An evolving model of online bipartite networks

• Published in: Physica A 2013-12, Vol.392 (23), p.6100-6106
• Main Authors: Zhang, Chu-Xu, Zhang, Zi-Ke, Liu, Chuang
• Format: Article
• Language: English
• Subjects: Bipartite networks; Empirical analysis; Evolution; Evolving model; Law; Mathematical models; Network dynamics; Networks; On-line systems; Online; Tasks
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2013.07.027

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, the so-called Mandelbrot’s 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, Delicious and 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. •We propose a model to show the user selection and item patterns.•It shows the model can characterize network of user and object degree distributions.•We introduce a structural parameter to show the hybrid behavior leads to the results.•We apply the model in two real datasets and show good agreements.