Self-similar disk packings as model spatial scale-free networks

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

Volumn 71, Issue 1, 2005, Pages

  Doye, Jonathan P K ^a   Massen, Claire P ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DISK PACKINGS; ENERGY LANDSCAPES; SCALE-FREE NETWORKS; TOPOLOGICAL LEVELS;

CATCHMENTS; ECOLOGY; GRAPH THEORY; INFORMATION TECHNOLOGY; INTERNET; MATHEMATICAL MODELS; POTENTIAL ENERGY;

NEURAL NETWORKS;

EID: 41349109486     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.71.016128     Document Type: Article

References (74)

1. D. J. Watts and S. H. Strogatz, Nature (London) 393, 440 (1998).
2. S. H. Strogatz, Nature (London) 410, 268 (2001).
3. R. Albert and A. L. Barabási, Rev. Mod. Phys. 74, 47 (2002).
4. A. L. Barabási, Linked: The New Science of Networks (Perseus, Cambridge, 2002).
5. Handbook of Graphs and Networks: From the Genome to the Internet, edited by S. Bornholdt and H. G. Schuster (Wiley-VCH, Weinheim, 2003).
6. S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, Oxford, 2003).
7. M. E. J. Newman, SIAM Rev. 45, 167 (2003).
8. D. Hughes, M. Paczuski, R. O. Dendy, P. Heiander, and K. G. McClements, Phys. Rev. Lett. 90, 131101 (2003).
9. M. Baiesi and M. Paczuski, Phys. Rev. E 69, 066106 (2004).
10. R. Albert, H. Jeong, and A. L. Barabási, Nature (London) 401, 130 (1999).
11. H. Jeong, B. Tombor, R. Albert, Z. N. Oltvai, and A. L. Barabási, Nature (London) 407, 651 (2000).
12. H. Jeong, S. Mason, A. L. Barabási, and Z. N. Oltvai, Nature (London) 411, 41 (2001).
13. J. A. Dunne, R. J. Williams, and N. D. Martinez, Proc. Natl. Acad. Sci. U.S.A. 99, 12917 (2002).
14. F. Liljeros, C. R. Edling, L. A. N. Amaral, H. E. Stanley, and Y. Aberg, Nature (London) 411, 907 (2001).
15. A. L. Barabási and R. Albert, Science 286, 509 (1999).
16. S. Maslov and K. Sneppen, Science 296, 910 (2002).
17. M. Girvan and M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 99, 7821 (2002).
18. M. T. Gastner and M. E. J. Newman, e-print cond-mat/0407680.
19. S.-H. Yook, H. Jeong, and A. L. Barabási, Proc. Natl. Acad. Sci. U.S.A. 99, 13 382 (2002).
20. S. S. Manna and P. Sen, Phys. Rev. E 66, 066114 (2002).
21. R. Xulvi-Brunet and I. M. Sokolov, Phys. Rev. E 66, 026118 (2002).
22. P. Sen and S. S. Manna, Phys. Rev. E 68, 026104 (2003).
23. M. Barthélemy, Europhys. Lett. 63, 915 (2003).
24. A. F. Rozenfeld, R. Cohen, D. ben Avraham, and S. Havlin, Phys. Rev. Lett. 89, 218701 (2002).
25. C. P. Warren, L. M. Sander, and I. M. Sokolov, Phys. Rev. E 66, 056105 (2002).
26. D. ben Avraham, A. F. Rozenfeld, R. Cohen, and S. Havlin, Physica A 330, 107 (2003).
27. C. Herrmann, M. Barthélemy, and P. Provero. Phys. Rev. E 68, 026128 (2003).
28. J. P. K. Doye, Phys. Rev. Lett. 88, 238701 (2002).
29. J. P. K. Doye and C. P. Massen, J. Chem. Phys. (to be published), e-print cond-mat/0411144.
30. F. H. Stillinger and T. A. Weber, Science 225, 983 (1984)
