A fractal and scale-free model of complex networks with hub attraction behaviors

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• 作者：Li Kuang (1)
  BoJin Zheng (1) (2)
  DeYi Li (3)
  YuanXiang Li (1)
  Yu Sun (4)
  
  1. State Key Laboratory of Software Engineering ; Computer School ; Wuhan University ; Wuhan ; 430072 ; China
  2. College of Computer Science ; South-Central University For Nationalities ; Wuhan ; 430074 ; China
  3. School of Software ; Tsinghua University ; Beijing ; 100084 ; China
  4. School of Computer and Electronics and Information ; Guangxi University ; Nanning ; 530004 ; China
  
• 关键词：scale ; free ; fractal network ; self ; similarity ; fractal dimension ; hub attraction ; 012111
• 刊名：SCIENCE CHINA Information Sciences
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：58
• 期：1
• 页码：1-10
• 全文大小：788 KB
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• 刊物类别：Computer Science
• 刊物主题：Chinese Library of Science
  Information Systems and Communication Service
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1919

文摘

It is widely believed that fractality of complex networks originate from hub repulsion behaviors (anticorrelation or disassortativity), which means that large degree nodes tend to connect with small degree nodes. This hypothesis was demonstrated by a dynamical growth model, which evolves as the inverse renormalization procedure, proposed by Song et al. Now we find that the dynamical growth model is based on the assumption that all the cross-box links have the same probability e to link to the most connected nodes inside each box. Therefore, we modify the growth model by adopting the flexible probability e, which makes hubs to have higher probability to connect with hubs than non-hubs. With this model, we find that some fractal and scale-free networks have hub attraction behaviors (correlation or assortativity). The results are the counter-examples of former beliefs. Actually, the real-world collaboration network of movie actors also is fractal and shows assortative mixing.