复杂网络中社团结构发现的多分辨率密度模块度

张聪; 沈惠璋; 李峰; 杨何群

doi:10.7498/aps.61.148902

摘要

现实中的许多复杂网络呈现出明显的模块性或社团性.模块度是衡量社团结构划分优劣的效益函数, 它也通常被用作社团结构探测的目标函数,但最为广泛使用的Newman-Girvan模块度却存在着分辨率限制问题,多分辨率模块度也不能克服误合并社团和误分裂社团同时存在的缺陷. 本文在网络密度的基础上提出了多分辨率的密度模块度函数, 通过实验和分析证实了该函数能够使社团结构的误划分率显著降低, 而且能够体现出网络社团结构是一个有机整体,不是各个社团的简单相加.

关键词:

Abstract

In reality many complex networks present modules or community structures obviously. Modularity is a benefit function used in quantifying the quality of a division of a network into communities. And it usually can be used as a basis for optimization methods of detecting community structure in networks. But the most popular modularity which is proposed by M. E. J. Newman and M. Girvan has the resolution limit in community detection. Multi-resolution modularity cannot overcome the misclassifications caused by merging and splitting the communities either. In this paper, we propose a multi-resolution density modularity based on the network density. The proposed function is tested on the artificial networks. Computational results show that it can reduce the rate of misclassification considerably. And the systematicness of the community structures can be demonstrated by the multi-resolution density modularity.

Keywords:

作者及机构信息

1.
上海交通大学安泰经济与管理学院, 上海 200052;

2.
上海市卫星遥感与测量应用中心, 上海 201199

基金项目: 国家自然科学基金(批准号: 71071096, 71001068)资助的课题.

Authors and contacts

1.
Antai College of Economics and Management, Shanghai Jiaotong University, Shanghai 200052, China;

2.
Shanghai Center for Satellite Remote Sensing and Measurement Application, Shanghai 201199, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 71071096, 71001068).

参考文献

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[19]	Zhang S, Wang R S, Zhang X S 2007 Physica A 374 483
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[23]	Shen Y, Xu H L 2010 Acta Phys. Sin. 59 6022 (in Chinese) [沈毅, 徐焕良 2010 59 6022]
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[26]	Newman M E J, Girvan M 2004 Phys. Rev. E 69 026113
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[28]	Rosvall M, Bergstrom C T 2007 Proc. Natl. Acad. Sci. USA 104 7327
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[30]	Li Z, Zhang S, Wang R S 2008 Phys. Rev. E 77 036109
[31]	Radicchi F, Castellano C, Cecconi F, Loreto V, Parisi D 2004 Proc. Natl. Acad. Sci. USA 101 2658
[32]	Reichardt J, Bornholdt S 2006 Phys. Rev. E 74 016110
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[34]	Lancichinetti A, Fortunato S 2011 arXiv: 1107. 1155v1 [physics. soc-ph]
[35]	Lancichinetti A, Fortunato S, Radicchi F 2008 Phys. Rev. E 78 046110

