and disadvantages, and the academic cause is analyzed, it is that the different understanding on the community structure results in the different reference model. In the end, weighted LC modularity is proposed, and some serviceable suggestions on the independence and equity are presented, and it proves that the collective decision-making community pattern surpasses the single self-centered vertex pattern.