31. F. Rao and A. Caflisch, J. Mol. Biol. 342, 299 (2004).
32. J. P. K. Doye, D. J. Wales, and M. A. Miller, J. Chem. Phys. 109, 8143 (1998).
33. J. S. Andrade, H. J. Herrmann, R. F. S. Andrade, and L. R. da Suva, e-print cond-mat/0406295.
34. F. Soddy, Nature (London) 137, 1021 (1936).
35. T. Aste, T. Di Matteo, and S. T. Hyde, Physica A 346, 20 (2005).
36. E. Ravasz and A. L. Barabási, Phys. Rev. E 67, 026112 (2003).
37. S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Phys. Rev. E 65, 066122 (2002).
38. F. Comellas, G. Fertin, and A. Raspaud, Phys. Rev. E 69, 037104 (2004).
39. A. L. Barabási, Nat. Rev. Genet. 5, 101 (2004).
40. S. N. Soffer and A. Vázquez, e-print cond-mat/0409686.
41. P. Erdös and A. Rényi, Publ. Math. (Debrecen) 6, 290 (1959).
42. P. Erdös and A. Rényi, Magy. Tud. Akad. Mat. Fiz. Tud. Oszt. Kozl. 5, 17 (1960).
43. K.-I. Goh, E. Oh, H. Jeong, B. Kahng, and D. Kim, Proc. Natl. Acad. Sci. U.S.A. 99, 12 583 (2002).
44. V. M. Eguíluz and K. Klemm, Phys. Rev. Lett. 89, 108701 (2002).
45. M. Boguñá, R. Pastor-Satorras, and A. Vespignani, Phys. Rev. Lett. 90, 028701 (2003).
46. P. Echenique, J. Gómez-Gardenes, Y. Moreno, and A. Vázquez, e-print cond-mat/0406547.
47. A. Vázquez and M. Weigt, Phys. Rev. E 67, 027101 (2003).
48. J. Park and M. E. J. Newman, Phys. Rev. E 68, 026112 (2003).
49. R. Milo, N. Kashtan, S. Itzkovitz, M. E. J. Newman, and U. Alon, e-print cond-mat/0312028.
50. M. E. J. Newman, Phys. Rev. Lett. 89, 208701 (2002).
51. M. E. J. Newman and M. Girvan, Phys. Rev. E 69, 026113 (2004).
52. M. E. J. Newman, Phys. Rev. E 69, 066133 (2004).
53. A. Trusina, S. Maslov, P. Minnhagen, and K. Sneppen, Phys. Rev. Lett. 92, 178702 (2004).
54. S. S. Manna and H. J. Herrmann, J. Phys. A 24, L481 (1991).
55. H. J. Herrmann, G. Mantica, and D. Bessis, Phys. Rev. Lett. 65, 3223 (1990).
56. S. S. Manna and T. Viscek, J. Stat. Phys. 64, 525 (1991).
57. G. Oron and H. J. Herrmann, J. Phys. A 33, 1417 (2000).
58. R. Mahmoodi Baram, H. J. Herrmann, and N. Rivier, Phys. Rev. Lett. 92, 044301 (2004).
59. R. Mahmoodi Baram and H. J. Herrmann, Fractals 12, 293 (2004).
60. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1983).
61. O. Wesler, Proc. Am. Math. Soc. 11, 324 (1960).
62. P. B. Thomas and D. Dhar, J. Phys. A 27, 2257 (1994).
63. K. E. Hirst, J. Lond. Math. Soc. 42, 281 (1967).
64. D. G. Larman, J. Lond. Math. Soc. 42, 292 (1967).
65. D. W. Boyd, Mathematika 20, 170 (1973).
66. D. W. Boyd, Math. Comput. 39, 249 (1982).
67. Z. A. Melzak, Can. J. Math. 16, 838 (1966).
68. M. Borkovec, W. De Paris, and R. Peikert, Fractals 2, 521 (1994).
69. Z. A. Melzak, Math. Comput. 16, 838 (1966).
70. F. H. Stillinger and T. A. Weber, Phys. Rev. A 25, 978 (1982).
71. J. P. K. Doye and D. J. Wales, J. Chem. Phys. 116, 3777 (2002).
72. C. P. Massen and J. P. K. Doye (unpublished).
73. A. L. Barabási and E. Ravasz, Physica A 299, 559 (2001).
74. S. Jung, S. Kim, and B. Kahng, Phys. Rev. E 65, 056101 (2002).