Human society operates on large-scale cooperation. However, individual differences in cooperativeness and incentives to free-ride on others’ cooperation make large-scale cooperation fragile and can lead to reduced social-welfare. Thus, how individual cooperation spreads through human social networks remains puzzling from ecological, evolutionary and societal perspectives. Here, we identify oxytocin and costly punishment as biobehavioral mechanisms that facilitate the propagation of cooperation in social networks. In three laboratory experiments ( n = 870 human participants, 373 males and 497 females), individuals were embedded in heterogeneous networks and made repeated decisions with feedback in games of trust ( n = 342), ultimatum bargaining ( n = 324), and prisoner’s dilemma with punishment ( n = 204). In each heterogeneous network, individuals at central positions (hub nodes) were given intranasal oxytocin (or placebo). Giving oxytocin (versus matching placebo) to central individuals increased their tr...