Scaling of weighted spectral distribution in weighted small-world networks

doi:10.1088/1674-1056/26/2/028901

中国物理B ›› 2017, Vol. 26 ›› Issue (2): 28901-028901.doi: 10.1088/1674-1056/26/2/028901

• INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇下一篇

Scaling of weighted spectral distribution in weighted small-world networks

Bo Jiao(焦波), Xiao-Qun Wu(吴晓群)

1 Luoyang Electronic Equipment Test Center, Luoyang 471003, China;
2 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2016-09-26 修回日期:2016-11-01 出版日期:2017-02-05 发布日期:2017-02-05
通讯作者: Bo Jiao E-mail:jiaoboleetc@outlook.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61402485, 61573262, and 61303061).

Scaling of weighted spectral distribution in weighted small-world networks

Bo Jiao(焦波)¹, Xiao-Qun Wu(吴晓群)²

1 Luoyang Electronic Equipment Test Center, Luoyang 471003, China;
2 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2016-09-26 Revised:2016-11-01 Online:2017-02-05 Published:2017-02-05
Contact: Bo Jiao E-mail:jiaoboleetc@outlook.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61402485, 61573262, and 61303061).

摘要/Abstract

摘要： Many real-world systems can be modeled by weighted small-world networks with high clustering coefficients. Recent studies for rigorously analyzing the weighted spectral distribution (WSD) have focused on unweighted networks with low clustering coefficients. In this paper, we rigorously analyze the WSD in a deterministic weighted scale-free small-world network model and find that the WSD grows sublinearly with increasing network order (i.e., the number of nodes) and provides a sensitive discrimination for each input of this model. This study demonstrates that the scaling feature of the WSD exists in the weighted network model which has high and order-independent clustering coefficients and reasonable power-law exponents.

关键词: weighted spectral distribution, weighted small-world network, scaling

Abstract: Many real-world systems can be modeled by weighted small-world networks with high clustering coefficients. Recent studies for rigorously analyzing the weighted spectral distribution (WSD) have focused on unweighted networks with low clustering coefficients. In this paper, we rigorously analyze the WSD in a deterministic weighted scale-free small-world network model and find that the WSD grows sublinearly with increasing network order (i.e., the number of nodes) and provides a sensitive discrimination for each input of this model. This study demonstrates that the scaling feature of the WSD exists in the weighted network model which has high and order-independent clustering coefficients and reasonable power-law exponents.

Key words: weighted spectral distribution, weighted small-world network, scaling

中图分类号: (Structures and organization in complex systems)

89.75.Fb

89.75.Da (Systems obeying scaling laws)

焦波, 吴晓群. Scaling of weighted spectral distribution in weighted small-world networks[J]. 中国物理B, 2017, 26(2): 28901-028901.

Bo Jiao(焦波), Xiao-Qun Wu(吴晓群). Scaling of weighted spectral distribution in weighted small-world networks[J]. Chin. Phys. B, 2017, 26(2): 28901-028901.

参考文献 33

[1]	Fay D, Haddadi H, Thomason A, Moore A W, Mortier R, Jamakovic A, Uhlig S and Rio M 2010 IEEE ACM T. Network 18 164
[2]	Fay D, Haddadi H, Uhlig S, Kilmartin L, Moore A W, Kunegis J and Lliofotou M 2011 Comput. Netw. 55 3458
[3]	Haddadi H, Fay D, Jamakovic A, Maennel O, Moore A W, Mortier R and Uhlig S 2009 21st International Teletraffic Congress, September 15-17, Paris, France, p. 1
[4]	Jiao B, Zhou Y, Du J, Huang C, Lu Z and Liu Y 2014 IET Commun. 8 2845
[5]	Jiao B, Shi J, Wu X, Nie Y, Huang C, Du J, Zhou Y, Guo R and Tao Y 2016 Chaos 26 023110
[6]	Jiao B, Nie Y, Shi J, Huang C, Zhou Y, Du J, Guo R and Tao Y 2016 Physica A 451 632
[7]	Jiao B, Nie Y, Huang C, Du J, Guo R, Huang F and Shi J 2016 Chin. Phys. B 25 058901
[8]	Jiao B and Shi J 2016 Comput. Commun. 76 77
[9]	Jiao B, Nie Y, Shi J, Lu G, Zhou Y and Du J 2016 Telecommun. Syst. 62 231
[10]	Burda Z, Correia J D and Krzywicki A 2001 Phys. Rev. E 64 046118
[11]	Dorogovtsev S N, Goltsev A V and Mendes J F F 2002 Phys. Rev. E 65 066122
[12]	Chung F and Radcliffe M 2011 Electron. J. Comb. 18 215
[13]	Zou Z Y, Liu P, Li L and Gao J Z 2012 Chin. Phys. B 21 028904
[14]	Xu X L, Liu C P and He D R 2016 Chin. Phys. Lett. 33 048901
[15]	Guo J L 2014 Chin. Phys. B 23 070206
[16]	Shu P P, Wang W, Tang M and Shang M S 2015 Acta Phys. Sin. 64 208901 (in Chinese)
[17]	Zhang J Y, Sun W G and Chen G R 2012 Chin. Phys. B 21 038901
[18]	Sun W G, Zhang J Y and Chen G R 2013 Chin. Phys. B 22 108904
[19]	Dai M, Hou J, Gao J, Su W, Xi L and Ye D 2016 Chaos, Solitons & Fractals 87 268
[20]	Barab'si A L, Ravasz E and Vicsek T 2001 Physica A 299 559
[21]	Zhang Z, Rong L and Guo C 2006 Physica A 363 567
[22]	Zhang Z, Rong L and Zhou S 2007 Physica A 377 329
[23]	Zhang Y, Zhang Z, Zhou S and Guan J 2010 Physica A 389 3316
[24]	Comellas F and Miralles A 2010 Phys. Rev. E 81 061103
[25]	Dai M, Chen D, Dong Y and Liu J 2012 Physica A 391 6165
[26]	Sun Y, Dai M and Xi L 2014 Physica A 407 110
[27]	Dai M, Li X and Xi L 2013 Chaos 23 033106
[28]	Zhang Z, Lin Y and Guo X 2015 Phys. Rev. E 91 062808
[29]	Zhang Z, Sheng Y, Hu Z and Chen G 2012 Chaos 22 043129
[30]	Dai M, Wang X and Chen D 2012 Chaos, Solitons & Fractals 45 137
[31]	Zhang Y, Aziz-Alaoui M A, Bertelle C, Zhou S and Wang W 2014 J. Phys. A: Math. Theor. 47 225003
[32]	Zhang Y, Zhou S, Zhang Z, Guan J and Zhou S 2013 Phys. Rev. E 87 032133
[33]	Barrat A, Barthelemy M and Vespignani A 2004 Phys. Rev. E 70 066149

