Poor–rich demarcation of Matthew effect on scale-free systems and its application

doi:10.1088/1674-1056/20/4/040205

中国物理B ›› 2011, Vol. 20 ›› Issue (4): 40205-040205.doi: 10.1088/1674-1056/20/4/040205

Poor–rich demarcation of Matthew effect on scale-free systems and its application

董明¹, Abdelaziz Bouras², 闫栋³, 于随然³

(1)College of Economics & Management, Shanghai Jiao Tong University, Shanghai 200052, China; (2)IUT Lumiμere Technology Institute, Universit?e Lumiμere Lyon 2, Lyon 69007, France; (3)School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

收稿日期:2010-04-22 修回日期:2010-12-01 出版日期:2011-04-15 发布日期:2011-04-15
基金资助:
Project supported by the "Shu Guang" Project of Shanghai Municipal Education Commission, China (Grant No. 09SG17), and EU ELINK--East--West Link for Innovation, Networking and Knowledge Exchange (Grant No. 149674-EM-1-2008-1-UK-ERAMUNDUS).

Poor–rich demarcation of Matthew effect on scale-free systems and its application

Yan Dong(闫栋)^a)†, Dong Ming(董明)^b), Abdelaziz Bouras^c), and Yu Sui-Ran(于随然)^a)

^a School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; ^b College of Economics & Management, Shanghai Jiao Tong University, Shanghai 200052, China; ^c IUT Lumiμere Technology Institute, Université Lumière Lyon 2, Lyon 69007, France

Received:2010-04-22 Revised:2010-12-01 Online:2011-04-15 Published:2011-04-15
Supported by:
Project supported by the "Shu Guang" Project of Shanghai Municipal Education Commission, China (Grant No. 09SG17), and EU ELINK–East–West Link for Innovation, Networking and Knowledge Exchange (Grant No. 149674-EM-1-2008-1-UK-ERAMUNDUS).

摘要/Abstract

摘要： In a scale-free network, only a minority of nodes are connected very often, while the majority of nodes are connected rarely. However, what is the ratio of minority nodes to majority nodes resulting from the Matthew effect? In this paper, based on a simple preferential random model, the poor-rich demarcation points are found to vary in a limited range, and form a poor-rich demarcation interval that approximates to k/m ∈ [3,4]. As a result, the (cumulative) degree distribution of a scale-free network can be divided into three intervals: the poor interval, the demarcation interval and the rich interval. The inequality of the degree distribution in each interval is measured. Finally, the Matthew effect is applied to the ABC analysis of project management.

关键词: Matthew effect, scale-free networks, poor--rich demarcation, project management

Abstract: In a scale-free network, only a minority of nodes are connected very often, while the majority of nodes are connected rarely. However, what is the ratio of minority nodes to majority nodes resulting from the Matthew effect? In this paper, based on a simple preferential random model, the poor-rich demarcation points are found to vary in a limited range, and form a poor-rich demarcation interval that approximates to k/m ∈ [3,4]. As a result, the (cumulative) degree distribution of a scale-free network can be divided into three intervals: the poor interval, the demarcation interval and the rich interval. The inequality of the degree distribution in each interval is measured. Finally, the Matthew effect is applied to the ABC analysis of project management.

Key words: Matthew effect, scale-free networks, poor--rich demarcation, project management

中图分类号: (Probability theory, stochastic processes, and statistics)

02.50.-r

05.65.+b (Self-organized systems) 89.75.Fb (Structures and organization in complex systems)

闫栋, 董明, Abdelaziz Bouras, 于随然. Poor–rich demarcation of Matthew effect on scale-free systems and its application[J]. 中国物理B, 2011, 20(4): 40205-040205.

Yan Dong(闫栋), Dong Ming(董明), Abdelaziz Bouras, and Yu Sui-Ran(于随然) . Poor–rich demarcation of Matthew effect on scale-free systems and its application[J]. Chin. Phys. B, 2011, 20(4): 40205-040205.

参考文献 15

[1]	Merton R K 1968 Science 159 56
[2]	Price D J de S 1965 Science 149 510
[3]	Barabási A L and Albert R 1999 Science 286 509
[4]	Hu H B and Wang X F 2008 Physica A 387 3769
[5]	Wu J, Tan Y J, Deng H Z and Zhu D Z 2007 Chin. Phys. 16 1576
[6]	Newman M E J 2003 SIAM Rev. 45 167
[7]	Myers C R 2003 Phys. Rev. E 68 046116
[8]	Zhao W, He H S, Lin Z C and Yang K Q 2006 Acta Phys. Sin. 55 3906 (in Chinese)
[9]	Wang G Z, Cao Y J, Bao Z J and Han Z X 2009 Acta Phys. Sin. 58 3597 (in Chinese)
[10]	Concas G, Marchesi M, Pinna S and Serra N 2007 IEEE Trans. Software Eng. 33 687
[11]	Yan D, Qi G N and Gu X J 2006 Chin. Phys. 15 2489
[12]	Valverde S, Cancho1 R F and Solé R V 2002 Europhys. Lett. 60 512
[13]	Barabási A L, Albert R and Jeong H 1999 Physica A 272 173
[14]	Santos F C, Rodrigues J F and Pacheco J M 2006 Proc. R. Soc. B 273 51
[15]	Qi G N, Schottner J (Germany), Gu X J and Han Y S 2005 The Graphic Product Data Management (Beijing: China Machine Press) p. 133 (in Chinese) endfootnotesize

Poor–rich demarcation of Matthew effect on scale-free systems and its application

Poor–rich demarcation of Matthew effect on scale-free systems and its application

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 15

相关文章 11

Metrics

本文评价

推荐阅读 0

[1]	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.
[2]	濮存来, 李杰, 陈荣斌, 许忠奇. Multiple-predators-based capture process on complex networks[J]. 中国物理B, 2017, 26(3): 38901-038901.
[3]	朱振涛, 周晶, 李平, 陈星光. Symmetry breaking in the opinion dynamics of a multi-group project organization[J]. 中国物理B, 2012, 21(10): 100503-100503.
[4]	蔡绍洪, 张达敏, 龚光武, 郭长睿. Integrated systemic inflammatory response syndrome epidemic model in scale-free networks[J]. 中国物理B, 2011, 20(9): 90503-090503.
[5]	周思源, 王开, 张毅锋, 裴文江, 濮存来, 李微. Generalized minimum information path routing strategy on scale-free networks[J]. 中国物理B, 2011, 20(8): 80501-080501.
[6]	张连明, 邓晓衡, 余建平, 伍祥生. Degree and connectivity of the Internet's scale-free topology[J]. 中国物理B, 2011, 20(4): 48902-048902.
[7]	郭进利, 郭曌华, 刘雪娇. Mobile user forecast and power-law acceleration invariance of scale-free networks[J]. 中国物理B, 2011, 20(11): 118902-118902.
[8]	刘锋, 赵寒, 李明, 任丰原, 朱衍波. Adaptive local routing strategy on a scale-free network[J]. 中国物理B, 2010, 19(4): 40513-040513.
[9]	孙巍, 窦丽华. Convergence speed of consensus problems over undirected scale-free networks[J]. 中国物理B, 2010, 19(12): 120513-120513.
[10]	祁伟, 许新建, 汪映海. Improving consensual performance of multi-agent systems in weighted scale-free networks[J]. 中国物理B, 2009, 18(10): 4217-4221.
[11]	吴俊, 谭跃进, 邓宏钟, 朱大智. Normalized entropy of rank distribution: a novel measure of heterogeneity of complex networks[J]. 中国物理B, 2007, 16(6): 1576-1580.