Scale-free property of copying model

We study and generalize the copying model of Kumar et al. [Stochastic models for the Web graph, FOCS 2000]. The basic idea is that a new Web is often made by copying an old one, and then changing some of the links. Our main contributions are as follows: we show that (1) the copying model of Kumar et al. does generate a power-law degree distribution as stated in Kumar et al. [Stochastic models for the Web graph, FOCS 2000]; (2) We generalize the Kumar et al. copying process. We prove that this generalized model has a power-law degree distribution and give the exact solution from the perspective of Markov chain.