A new network structure entropy based node difference and edge difference

Cai Meng; Du Hai-Feng; Ren Yi-Ke; Marcus W

doi:10.7498/aps.60.110513

Abstract

Entropy is a very important indicator which describes the heterogeneity of the networks. Two kinds of structure entropies, which are based on degree distribution and relative degree respectively, have some problems to describe the characteristics of network structure. Because they focus only on one of node or edge factors. In this paper, We consider the difference between node and edge to define a new network structure entropy. The theoretical analyses and the simulation experiments on regular network, random network and scale-free network prove that this new network structure entropy is more effective to reflect the characteristics of network structure, especially more reasonable to describe the sparse network and star network.

Keywords:

Authors and contacts

1.
School of Management, Xi'an Jiaotong University, Xi'an 710049,China;
2.
Center for Administration and Complexity Science, Xi'an Jiaotong University, Xi'an 710049, China;
3.
School of Management, Shanxi Normal University, Linfen 041004, China;
4.
Morrison Institute for Population and Resource Studies,Stanford University,Stanford 94305,USA

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Cited By

[1]	Bose T, Trimper S 2009 Phys. Rev. E 79 051903
[2]	Gumel A B, McCluskey C C, Vanden Priessche P 2006 Bull. Math. Biol. 68 2105
[3]	Wang Y,Zheng Z G 2009 Acta Phys. Sin. 58 4421 (in Chinese)[王延、郑志刚 2009 58 4421]
[4]	Wang Y Q,Jiang G P 2010 Acta Phys. Sin. 59 6734 (in Chinese)[王亚奇、蒋国平 2010 59 6734]
[5]	Song Y R,Jiang G P 2009 Acta Phys. Sin. 58 5911 (in Chinese)[宋玉蓉、蒋国平 2009 58 5911]
[6]	Song Y R,Jiang G P 2010 Acta Phys. Sin. 59 705 (in Chinese)[宋玉蓉、蒋国平 2010 59 705]
[7]	Piot P, Bartos M, Ghys P D, Walker N, Schwartl B 2001 Nature 410 968
[8]	Helbing D, Molini R 1995 Phys. Lett. A 212 130
[9]	Song Y R,Jiang G P 2010 Acta Phys. Sin. 59 7546 (in Chinese)[宋玉蓉、蒋国平 2010 59 7546]
[10]	Sole’R V,Valverde S 2004 Lect. Notes Phys. 650 189
[11]	Costa L F,Rodrigues F A,Travieso G,Boas P R V 2007 Adv. in Phy. 56 167
[12]	Wu J,Tan Y J,Deng H Z,Zhu D Z 2007 Sys. Engin. Theo. Pract. 27 101 (in Chinese)[吴俊、谭跃进、郑宏钟、朱大智 2007 系统工程理论与实践 27 101]
[13]	Wang B,Tang H W,Guo C H,Xiu Z L 2006 Phys. A 363 591
[14]	Tan Y J,Wu J 2004 Syst. Engin. Theo. Prac. 24 1 (in Chinese)[谭跃进、吴俊 2004系统工程理论与实践 24 1]
[15]	Newman M E J,Park J 2003 Phys. Rev. E 68 036122
[16]	Wang X F,Li X,Chen G R 2006 Complex Network Theory and Application (Vol. 1)(Beijing: Tsinghua University Press)p18(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18页]
[17]	Erods P,Renyi A 1960 Publ. Math. Inst. Hungary Acd. Sci. 5 17
[18]	Li J,Xiao J H,Jiang P Q,Zhou T,Wang W X 2006 Acta Phys. Sin. 55 4051 (in Chinese)[李季、肖井华、蒋品群、周涛、王文旭 2006 55 4051]
[19]	Pan Z F,Wang X F 2006 Acta Phys. Sin. 55 4058 (in Chinese)[潘灶烽、汪小帆 2006 55 4058]
[20]	Barabasi A L,Albert R 1999 Science 286 509
[21]	He D R,Liu Z H,Wang B H 2009 Complex Systems and Complex Networks(Vol. 1)(Beijing: Higher Education Press)p141(in Chinese)[何大韧、刘宗华、汪秉宏 2009复杂系统与复杂网络 (北京:高等教育出版社) 第141页]
[22]	Wang L,Dai G Z 2009 Scale-free Characteristic,Scale-free Phenomenon and Their Control of Complex Networks (Vol. 1) (Beijing: Science Press)p38(in Chinese)[王林、戴冠中 2009复杂网络的Scale-free性、Scale-free现象及其控制 (北京:科学出版社) 第38页]
[23]	Newman M E J 2005 Social Network 27 39
[24]	Fischback K, Gloor P A, Schoder D 2009 Busin. Inform. Sys. Engin. 1 140
[25]	Salathé M, Kazandjieva M, Lee J W, Leris P, Feldman M W, Jones J H 2010 PNSA 107 22020

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Vol. 60, Issue 11 - 2011-06-05

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