有倾向性重连产生的反匹配网络

屈静; 王圣军

doi:10.7498/aps.64.198901

摘要

在具有网络结构的系统中度关联属性对于动力学行为具有重要的影响, 所以产生适当度关联网络的方法对于大量网络系统的研究具有重要的作用. 尽管产生正匹配网络的方法已经得到很好的验证, 但是产生反匹配网络的方法还没有被系统的讨论过. 重新连接网络中的边是产生度关联网络的一个常用方法. 这里我们研究使用重连方法产生反匹配无标度网络的有效性. 我们的研究表明, 有倾向的重连可以增强网络的反匹配属性. 但是有倾向重连不能使皮尔森度相关系数下降到-1, 而是存在一个依赖于网络参数的最小值. 我们研究了网络的主要参数对于网络度相关系数的影响, 包括网络尺寸, 网络的连接密度和网络节点的度差异程度. 研究表明在网络尺寸大的情况下和节点度差异性强的情况下, 重连的效果较差. 我们研究了真实Internet网络, 发现模型产生的网络经过重连不能达到真实网络的度关联系数.

关键词:

度关联网络 /
重连

Abstract

The degree correlation of nodes is known to considerably affect the network dynamics in systems with a complex network structure. Thus it is necessary to generate degree correlated networks for the study of network systems. The assortatively correlated networks can be generated effectively by rewiring connections in scale-free networks. However, disassortativity in scale-free networks due to rewiring has not been studied systematically.In this paper, we present the effectiveness of generating disassortative scale-free networks by rewiring the already formed structure of connections which are built using the evolving network model. In the rewiring, two randomly selected links are cut and the four ends are connected randomly by two new links. The rewiring will be reserved if the disassortativity changes to the direction we need, otherwise it will be aborted. However, if one or both of the new links already exist in the network or a node is connected to itself, the rewiring step is aborted and two new links are selected. Our result shows that the rewiring method can enhance the disassortativity of scale-free networks. However, it is notable that the disassortativity measured by the Pearson correlation coefficient cannot be tuned to-1 which is believed to be the complete disassortativity. We obtain that the minimum value of the Pearson correlation coefficient depends on the parameters of networks, and we study the effect of network parameters on the degree correlation of the rewired networks, including the network size, the connection density of the network, and the heterogeneity of node degrees in the network. The result suggests that the effect of rewiring process is poorer in networks with higher heterogeneity, large size and sparse density. Another measurement of degree correlation called Kendall-Gibbons' coefficient is also used here, which gives the value of degree correlation independent of the network size. We give the relation of Kendall-Gibbons' coefficient to network sizes in both original scale-free networks and rewired networks. Results show that there is no obvious variance in rewired networks when the network size changes. The Kendall-Gibbons' coefficient also shows that rewiring can effectively enhance the disassortativity of the scale-free network.We also study the effectiveness of rewiring by comparing it with two sets of data of real Internets. We use the evolving network model to generate networks which have the same parameters as the real Internet, including network sizes, connection density and degree distribution exponents. We obtain that the networks generated by rewiring procedure cannot reach the same degree correlation as the real networks. The degree distribution of real networks diverges from the model at the largest degree or the smallest degree, which provides a heuristic explanation for the special degree correlation of real networks. Therefore, the difference at the end of the distribution is not negligible.

Keywords:

degree correlated network /
rewiring

作者及机构信息

屈静,
王圣军

1.
陕西师范大学物理学与信息技术学院, 西安 710119

通信作者: 王圣军, wangshjun@snnu.edu.cn

基金项目: 国家自然科学基金(批准号: 11305098)、陕西省自然科学基础研究计划(批准号: 2014JQ1028)、中央高校基本科研业务费专项资金(批准号: GK201302008)和陕西师范大学交叉学科培育计划(批准号: 5)资助的课题.

Authors and contacts

1.
School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710119, China

Corresponding author: Wang Sheng-Jun, wangshjun@snnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11305098), the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2014JQ1028), the Fundamental Research Funds for the Central Universities, China (Grant No. GK201302008), and the Interdisciplinary Incubation Project of Shaanxi Normal University, China (Grant No. 5).

