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

作　　者：KUANG Li ZHENG BoJin LI DeYi LI YuanXiang SUN Yu 

机构地区：[1]State Key Laboratory of Software Engineering,Computer School,Wuhan University [2]College of Computer Science,South-Central University For Nationalities [3]School of Software,Tsinghua University [4]School of Computer and Electronics and Information,Guangxi University

出　　处：《Science China(Information Sciences)》2015年第1期175-184,共10页中国科学（信息科学）（英文版）

基　　金：financially supported by Doctoral Fund of Ministry of Education of China (Grant No. 20100141120046);Natural Science Foundation of Hubei Province of China (Grant No. 2010CDB08504);111 Programme of Introducing Talents of Discipline to Universities (Grant No. B07037);Wuhan University Academic Development Plan for Scholars After the 1970s ("Research on Internet User Behavior");State Key Laboratory of Software Engineering of China (Grant No. SKLSE2012-09-15);Fundamental Research Funds for the Central Universities (Grant No. CZY13010);China Scholarship Council;National Nature Science Foundation of China (Grant No. 61103125)

摘　　要：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.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.

关 键 词：SCALE-FREE fractal network SELF-SIMILARITY fractal dimension hub attraction 

分 类 号：O157.5[理学—数学]