We study general properties of pairwise stable networks in homogeneous societies, i.e. when

agents' utilities differ only with respect to their network position while their names do not

matter. Rather than assuming a particular functional form of utility, we impose general link

externality conditions on utility such as ordinal convexity and ordinal strategic complements.

Depending on these rather weak notions of link externalities, we show that pairwise stable

networks of various structure exist. For stronger versions of the convexity and strategic

complements conditions, we are even able to characterize all pairwise stable networks: they

are nested split graphs (NSG). We illustrate these results with many examples from the

literature, including utility funtions that arise from games with strategic complements played

on the network and utility funtions that depend on centrality measures such as Bonacich

centrality.