Protein-protein interaction networks have evolved mainly through connectivity rewiring and gene duplication. However, how protein function influences these processes and how a network grows in time have not been well studied. Using protein-protein interaction data and genomic data from the budding yeast, we first examined whether there is a correlation between the age and connectivity of yeast proteins. A steady increase in connectivity with protein age is observed for yeast proteins except for those that can be traced back to Eubacteria. Second, we investigated whether protein connectivity and duplicability vary with gene function. We found a higher average duplicability for proteins interacting with external environments than for proteins localized within intracellular compartments. For example, proteins that function in the cell periphery (mainly transporters) show a high duplicability but are lowly connected. Conversely, proteins that function within the nucleus (e.g., transcription, RNA and DNA metabolisms, and ribosome biogenesis and assembly) are highly connected but have a low duplicability. Finally, we found a negative correlation between protein connectivity and duplicability.