参考文献

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[21]	Wu Y, Li P, Chen M, Xiao J, Kurths J 2009 Physica A 388 2987
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[25]	Ren Z M, Liu J G, Shao F, Hu Z L, Guo Q 2013 Acta Phys. Sin. 62 108902(in Chinese) [任卓明, 刘建国, 邵凤, 胡兆龙, 郭强 2013 62 108902]
[26]	Rong Z, Li X, Wang X 2007 Phys. Rev. E 76 027101
[27]	Rong Z, Wu Z X 2009 Europhys. Lett. 87 30001
[28]	Rong Z, Wu Z X, Chen G 2013 Europhys. Lett. 102 68005
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施引文献

[1]	Goh K-I, Oh E, Kahng B, Kim D 2003 Phys. Rev. E 67 017101
[2]	Liu G, Li Y S, Zhang X P 2013 Chin. Phys. B 22 068901
[3]	Contreras M G A, Fagiolo G 2014 Phys. Rev. E 90 062812
[4]	Wang Z, Szolnoki A, Perc M 2014 Phys. Rev. E 90 032813
[5]	Mastrandrea R, Squartini T, Fagiolo G, Garlaschelli D 2014 Phys. Rev. E 90 062804
[6]	Pastor-Satorras R, Vzquez A, Vespignani A 2001 Phys. Rev. Lett. 87 258701
[7]	Kenmogne F, Yeml D, Kengne J, Ndjanfang D 2014 Phys. Rev. E 90 052921
[8]	Wang S J, Hilgetag C C, Zhou C 2011 Front. Comput. Neurosci. 5 30
[9]	Wang S J, Zhou C 2012 New J. Phys. 14 023005
[10]	Guez O C, Gozolchiani A, Havlin S 2014 Phys. Rev. E 90 062814
[11]	Xia H J, Li P P, Ke J H, Lin Z Q 2015 Chin. Phys. B 24 040203
[12]	Zhou T, Bai W J, Wang B H, Liu Z J, Yan G 2005 Physics 34 31 (in Chinese) [周涛, 柏文洁, 汪秉宏, 刘之景, 严钢 2005 物理 34 31]
[13]	Chen G R 2008 Advances in Mechanics 38 653 (in Chinese) [陈关荣 2008 力学进展 38 653]
[14]	Wang X F, Li X, Chen G R 2006 Complex Networks: Theory and It's Applications (Beijing: Tsinghua University Press) p49 (in Chinese) [汪小帆, 李翔, 陈关荣 2006 复杂网络理论及其应用 (北京: 清华大学出版社) 第49页]
[15]	Newman M E J 2002 Phys. Rev. Lett. 89 208701
[16]	Newman M E J 2003 SIAM Rev. 45 167
[17]	Hu M B, Jiang R, Wu Q S 2013 Chin. Phys. B 22 066301
[18]	Hu Y G, Wang S J, Jin T, Qu S X 2015 Acta Phys. Sin. 64 028901(in Chinese) [胡耀光, 王圣军, 金涛, 屈世显 2015 64 028901]
[19]	Wang S J, Wu A C, Wu Z X, Xu X J, Wang Y H 2007 Phys. Rev. E 75 046113
[20]	Menche J, Valleriani A, Lipowsky R 2010 Phys. Rev. E 81 046103
[21]	Wu Y, Li P, Chen M, Xiao J, Kurths J 2009 Physica A 388 2987
[22]	Menche J, Valleriani A, Lipowsky R 2010 Europhys. Lett. 89 18002
[23]	Jin Y G, Zhong S M, An N 2015 Chin. Phys. B 24 049202
[24]	Li R Q, Tang M, Xu B M 2013 Acta Phys. Sin. 62 168903(in Chinese) [李睿琪, 唐明, 许伯铭 2013 62 168903]
[25]	Ren Z M, Liu J G, Shao F, Hu Z L, Guo Q 2013 Acta Phys. Sin. 62 108902(in Chinese) [任卓明, 刘建国, 邵凤, 胡兆龙, 郭强 2013 62 108902]
[26]	Rong Z, Li X, Wang X 2007 Phys. Rev. E 76 027101
[27]	Rong Z, Wu Z X 2009 Europhys. Lett. 87 30001
[28]	Rong Z, Wu Z X, Chen G 2013 Europhys. Lett. 102 68005
[29]	Maslov S, Sneppen K 2002 Science 296 910
[30]	Watts D J, Strogatz S H 1998 Nature 393 440
[31]	Xulvi-Brunet R, Sokolov I M 2004 Phys. Rev. E 70 066102
[32]	Barabsi A L, Albert R 1999 Science 286 509
[33]	Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Phys. Rep. 424 175
[34]	Larremore D B, Shew W L, Restrepo J G 2011 Phys. Rev. Lett. 106 058101
[35]	Raschke M, Schlpfer M, Nibali R 2010 Phys. Rev. E 82 037102
[36]	Dorogovtsev S N, Ferreira A L, Goltsev A V, Mendes J F F 2010 Phys. Rev. E 81 031135
[37]	Zhou S, Mondragn R J 2007 New J. Phys. 9 173
[38]	Zhang G Q, Zhang G Q, Yang Q F, Cheng S Q, Zhou T 2008 New J. Phys. 10 123027

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