Latent space models for network formation assume that nodes possess latent attributes that determine their propensity to connect. We propose a new model for network formation, ranking networks, in which these attributes are rankings over some space of alternatives. Such rankings may reflect user preferences, relevance/quality judgements, etc., while ranking networks capture correlations of, say, user preferences across a social network. We present preliminary theoretical and empirical analyses of structural properties of such networks, and develop algorithmic approximations to help efficiently predict these properties. Empirical results demonstrate the quality of these approximations.