Cooperative behavior constitutes a key aspect of human society and non-human animal systems, but explaining how cooperation evolves represents a major scientific challenge. It is now well established that social network structure plays a central role for the viability of cooperation. However, not much is known about the importance of the positions of cooperators in the networks for the evolution of cooperation. Here, we investigate how the spread of cooperation is affected by correlations between cooperativeness and individual social connectedness (such that cooperators occupy well-connected network positions). Using simulation models, we find that these correlations enhance cooperation in standard scale-free networks but not in standard Poisson networks. In contrast, when degree assortativity is increased such that individuals cluster with others of similar social connectedness, we find that Poisson networks can maintain high levels of cooperation, which can even exceed those of scale-free networks. We show that this is due to dynamics where bridge areas between social clusters act as barriers to the spread of defection. We also find that this positive effect on cooperation is sensitive to the presence of Trojan horses (defectors placed within cooperator clusters), which allow defection to invade. The results provide new knowledge about the conditions under which cooperation may evolve, and are also relevant to consider in regard to the design of cooperation studies.

For the directed edge preferential attachment network growth model studied by Bollobás et al. (2003) and Krapivsky and Redner (2001), we prove that the joint distribution of in-degree and out-degree has jointly regularly varying tails. Typically, the marginal tails of the in-degree distribution and the out-degree distribution have different regular variation indices and so the joint regular variation is nonstandard. Only marginal regular variation has been previously established for this distribution in the cases where the marginal tail indices are different.