A broad interest in the study of networks has been emerged in many scientific areas with the development of the network science and new mathematical models of complex networks. Therefore, the study of brain networks is also taken into consideration. As we know, the nervous system is composed of many neurons that are constantly active. These cells are dynamically connected together. The point is that it is unclear how these structures lead to consciousness. Our goal here is not to investigate the cause of consciousness but we have tried to make a model, reproduce and compare our results with the previous studies. In this thesis, the anesthesia is modeled and its effects on the EEG are investigated via percolation theory.