The Fractal Feature in Complex Networks

摘要：

In order to probe the complexity lies in complex network, the fractal feature is discussed in this paper. Inspired by the analogy of network growing and the inverse procedure of renormalization, a fractal modular tree model is established. By the fractal theory and Hausdorff measure, the critical state when the fractal structure emerges is analyzed and the fractal dimension which is one of the most important parameters to describe the complexity of fractal is studied. The results lies in three aspects: Firstly, the critical condition for emergence of fractal is a simple power law,which means complexity resides in simplicity.Secondly, the formula of fractal dimension is deduced showing that it can be computed by two system parameters m and a . Thirdly, the formula of Hausdorff measure is given to estimate the space covered by the network.Moreover, some empirical results in the reference are cited to validate our theoretical model.

关键词： Complex networks fractal modular tree model renormalization fractaldimension.

作者: Aili Fang Siying Zhang Haijun Zhang

作者单位: Institute of Complexity Science Qingdao University Qingdao, China Marketing department China mobile Beijing, China

会议类型: 国际会议

会议名称: 2007 Conference on Systems Science, Management Science and System Dynamics(第二届系统科学、管理科学与系统动力学国际会议)

会议地点: 上海

会议语种:英文

页码: 401-406

在线出版日期: 2007-10-19（万方平台首次上网日期，不代表论文的发表时间）