A series of numerical experiments using a co-evolutionary model for both networks and strategies for 2 - 2 games was carried out. It was proven that there was an interesting relation between assortative mixing of the evolved network and emerging cooperation. In the Prisoner's Dilemma (PD) game class, the evolutionary trail for a weak dilemma game leads to an assortative mixing network, and attains cooperative situation easily. A game implemented with a stronger dilemma, however, makes the network very heterogeneous, featuring a negative assortative coefficient to solve the dilemma situation. This implies that the dilemma strength in PD significantly affects the direction the assortative coefficient takes during evolutionary processes in theco-evolution model.