Probabilistic Model for Biological Networks

Recently there has been considerable interest in studying biological networks such as gene regulatory networks and protein-protein interaction networks. Are biological networks different from other large complex networks? Both large biological and other networks have power law degree distribution, yet the exponents fall into different ranges. This may be because random elimination of the information in the genome is a dominant evolutionary force in shaping biological networks. In this paper, we give a probabilistic model to examine the evolution of biological networks by random elimination processes of node degree as well as the preferential choice mechanisms. For the model, it is proved that there is a stationary power law degree distribution with exponents less than 2, consist with current data on biological networks.