An Evolving model of online bipartite networks

Understanding the structure and evolution of online bipartite networks is a significant task since they play a crucial role in various e-commerce services nowadays. Recently, various attempts have been tried to propose different models, resulting in either power-law or exponential degree distributions.However, many empirical results show that the user degree distribution actually follows a shifted power-law distribution, so-called \emph{Mandelbrot law}, which cannot be fully described by previous models. In this paper, we propose an evolving model, considering two different user behaviors: random and preferential attachment. Extensive empirical results on two real bipartite networks, \emph{Delicious} and \emph{CiteULike}, show that the theoretical model can well characterize the structure of real networks for both user and object degree distributions. In addition, we introduce a structural parameter $p$, to demonstrate that the hybrid user behavior leads to the shifted power-law degree distribution, and the region of power-law tail will increase with the increment of $p$. The proposed model might shed some lights in understanding the underlying laws governing the structure of real online bipartite networks.