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Physical Review E

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Empirical study on clique-degree distribution of networks

Wei-Ke Xiao^1,2, Jie Ren^2,3,4, Feng Qi², Zhi-Wei Song², Meng-Xiao Zhu², Hong-Feng Yang², Hui-Yu Jin², Bing-Hong Wang⁴, and Tao Zhou^3,4,*

¹Center for Astrophysics, University of Science and Technology of China, Hefei 230026, China
²Research Group of Complex Systems, University of Science and Technology of China, Hefei 230026, China
³Department of Physics, University of Fribourg, Chemin du Muse 3, CH-1700 Fribourg, Switzerland
⁴Department of Modern Physics and Nonlinear Science Center, University of Science and Technology of China, Hefei 230026, China

^*zhutou@ustc.edu

Phys. Rev. E 76, 037102 – Published 27 September, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.037102

Abstract

The community structure and motif-modular-network hierarchy are of great importance for understanding the relationship between structures and functions. We investigate the distribution of clique degrees, which are an extension of degree and can be used to measure the density of cliques in networks. Empirical studies indicate the extensive existence of power-law clique-degree distributions in various real networks, and the power-law exponent decreases with an increase of clique size.

Article Text

References (37)

D. J. Watts et al., Nature (London) 393, 440 (1998).
A.-L. Barabási et al., Science 286, 509 (1999).
R. Albert et al., Rev. Mod. Phys. 74, 47 (2002).
S. N. Dorogovtsev et al., Adv. Phys. 51, 1079 (2002).
M. E. J. Newman, SIAM Rev. 45, 167 (2003).
S. Boccaletti et al., Phys. Rep. 424, 175 (2006).
L. da F. Costa et al., Adv. Phys. 56, 167 (2007).
L. A. N. Amaral et al., Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000).
R. Milo et al., Science 298, 824 (2002).
A.-L. Barabási et al., Nat. Rev. Genet. 5, 101 (2004).
S. Itzkovitz, R. Milo, N. Kashtan, G. Ziv, and U. Alon, Phys. Rev. E 68, 026127 (2003).
R. Milo et al., Science 303, 1538 (2004).
A. Vázquez et al., Proc. Natl. Acad. Sci. U.S.A. 101, 17940 (2004).
Y. Artzy-Randrup et al., Science 305, 1107c (2004).
R. Milo et al., Science 305, 1107d (2004).
I. Derényi, G. Palla, and T. Vicsek, Phys. Rev. Lett. 94, 160202 (2005).
M. E. J. Newman and J. Park, Phys. Rev. E 68, 036122 (2003).
M. E. J. Newman, Contemp. Phys. 46, 323 (2005).
http://www.cosin.org/extra/data/internet/nlanr.html
http://www.isi.edu/scan/mercator/map.html
H. Jeong et al., Nature (London) 407, 651 (2000).
R. Albert et al., Nature (London) 401, 130 (1999).
http:/www.oakland.edu/~grossman
http://dip.doe-mbi.ucla.edu/
This network is constructed based on the BBS of USTC, wherein each node represents a BBS accounts and two nodes are neighboring if one appears in the other one’s friend list. Only the undirected network is considered.
M. L. Goldstein et al., Eur. Phys. J. B 41, 255 (2004).
P.-P. Zhang et al., Physica A 360, 599 (2006).
S. L. Pimm, Food Webs (University of Chicago Press, Chicago, 2002).
S. Maslov et al., Science 296, 910 (2002).
B. J. Kim, Phys. Rev. E 69, 045101(R) (2004).
M. Zhao et al., Physica A 371, 773 (2006).
M. E. J. Newman, Phys. Rev. Lett. 89, 208701 (2002).
E. Ravasz and A. L. Barabasi, Phys. Rev. E 67, 026112 (2003).
C. Song et al., Nature (London) 433, 392 (2005).
S. Zhou et al., IEEE Commun. Lett. 8, 180 (2004).
The theory in Ref. [13] is really accurate for $δ_{3}$ if belongs to type I; for example, $δ_{3}$ in random Apollonian networks [37] can be exactly predicted by the analytical result $δ_{3}^{'}$ .
T. Zhou et al., Phys. Rev. E 71, 046141 (2005).