This paper characterizes efficient networks in player and partner heterogeneity models for both the two‐way flow and the one‐way flow networks. Player (partner) dependent network formation allows benefits and costs to be player (partner) heterogeneous, which is an important extension for modeling social networks in the real world. This paper shows that efficient networks are minimally connected and have either a star‐type or a variation of star‐type architectures in the two‐way flow model, and have the wheel architecture in the one‐way flow model.