CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY |
|
|
|
|
The Fractal Dimensions of Complex Networks |
GUO Long, CAI Xu |
Complexity Science Center and Institute of Particle Physics, Huazhong Normal University, Wuhan 430079 |
|
Cite this article: |
GUO Long, CAI Xu 2009 Chin. Phys. Lett. 26 088901 |
|
|
Abstract It is shown that many real complex networks share distinctive features, such as the small-world effect and the heterogeneous property of connectivity of vertices, which are different from random networks and regular lattices. Although these features capture the important characteristics of complex networks, their applicability depends on the style of networks. To unravel the universal characteristics many complex networks have in common, we study the fractal dimensions of complex networks using the method introduced by Shanker. We find that the average `density' <ρ(r)> of complex networks follows a better power-law function as a function of distance r with the exponent df, which is defined as the fractal dimension, in some real complex networks. Furthermore, we study the relation between df and the shortcuts Nadd in small-world networks and the size N in regular lattices. Our present work provides a new perspective to understand the dependence of the fractal dimension df on the complex network structure.
|
Keywords:
89.75.Da
05.45.Df
|
|
Received: 05 June 2009
Published: 30 July 2009
|
|
|
|
|
|
[1] Watts D J and Strogatz S H Nature 393 440(1998) [2] Jeong H, Mason S P, Barabasi A L and Oltvai Z N 2001 Nature 411 41 [3] Newman M E J 2001 Phys. Rev. E 64 016131 [4] Newman M E J 2001 Phys. Rev. E 64 016132 [5] Guimer\`{a R, Danon L, Diaz-Guilera A, Giralt F andArenas A 2003 Phys. Rev. E 68 065103(R) [6] Milgram S 1967 Psychol. Today 2 60 [7] Albert R, Jeong H and Barabasi A L 1999 Nature 401 130 [8] Song C, Havlin S, and Makse H A 2006 Nature Phys. 2 275 [9] Song C, Havlin S and Makse H A 2005 Nature 433392 [10] Goh K I, Salvi G, Kahng B and Kim D 2006 Phys.Rev. Lett. 96 018701 [11] Kim J S, Goh K-I, Salvi G, Oh E, Kahng B and Kim D 2007 Phys. Rev. E 75 016110 [12] Kim J S, Goh K I, Kahng B and Kim D 2007 New J.Phys. 9 177 [13] Zhou W X, Jiang Z Q and Sornette D 2007 Physica A 375 741 [14] Lee C Y and Jung S 2006 Phys. Rev. E 73066102 [15] Song C, Gallos L K, Havlin S and Makse H A 2007 J.Stat. Mech. 03 P03006 [16] Gao L, Hu Y and Di Z 2008 Phys. Rev. E 78046109 [17] Shanker O 2007 Mod. Phys. Lett. B 21 321 [18] Shanker O 2007 Mod. Phys. Lett. B 21 639 [19] Bu D et al 2003 Nucl. Acids Res. 31 2443 [20] Gleiser P M and Danon L 2003 Adv. Complex Syst. 6 565 [21] Newman M E J and Watts D J 1999 Phys. Rev. E 60 7332 [22] Toral R and Tessone C J 2007 Commun. Comput. Phys. 2 177 [23] Guo L and Cai X 2009 Commun. Comput. Phys. 6586 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|