Effective dimensions and percolation in hierarchically structured scale-free networks

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

Volumn 68, Issue 5 2, 2003, Pages 551021-551024

  Eguíluz, Víctor M ^a   Hernández García, Emilio ^a   Piro, Oreste ^a   Klemm, Konstantin ^b,c  

^a INSTITUTO MEDITERRÁNEO DE ESTUDIOS AVANZADOS   (Spain)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

^c UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMMUNICATION SYSTEMS; COMPUTATIONAL GEOMETRY; CORRELATION THEORY; DIMENSIONAL STABILITY; FRACTALS; PERCOLATION (SOLID STATE); PHASE TRANSITIONS; PROBABILITY; TOPOLOGY;

CLUSTERING ANALYSIS; COMMUNICATION CONNECTIVITY; EUCLIDEAN LATTICES;

LARGE SCALE SYSTEMS;

EID: 0942267663     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.68.055102     Document Type: Article

References (27)

1. See, for example, Appendix B in E.A. Jackson, Perspectives of Nonlinear Dynamics (Cambridge University Press, Cambridge, 1989), Vol. 1, for a summary on the most important definitions.
2. B.B. Mandelbrot, Fractals: Form, Chance, and Dimension (Freeman, San Francisco, 1977).
3. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 1993).
4. R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002); S.N. Dorogovtsev and J.F.F. Mendes, Adv. Phys. 51, 1079 (2002).
5. R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002); S.N. Dorogovtsev and J.F.F. Mendes, Adv. Phys. 51, 1079 (2002).
6. M.E.J. Newman and D.J. Watts, Phys. Rev. E 60, 7332 (1999).
7. A.F. Rozenfeld, R. Cohen, D. ben-Avraham, and S. Havlin, Phys. Rev. Lett. 89, 218701 (2002).
8. C.F. Moukarzel and M.A. de Menezs, Phys. Rev. E 65, 056709 (2002).
9. M. Boguñá, R. Pastor-Satorras, and A. Vespignani, Phys. Rev. Lett. 90, 028701 (2003).
10. V.M. Eguíluz and K. Klemm, Phys. Rev. Lett. 89, 108701 (2002).
11. K. Klemm and V.M. Eguíluz, Phys. Rev. E 65, 036123 (2002); 65, 057102 (2002).
12. K. Klemm and V.M. Eguíluz, Phys. Rev. E 65, 036123 (2002); 65, 057102 (2002).
13. A. Rényi, Probability Theory (North-Holland, Amsterdam, 1970).
14. S. Havlin, in Kinetics of Aggregation and Gelation, edited by F. Family and D.P. Landau (Elsevier, Amsterdam, 1984).
15. H.G.E. Hentschel and I. Procaccia, Physica D 8, 435 (1983).
16. R. Benzi, G. Paladin, G. Parisi, and A. Vulpiani, J. Phys. A 17, 3521 (1984).
17. W. van de Water and P. Schram, Phys. Rev. A 37, 3118 (1988); M. de Rover and W. van de Water, Phys. Rev. E 51, 4132 (1995).
18. W. van de Water and P. Schram, Phys. Rev. A 37, 3118 (1988); M. de Rover and W. van de Water, Phys. Rev. E 51, 4132 (1995).
19. S.N. Dorogovtsev, A.V. Goltsev, and J.F.F. Mendes, Phys. Rev. E 65, 066122 (2002); S. Jung, S. Kim, and B. Kahng, ibid. 65, 056101 (2002).
20. S.N. Dorogovtsev, A.V. Goltsev, and J.F.F. Mendes, Phys. Rev. E 65, 066122 (2002); S. Jung, S. Kim, and B. Kahng, ibid. 65, 056101 (2002).
21. K. Klemm, Ph.D. thesis, Niels Bohr Institute, University of Copenhagen, 2003.
22. A. Vázquez, M. Boguñá, Y. Moreno, R. Pastor-Satorras, and A. Vespignani, Phys. Rev. E 67, 046111 (2003).
23. R. Pastor-Satorras and A. Vespignani, Phys. Rev. Lett. 86, 3200 (2001).
24. A.-L. Barabási and R. Albert, Science 286, 509 (1999).
25. Y. Gefen, B.B. Mandelbrot, and A. Aharony, Phys. Rev. Lett. 45, 855 (1980).
26. J.D. Noh, Phys. Rev. E 67, R045103 (2003).
27. C.P. Warren, L.M. Sander, and I.M. Sokolov, Phys. Rev. E 66, 056105 (2002).