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We show that the success of cooperation in an evolutionary prisoner's dilemmaon a complex network can be predicted by a simple, quantitative networkanalysis using mean field parameters. The criterion is shown to be accurate ona wide variety of networks with degree distributions ranging from regular toPoisson to scale-free. The network analysis uses a parameter that allows forcomparisons of networks with both similar, and distinct, topologies.Furthermore, we establish the criterion here as a natural network analogue ofHamilton's classical rule for kin selection, despite arising in an entirelydifferent context. The result is a network-based evolutionary rule for altruismthat parallels Hamilton's genetic rule.

A network criterion for the success of cooperation in an evolutionary prisoner's dilemma, and a variation on Hamilton's rule