Genes vary in their likelihood to undergo adaptive evolution. The genomic factors that determine adaptability, however, remain poorly understood. Genes function in the context of molecular networks, with some occupying more important positions than others and thus being likely to be under stronger selective pressures. However, how positive selection distributes across the different parts of molecular networks is still not fully understood. Here, we inferred positive selection using comparative genomics and population genetics approaches through the comparison of 10 mammalian and 270 human genomes, respectively. In agreement with previous results, we found that genes with lower network centralities are more likely to evolve under positive selection (as inferred from divergence data). Surprisingly, polymorphism data yield results in the opposite direction than divergence data: Genes with higher centralities are more likely to have been targeted by recent positive selection during recent human evolution. Our results indicate that the relationship between centrality and the impact of adaptive evolution highly depends on the mode of positive selection and/or the evolutionary time-scale.