Abstract: Community detection can identify salient structure and relations among individuals from the complex net- work. Researchers put forward many different methods,which are mainly used to detect the groups with dense connec- lions within groups but sparser connections between them. To detect more latent structures in reality networks,various models on statistical inference have been proposed since 2006 , which are on sound theoretical principles and have better performances identifying structures, and have become the statcof-thcart models. These models' aims arc to define a generative process to fit the observed network, and transfer the community detecting problem to I3ayesian inference. First, the concepts on generation model were defined. Then, the article divided the generation models on community de- tection into vertex community and link community based on composition in community, and discussed design ideas and algorithms of each model in detail. What these models adapt to was also summarized from aspects of network type and scale, community structure, complexity etc, and then a method was given on how to select an existed statistical model. hhe existing classical models were tested and analyzed on the popular benchmark datasets. In the end, main problems on these models were highlighted, as well as the future progress.

Key words: Community detection, Probabilistic model, Stochastic block model, Statistical inf erence, Mixed membership