Before revision:  The effect depends nontrivially on the combination of the social network structure (degree distribution and assortativity), the type of social dilemma, and the presence of Trojan horses , i.e. defectors placed within clusters of cooperators. Interestingly, the largest enhancement is observed in Poisson networks with increased degree assortativity, where cooperation does better than under scale-free degree distribution.
After revision:  The effect depends nontrivially on the combination of the social network structure (degree distribution and assortativity), the type of social dilemma, and the presence of Trojan horses , i.e. defectors placed within cooperator clusters).