Organization of growing random networks

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 63, Issue 6, 2001, Pages

  Krapivsky, P L ^a   Redner, S ^a  

^a Boston University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; ASYMPTOTIC STABILITY; FUNCTIONS; MATHEMATICAL MODELS; POISSON DISTRIBUTION; PROBABILITY;

ATTACHMENT PROBABILITY; CLASSICAL RANDOM GRAPHS; GROWING RANDOM NETWORKS;

COMPUTER SIMULATION;

EID: 0035363060     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.066123     Document Type: Article

References (57)

1. S. A. Kauffman, The Origin of Order: Self-Organization and Selection in Evolution (Oxford University Press, London, 1993).
2. Models of Neural Networks I, 2nd ed., edited by E. Domany, J. L. van Hemmen, and K. Schulten (Springer Verlag, New York, 1995).
3. See, e.g., G. Caldarelli, P. G. Higgs, and A. J. McKane, J. Theor. Biol. 193, 345 (1998), and references therein;
4. C. J. Camacho, R. Guimera, and L. A. N. Amaral, e-print cond-mat/0103114.
5. B. Bollobás, Random Graphs (Academic Press, London, 1985).
6. S. Janson, T. Luczak, and A. Rucinski, Random Graphs (Wiley, New York, 2000).
7. A. J. Lotka, J. Wash. Acad. Sci. 16, 317 (1926).
8. W. Shockley, Proc. IRE 45, 279 (1957).
9. E. Garfield, Science 178, 471 (1972).
10. L. Egghe and R. Rousseau, Introduction to Informetrics (Elsevier, Amsterdam, 1990).
11. N. Gilbert, Sociol. Res. 2, 2 (1997).
12. J. Lahererre and D. Sornette, Eur. Phys. J. B 2, 525 (1998).
13. S. Redner, Eur. Phys. J. B 4, 131 (1998).
14. M. E. J. Newman, e-print cond-mat/0007214.
15. R. Kumar, P. Raghavan, S. Rajagopalan, and A. Tomkins, in Proceedings of the Eighth World Wide Web Conference, Toronto, Canada, May 1999 (http://www8.org/w8-papers/4a-search-mining/trawling/trawling.html).
16. J. Kleinberg, R. Kumar, P. Raphavan, S. Rajagopalan, and A. Tomkins, in Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1999), Vol. 1627.
17. R. Kumar, P. Raghavan, S. Rajagopalan, and A. Tomkins, in VLDB’99 Proceedings of the 25th International Conference on Very Large Data Bases, Edinburgh, UK, September, 1999, edited by Malcolm P. Atkinson, Maria E. Orlowska, Patrick Valduriez, Stanley B. Zdonik, and Michael L. Brodie (Morgan Kaufmann, San Francisco, 1999), pp. 639–650.
18. B. A. Huberman, P. L. T. Pirolli, J. E. Pitkow, and R. Lukose, Science 280, 95 (1998).
19. B. A. Huberman and L. A. Adamic, Nature (London) 401, 131 (1999).
20. M. Faloutsos, P. Faloutsos, and C. Faloutsos, Comp. Commun. Rev. 29(4), 251 (1999).
21. A. L. Barabási and R. Albert, Science 286, 509 (1999).
22. A. Medina, I. Matta, and J. Byers, Comp. Commun. Rev. 30(2), 18 (2000).
23. R. R. Larson, in Proceedings of the 1996 Annual ASIS Meeting, Baltimore, MD, October 1996 (http://www.asis.org/annual-96/ElectronicProceedings/index.html#5).
24. S. Milgram, Psychol. Today2, 60 (1967).
25. D. J. Watts and S. H. Strogatz, Nature (London) 393, 440 (1998);
26. M. Barthelemy and L. A. N. Amaral, Phys. Rev. Lett. 82, 3180 (1999).
27. A. L. Barabási, R. Albert, and H. Jeong, Physica A 272, 173 (1999).
28. S. N. Dorogovtsev and J. F. F. Mendes, Phys. Rev. E 62, 1842 (2000).
29. S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, e-print cond-mat/0004434.
30. P. L. Krapivsky, S. Redner, and F. Leyvraz, e-print cond-mat/0005139.
31. M. H. Ernst, in Fundamental Problems in Statistical Physics VI, edited by E. G. D. Cohen (Elsevier, New York, 1985).
32. F. Leyvraz and S. Redner, Phys. Rev. Lett. 57, 163 (1986);
33. F. LeyvrazS. RednerPhys. Rev. A 36, 4033 (1987).
34. F. Calogero and F. Leyvraz, J. Phys. A 33, 5619 (2000).
35. H. A. Simon, Biometrika 42, 425 (1955).
36. H. A. Simon, Models of Man (Wiley, New York, 1957).
37. D. H. Zanette and S. C. Manrubia, e-print nlin.AO/009046.
38. E. Becker and W. Döring, Ann. Phys. (Leipzig) 24, 719 (1935);see also J. S. Langer, in Solids Far From Equilibrium, edited by C. Godrèche (Cambridge University Press, Cambridge, 1992).
39. E. M. Hendricks and M. H. Ernst, J. Colloid Interface Sci. 97, 176 (1984).
40. T. Matsoukas and E. Gulari, J. Colloid Interface Sci. 132, 13 (1989).
41. P. L. Krapivsky, J. F. F. Mendes, and S. Redner, Phys. Rev. B 59, 15 950 (1999).
42. P. L. Krapivsky, G. J. Rogers, and S. Redner (unpublished).
43. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science (Addison-Wesley, Reading, MA, 1989).
44. See, e.g., N. V. Brilliantov and P. L. Krapivsky, Fiz. Tverd. Tela. (Leningrad) 31, 172 (1989) [Sov. Phys. Solid State 31, 271 (1989)];
45. N. V. BrilliantovP. L. KrapivskyJ. Phys. A 24, 4787 (1991);
46. J. A. Blackman and A. Wielding, Europhys. Lett. 16, 115 (1991);
47. Ph. Laurencot, Nonlinearity 12, 229 (1999).
48. All of the citation data discussed here can be obtained from http://physics.bu.edu/∼redner.
49. M. Molloy and B. Reed, Random Struct. Alg. 6, 161 (1995);
50. M. MolloyB. ReedCombin. Probab. Comput. 7, 295 (1998).
51. W. Aiello, F. Chung, and L. Lu (unpublished).
52. M. E. J. Newman, S. H. Strogatz, and D. J. Watts, e-print cond-mat/0007235.
53. The apparently singular behavior at (Formula presented) indicates that a scale finer than linear in k is required in the proximity of (Formula presented) The proper scale is (Formula presented) and its use resolves the singularity and matches solutions for (Formula presented) and (Formula presented)
54. G. Caldarelli, R. Marchetti, and L. Pietronero, Europhys. Lett. 52, 386 (2000).
55. R. Albert, H. Jeong, and A. L. Barabási, Nature (London) 401, 130 (1999).
56. A. Broder, R. Kumar, F. Maghoul, P. Raphavan, S. Rajagopalan, R. Stata, A. Tomkins, and J. Wiener, Computer Networks 33, 309 (2000).
57. P. L. Krapivsky, G. J. Rodgers, and S. Redner, Phys. Rev. Lett. (to be published).