Protein interactions are central to most biological processes. We investigated the dynamics of emergence of the protein interaction network of Saccharomyces cerevisiae by mapping origins of proteins on an evolutionary tree. We demonstrate that evolutionary periods are characterized by distinct connectivity levels of the emerging proteins. We found that the most-connected group of proteins dates to the eukaryotic radiation, and the more ancient group of pre-eukaryotic proteins is less connected. We show that functional classes have different average connectivity levels and that the time of emergence of these functional classes parallels the observed connectivity variation in evolution. We take these findings as evidence that the evolution of function might be the reason for the differences in connectivity throughout evolutionary time. We propose that the understanding of the mechanisms that generate the scale-free protein interaction network, and possibly other biological networks, requires consideration of protein function.