In this work we study the emergence of mutational robustness in the evolution of several example proteins and how robustness is related to underlying phenotype space. We employ a Wright Fisher model where a population of proteins is randomly mutated and selected for energy of folding with various selection models in the presence and absence of genetic drift. Protein coordinates were obtained from the protein data bank. Our model predicts that the fluctuations of mutational robustness are exponentially distributed and that robustness is a consequence of a topological phase transition in genotype space. The process that drives this transition is described by Bianconi-Barabási model for preferential attachment. Additionally the emergence of error minimization is observed along with this phase transition.