The power-law degree distribution of scale-free networks plays an important role in the bloom of cooperation in the evolutionary games performed on them. In this paper we apply prisoner’s dilemma and public goods game on a family of scale-free networks with the same degree sequence, and show that power-law behavior alone does not determine the cooperative behavior in scale-free networks. Instead, we present that the direct connections among large-degree nodes have a crucial influence on the evolution of cooperation in the scale-free network family.
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