In this work, we analyze the degree frequency distribution in the yeast protein interaction network bystudying a previously proposed duplication network model. This model correctly predicts the observed degreedistribution ͑a power law for large degree values and a departure from this behavior for small degree͒. Wenumerically and analytically characterize this distribution as a mixture of random and power-law behavior, andmake a comparative study of the robustness of the network model against realistic perturbations. We concludethat the particular distribution observed in both the model and the experimental data has many advantages interms of dynamical and topological robustness and could have emerged in the evolutionary history as a sort ofcompromise between purely deterministic and random underlying mechanisms of network growth.