In this work we have used computer models of social-like networks to show by extensive numerical simulations that cooperation in evolutionary games can emerge and be stable on this class of networks. The amounts of cooperation reached are at least as much as in scale-free networks but here the population model is more realistic. Cooperation is robust with respect to different strategy update rules, population dynamics, and payoff computation. Only when straight average payoff is used or there is high strategy or network noise does cooperation decrease in all games and disappear in the Prisoner's Dilemma.