Symmetric and semisymmetric graphs are used in many scientific domains, especially parallel computation and interconnection networks. The industry and the research world make a huge usage of such graphs. Constructing symmetric and semisymmetric graphs is a large and hard problem. In this paper a tool called G-graphs and based on group theory is used. We show the efficiency of this tool for constructing symmetric and semisymmetric graphs and we exhibit experimental results. Categories and Subject Descriptors G.2.2 [Discrete Mathematics]: Graph Theory—Graph algorithms General Terms Algorithms, Theory Keywords Symmetric graphs, semisymmetric graph, graphs from group, G-graphs.