A New Method to Estimate Scaling Exponents of Power-Law Degree Distribution and Hierarchical Clustering Function for Complex Networks

YANG Bo; DUAN Wen-qi; CHEN Zhong

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(11): 1292-1296

YANG Bo, DUAN Wen-qi, CHEN Zhong. A New Method to Estimate Scaling Exponents of Power-Law Degree Distribution and Hierarchical Clustering Function for Complex Networks[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1292-1296.

Citation:

PDF( 1340 KB)

A New Method to Estimate Scaling Exponents of Power-Law Degree Distribution and Hierarchical Clustering Function for Complex Networks

1.
Antai College of Economics & Management, Shanghai Jiaotong University, Shanghai 200052, P. R. China;

Received Date: 2005-09-30
Rev Recd Date: 2006-07-06
Publish Date: 2006-11-15

Abstract

Abstract

A new method and corresponding numerical procedure were introduced to estimate scaling exponents of power-law degree distribution and hierarchical clustering function for complex networks. This method could overcome the biased and inaccurate faults of graphical linear fitting methods commonly used in current network research.Furthermore,it has been verified to have higher goodness- of-fit than graphical methods by comparing the KS test statistics for 10 CNN networks.
- parameter estimation,
- complex networks,
- power-law,
- degree distribution,
- hierarchical modularity

FullText(HTML)

References(18)

References

[1]	Newman M E J.The structure and function of complex networks[J].SIAM Review,2003,45(2):167—256. doi: 10.1137/S003614450342480
[2]	Albert R,Jeong H,Barabási A- L.Diameter of the World Wide Web[J].Nature,1999,401(6749):130—131. doi: 10.1038/43601
[3]	Faloutsos M,Faloutsos P,Faloutsos C.On power-law relationships of the Internet topology[J].ACM SIGCOMM Computer Communications Review,1999,29(4):251—262. doi: 10.1145/316194.316229
[4]	Liljeros F,Edling C R,Amaral L A N，et al.The web of human sexual contacts[J].Nature,2001,411(6840):907—908. doi: 10.1038/35082140
[5]	Redner S. How popular is your paper? an empirical study of the citation distribution[J].Eur Phys J B,1998,4(2):131—134. doi: 10.1007/s100510050359
[6]	Albert R,Barabási A- L.Topology of evolving networks: local events and universality[J].Phys Rev Lett,2000,85(24):5234—5237. doi: 10.1103/PhysRevLett.85.5234
[7]	Sigman M,Cecchi G.Global organization of the Wordnet lexicon[J].Proc Nat Acad Sci USA,2002,99(3):1742—1747. doi: 10.1073/pnas.022341799
[8]	Eckmann J- P,Moses E.Curvature of co-links uncovers hidden thematic layers in the World Wide Web[J].Proc Nat Acad Sci USA,2002,99(9):5825—5829. doi: 10.1073/pnas.032093399
[9]	Ravasz E,Somera A L,Mongru D A,et al.Hierarchical organization of modularity in metabolic networks[J].Science,2002,297(5586):1551—1555. doi: 10.1126/science.1073374
[10]	Ravasz E,Barabási A- L.Hierarchical organization in complex networks[J].Phys Rev E,2003,67(2):026112. doi: 10.1103/PhysRevE.67.026112
[11]	Vázquez A, Dobrin R,Sergi D,et al.The topological relationship between the large-scale attributes and local interaction patterns of complex networks[J].Proc Nat Acad Sci USA,2004,101(52):17940—17945. doi: 10.1073/pnas.0406024101
[12]	Alderson D,Doyle J C,Li L,et al.Towards a theory of scale-free graphs: definition,properties,and implications[J].Internet Math,2005,2(4):431—523. doi: 10.1080/15427951.2005.10129111
[13]	Goldstein M L,Morris S A,Yen G G.Problems with fitting to the power-law distribution[J].Eur Phys J B,2004,41(2):255—258. doi: 10.1140/epjb/e2004-00316-5
[14]	Zhou T,Wang B H.Catastrophes in scale-free networks[J].Chinese Phys Lett,2005,22(5):1072—1075. doi: 10.1088/0256-307X/22/5/012
[15]	Duan W Q,Chen Z,Liu Z R.Phase transition dynamics of collective decision in scale-free networks[J].Chinese Phys Lett,2005,22(5):2137—2139. doi: 10.1088/0256-307X/22/8/087
[16]	Albert R,Barabási A- L.Statistical mechanics of complex networks[J].Rev Modern Phys,2002,74(1):47—97. doi: 10.1103/RevModPhys.74.47
[17]	Dorogovtsev S N,Goltsev A V,Mendes J F F.Pseudofractal scale-free web[J].Phys Rev E,2002,65(6):066122. doi: 10.1103/PhysRevE.65.066122
[18]	Vazquez A.Growing network with local rules: preferential attachment, clustering hierarchy, and degree correlations[J].Phys Rev E,2003,67(5):056104. doi: 10.1103/PhysRevE.67.056104