施引文献

[1]	Wang X F, Li X, Chen G R 2006 Complex Networks Theory and its Application (Beijing: Tsinghua University Press) (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)]
[2]	He D R, Lin Z H, Wang B H 2008 Complex System and Complex Networks (Beijing: Higher Education Press) (in Chinese) [何大韧, 刘宗华, 汪秉宏 2008 复杂系统与复杂网络 (北京: 高等教育出版社)]
[3]	Wang L, Dai G Z 2009 Scale-free Feature, Phenomena and Control in Complex Networks (Beijing: Science Press) (in Chinese) [王林, 戴贯中 2009 复杂网络的Scale-free性、Scale-free现象及其控制 (北京: 科学出版社)]
[4]	Zhang P P, He Y, Zhou T, Su B B, Chang H, Zhou Y P, Wang B H, He D R 2006 Acta Phys. Sin. 55 60 (in Chinese) [张培培, 何阅, 周涛, 苏蓓蓓, 常慧, 周月平, 汪秉宏, 何大韧 2006 55 60]
[5]	Liu H K, Zhou T 2007 Acta Phys. Sin. 56 106 (in Chinese) [刘宏鲲, 周涛 2007 56 106]
[6]	Xu D, Li X, Wang X F 2007 Acta Phys. Sin. 56 1313 (in Chinese) [许丹, 李翔, 汪小帆 2007 56 1313]
[7]	Albert R, Jeong H, Barabasi A L 1999 Nature 401 130
[8]	Andrei B, Ravi K, Farzin M, Prabhakar R, Sridhar R, Raymie S, Andrew T, Janet W 2000 Comput. Netw. 33 309
[9]	Williams R J, Martinez N D 2000 Nature 404 180
[10]	Amaral L A N, Scala A, Barthelemy M, Stanley H E 2000 Proc. Natl. Acad. Sci. USA 97 11149
[11]	Gleiser P, Danon L 2003 Adv. Complex Syst. 6 565
[12]	Fortunato S 2010 Phys. Rep. 486 75
[13]	Girvan M, Newman M E J 2002 Proc. Natl. Acad. Sci. USA 99 7821
[14]	Newman M E J 2009 Phys. Rev. Lett. 103 058701
[15]	Newman M E J 2004 Eur. Phys. J. B 38 321
[16]	Sales-Pardo M, Guimera R, Moreira A A, Amaral L A N 2007 Proc. Natl. Acad. Sci. USA 104 15224
[17]	Blondel V D, Guillaume J L, Lambiotte R, Lefebvre E 2008 J. Stat. Mech. 2008 10008
[18]	Shen H, Cheng X, Cai K, Hu M B 2009 Physica A 388 1706
[19]	Zhang S, Wang R S, Zhang X S 2007 Physica A 374 483
[20]	Zhang S Wang R S, Zhang X S 2007 Phys. Rev. E 76 046103
[21]	Gao Z K, Jin N D 2008 Acta Phys. Sin. 57 6909 (in Chinese) [高忠科, 金宁德 2008 57 6909]
[22]	Wang J W, Rong L L 2009 Acta Phys. Sin. 58 3714 (in Chinese) [王建伟, 荣莉莉 2009 58 3714]
[23]	Shen Y, Xu H L 2010 Acta Phys. Sin. 59 6022 (in Chinese) [沈毅, 徐焕良 2010 59 6022]
[24]	Wang G X, Shen Y 2010 Acta Phys. Sin. 59 842 (in Chinese) [王高峡, 沈轶 2010 59 842]
[25]	Shao F, Jiang G P 2011 Acta Phys. Sin. 60 078902 (in Chinese) [邵斐, 蒋国平 2011 60 078902]
[26]	Newman M E J, Girvan M 2004 Phys. Rev. E 69 026113
[27]	Fortunato S, Barthélemy M 2007 Proc. Natl. Acad. Sci. USA 104 36
[28]	Rosvall M, Bergstrom C T 2007 Proc. Natl. Acad. Sci. USA 104 7327
[29]	Muff S, Rao F, Caflisch A 2005 Phys. Rev. E 72 056107
[30]	Li Z, Zhang S, Wang R S 2008 Phys. Rev. E 77 036109
[31]	Radicchi F, Castellano C, Cecconi F, Loreto V, Parisi D 2004 Proc. Natl. Acad. Sci. USA 101 2658
[32]	Reichardt J, Bornholdt S 2006 Phys. Rev. E 74 016110
[33]	Arenas A, Fernández A, Gómez S 2008 New J. Phys. 10 053039
[34]	Lancichinetti A, Fortunato S 2011 arXiv: 1107. 1155v1 [physics. soc-ph]
[35]	Lancichinetti A, Fortunato S, Radicchi F 2008 Phys. Rev. E 78 046110

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