In the social network study the graph isomorphism is fundamental issue in computation of graphs network. In this paper we examine the early identification of isomorphic structure to sole the complex network using group theory. With the use of combination of groups, orbital stabilizer, automorphism complex computational that recommended solution at right structures. It is simpler to find community equivalences, hidden symmetries, and structure peculiarities in social graphs that are always evolving when you use algebraic methods combined. The result finding demonstrate that the used method in more reliable and scalable for the network as compare to the other methods. The research study represents the group theory that improves the graph isomorphism algorithm used for social network structure that update over the tile.