Much of the large-scale molecular data from living cells can be represented in terms of networks. Such networks occupy a central position in cellular systems biology. In the protein-protein interaction (PPI) network, nodes represent proteins and edges represent connections between them, based on experimental evidence. As PPI networks are rich and complex, a mathematical model is sought to capture their properties and shed light on PPI evolution. The mathematical literature contains various generative models of random graphs. It is a major, still largely open question, which of these models (if any) can properly reproduce various biologically interesting networks. Here, we consider this problem where the graph at hand is the PPI network of Saccharomyces cerevisiae. We are trying to distinguishing between a model family which performs a process of copying neighbors, represented by the duplication-divergence (DD) model, and models which do not copy neighbors, with the Barabxc3xa1si-Albert (BA) preferential attachment model as a leading example.