All the social networks can be modeled as a graph, where each roles as vertex and each relation roles as an edge. The graph can be show as $G = [V;E]$, where $V$ is the set of vertices and $E$ is the set of edges. All social networks can be segmented to $K$ groups, where there are members in each group with same features. In each group each person knows other individuals and is in touch with them. In this study, the main goal is introducing a new approach for detecting these groups and minimizing the number of these groups using a cellular automat algorithm. There are two types of social networks, containing simulated social network and real social network. The results show that the introduced method has a great potential to significantly reduce the number of colors assigned and running time of the program.