Understanding the degree distribution pattern of protein-protein interaction networks

This paper aims to find the reason why protein-protein interaction networks present a unique degree distribution pattern, where the majority of the proteins are sparsely connected, while densely-connected proteins also exist. This paper proposes the random duplication graph model to depict protein-protein interaction networks, where the gene duplication process is modeled as random vertex duplication. And we show that it is the gene duplication process combined with the sparsely-connected initial condition that leads to the unique degree distribution pattern of protein-protein interaction networks. In addition, we make a further prediction based on our degree distribution function: as the gene duplication process proceeds, the percentage of densely-connected proteins becomes higher.