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Genes and proteins interact in many ways to form complex networks that are amenable to graph-theoretic analyses. We show that the protein-protein interaction network in yeast, while possessing a power-law degree distribution, actually admits various "scales" that enable one to identify different classes of proteins based on their network properties alone. This classification further results in the identification of functionally homogenous sub-networks and thus provides clues towards predicting the function of unannotated proteins. We also show that protein interaction network properties can be used to predict synthetically lethal pairs of genes in yeast with reasonable accuracy. Finally, we discuss how a combined analysis of seven putative predictors of evolutionary rates of yeast genes, including two network properties, reveals a single dominant predictor for evolutionary rate that is linked to the number of translation events.