Scaling of weighted spectral distribution in weighted small-world networks

Scaling of weighted spectral distribution in weighted small-world networks

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 33

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Mu-Hong Hu(胡木宏), Nan Wang(王楠), Pin-Jun Ouyang(欧阳品均),Xin-Jie Feng(冯新杰), Yang Yang(杨扬), and Chen-Sheng Wu(武晨晟). Energy levels and magnetic dipole transition parameters for the nitrogen isoelectronic sequence[J]. 中国物理B, 2022, 31(9): 93101-093101.
[2]	Shu-Xing Wang(汪书兴) and Lin-Fan Zhu(朱林繁). Integral cross sections for electron impact excitations of argon and carbon dioxide[J]. 中国物理B, 2022, 31(8): 83401-083401.
[3]	Zeyu Zhang(张泽宇), Qiang Zhang(张强), and Wenbo Mi(米文博). Anomalous Hall effect of facing-target sputtered ferrimagnetic Mn₄N epitaxial films with perpendicular magnetic anisotropy[J]. 中国物理B, 2022, 31(4): 47305-047305.
[4]	Yanbang Chu(褚衍邦), Le Liu(刘乐), Yiru Ji(季怡汝), Jinpeng Tian(田金朋), Fanfan Wu(吴帆帆), Jian Tang(汤建), Yalong Yuan(袁亚龙), Yanchong Zhao(赵岩翀), Xiaozhou Zan(昝晓州), Rong Yang(杨蓉), Kenji Watanabe, Takashi Taniguchi, Dongxia Shi(时东霞), Wei Yang(杨威), and Guangyu Zhang(张广宇). Observation of quadratic magnetoresistance in twisted double bilayer graphene[J]. 中国物理B, 2022, 31(10): 107201-107201.
[5]	Shun Wang(王顺) and Wei-Chao Jiang(姜维超). Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator[J]. 中国物理B, 2022, 31(1): 13201-013201.
[6]	苏桂锋, 李晓温, 张小兵, 张一. Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks[J]. 中国物理B, 2020, 29(8): 88904-088904.
[7]	王与烨, 任宇琛, 徐德刚, 唐隆煌, 贺奕焮, 宋词, 陈霖宇, 李长昭, 闫超, 姚建铨. Energy scaling and extended tunability of a ring cavity terahertz parametric oscillator based on KTiOPO₄ crystal[J]. 中国物理B, 2018, 27(11): 114213-114213.
[8]	周志刚, 蒋亦民, 厚美瑛. Ultrasound wave propagation in glass-bead packing under isotropic compression and uniaxial shear[J]. 中国物理B, 2017, 26(8): 84502-084502.
[9]	董善思, 韩秋静, 张敬涛. Equivalent electron correlations in nonsequential double ionization of noble atoms[J]. 中国物理B, 2017, 26(2): 23202-023202.
[10]	李春彪, 张若洵, 陆天爱. Linear synchronization and circuit implementation of chaotic system with complete amplitude control[J]. 中国物理B, 2017, 26(12): 120501-120501.
[11]	谢含章, 蒋纯, 谢柏松. Studies on convergence and scaling law of Thomson backscattering spectra in strong fields[J]. 中国物理B, 2017, 26(12): 124101-124101.
[12]	于杰, 陈坤基, 马忠元, 张鑫鑫, 江小帆, 吴仰晴, 黄信凡, Shunri Oda. Scaling dependence of memory windows and different carrier charging behaviors in Si nanocrystal nonvolatile memory devices[J]. 中国物理B, 2016, 25(9): 97304-097304.
[13]	焦波, 聂原平, 黄赪东, 杜静, 郭荣华, 黄飞, 石建迈. Stability of weighted spectral distribution in a pseudo tree-like network model[J]. 中国物理B, 2016, 25(5): 58901-058901.
[14]	万吴兵, 吕红红, 候格, 吴晨旭. Static and dynamic properties of polymer brush with topological ring structures: Molecular dynamic simulation[J]. 中国物理B, 2016, 25(10): 106101-106101.
[15]	张振刚, 丁卓, 樊京芳, 孟君, 丁益民, 叶方富, 陈晓松. Structural and robustness properties of smart-city transportation networks[J]. 中国物理B, 2015, 24(9): 90201-090201.