Based on previous works, we give further investigations on the Prisoners Dilemma Game (PDG) on two different types of homogeneous networks, i.e. the homogeneous small-world network (HSWN) and the regular ring graph. We find that the so-called resonance-like character can occur on both the networks. Different from the viewpoint in previous publications, we think the small-world effect may be unnecessary to produce this character. Therefore, over these two types of networks, we suggest a common understanding in the viewpoint of clustering coefficient. Detailed simulation results can sustain our viewpoint quite well. Furthermore, we investigate the Snowdrift Game (SG) on the same networks. The difference between the outputs of the PDG and the SG can also sustain our viewpoint.