Fractality in complex networks: Critical and supercritical skeletons

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 75, Issue 1, 2007, Pages

  Kim, J S ^a   Goh, K I ^b,c   Salvi, G ^a   Oh, E ^a   Kahng, B ^a,d   Kim, D ^a  

^a Seoul National University   (South Korea)

^b UNIVERSITY OF NOTRE DAME   (United States)

^c Korea University   (South Korea)

^d CENTER FOR NONLINEAR STUDIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FUNCTIONS; MATHEMATICAL MODELS; PROTEINS; TREES (MATHEMATICS); WORLD WIDE WEB;

FRACTAL NETWORK MODELS; FRACTAL NETWORKS; NONFRACTAL NETWORKS; POWER LAW;

FRACTALS;

EID: 33846661167     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.75.016110     Document Type: Article

References (39)

1. C. Song, S. Havlin, and H. A. Makse, Nature (London) NATUAS 0028-0836 10.1038/nature03248 433, 392 (2005).
2. R. Albert, H. Jeong, and A.-L. Barabási, Nature (London) NATUAS 0028-0836 10.1038/43601 401, 130 (1999).
3. H. Jeong, B. Tombor, R. Albert, Z. N. Oltvai, and A.-L. Barabási, Nature (London) NATUAS 0028-0836 10.1038/35036627 407, 651 (2000).
4. I. Xenarious, Nucleic Acids Res. NARHAD 0305-1048 10.1093/nar/28.1.289 28, 289 (2000).
5. A.-L. Barabási and R. Albert, Science SCIEAS 0036-8075 10.1126/science.286.5439.509 286, 509 (1999).
6. J. Feder, Fractals (Plenum, New York, 1988).
7. S.-H. Yook, F. Radicchi, and H. Meyer-Ortmanns, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.045105 72, 045105 (R) (2005).
8. C. Song, S. Havlin, and H. A. Makse, Nat. Phys. ZZZZZZ 1745-2473 2, 275 (2006).
9. K.-I. Goh, G. Salvi, B. Kahng, and D. Kim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.018701 96, 018701 (2006).
10. D.-H. Kim, J. D. Noh, and H. Jeong, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.046126 70, 046126 (2004).
11. L. C. Freeman, Sociometry ZZZZZZ 0038-0431 40, 35 (1977).
12. M. Girvan and M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.122653799 99, 7821 (2002).
13. K.-I. Goh, B. Kahng, and D. Kim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.278701 87, 278701 (2001).
14. T. E. Harris, Theory of Branching Processes (Springer-Verlag, Berlin, 1963).
15. Z. Burda, J. D. Correia, and A. Krzywicki, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.046118 64, 046118 (2001).
16. K.-I. Goh, D.-S. Lee, B. Kahng, and D. Kim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.148701 91, 148701 (2003).
17. L. Donetti and C. Destri, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/37/23/004 37, 6003 (2004).
18. A. Saichev, A. Helmstetter, and D. Sornette, Pure Appl. Geophys. PAGYAV 0033-4553 10.1007/s00024-004-2663-6 162, 1113 (2005).
19. D.-S. Lee (unpublished).
20. The fractal scaling of the protein interaction network for S. cerevisiae behaves differently depending on the dataset. The dataset we use is from J.-D. Han, Nature (London) NATUAS 0028-0836 10.1038/nature02555 430, 88 (2004).
21. Internet Movie Database, http://imdb.com/
22. M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.021544898 98, 404 (2001).
23. University of Oregon Route Views Archive Project, http://archive. routeviews.org/
24. SCAN project, http://www.isi.edu/scan/scan.html
25. D. J. Watts and S. H. Strogatz, Nature (London) NATUAS 0028-0836 10.1038/30918 393, 440 (1998).
26. L. A. Braunstein, S. V. Buldyrev, R. Cohen, S. Havlin, and H. E. Stanley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.168701 91, 168701 (2003).
27. R. Cohen, in Handbook of Graphs and Networks, edited by, S. Bornholdt, and, H. G. Schuster, (Wiley-VCH, New York, 2002), Chap. 4.
28. S. Jung, S. Kim, and B. Kahng, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.056101 65, 056101 (2002).
29. E. Ravasz and A.-L. Barabási, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.026112 67, 026112 (2003).
30. P. Bialas, Z. Burda, J. Jurkiewicz, and A. Krzywicki, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.066106 67, 066106 (2003).
31. K.-I. Goh, E. S. Oh, H. Jeong, B. Kahng, and D. Kim, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.202301299 99, 12583 (2002).
32. M. Molloy and B. Reed, Random Struct. Algorithms RSALFD 1042-9832 6, 161 (1995).
33. J. S. Kim (unpublished).
34. E. Almaas, B. Kovacs, T. Vicsek, Z. N. Oltvai, and A.-L. Barabási, Nature (London) NATUAS 0028-0836 10.1038/nature02289 427, 839 (2004).
35. C.-M. Ghim, K.-I. Goh, and B. Kahng, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2005.04.025 237, 401 (2005).
36. M. den Nijs, Physica A PHYADX 0378-4371 251, 52 (1998).
37. P. L. Leath and G. R. Reich, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/11/19/013 11, 4017 (1978).
38. R. F. Voss, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/17/7/001 17, L373 (1984).
39. S. Sreenivasan, T. Kalisky, L. A. Braunstein, S. V. Buldyrev, S. Havlin, and H. E. Stanley, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.046133 70, 046133 (2004).