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We generalize the analysis of Brueckner's [(2006). Friendship networks. Journal of Regional Science, 847–865] friendship networks under different types of asymmetries. We first study cost asymmetries by allowing for cost-magnetic agents. These are players whose linking costs are the lowest. Next we focus on network-based asymmetries by allowing for knows-everyone agents. We identify conditions under which Nash networks are interlinked stars in both these cases. We also find that for asymmetric situations (whether in costs, values, or architectures), the equilibrium effort choices regarding the links between different types of agents are robust across the various friendship network models. [ABSTRACT FROM AUTHOR]