Scaling properties of scale-free evolving networks: Continuous approach

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

Volumn 63, Issue 5, 2001, Pages

  Dorogovtsev, S N ^a   Mendes, J F F ^b  

^a UNIVERSITY OF PORTO   (Portugal)

^b IOFFE INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; LINEAR EQUATIONS; LINEAR NETWORK ANALYSIS; MATHEMATICAL MODELS; NONLINEAR NETWORK ANALYSIS; NUMERICAL ANALYSIS; WORLD WIDE WEB;

SCALING PROPERTIES;

TELECOMMUNICATION NETWORKS;

EID: 0035334069     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.056125     Document Type: Article

References (43)

1. R. Albert, H. Jeong, and A.-L. Barabási, Nature (London) 401, 130 (1999).
2. B. A. Huberman and L. A. Adamic, Nature (London) 401, 131 (1999).
3. R. Kumar, P. Raghavan, S. Rajagopalan, and A. Tomkins, in Proceedings of the 25th VLDB ’99 Conference (Edinburgh, 1999) (Morgan Kaufman, New York, 1999), pp. 639–650.
4. A. Broder, R. Kumar, F. Maghoul, P. Raghavan, S. Rajagopalan, R. Stata, A. Tomkins, and J. Wiener, in Proceedings of the 9th WWW Conference (Amsterdam, 2000) (Elsevier, Amsterdam, 2000), pp. 309–320.
5. A.-L. Barabási and R. Albert, Science 286, 509 (1999).
6. M. Faloutsos, P. Faloutsos, and C. Faloutsos, Comput. Commun. Rev. 29, 251 (1999).
7. P. Baran, Introduction to Distributed Communications Networks, RM-3420-PR, August 1964, http://www.rand.org/publications/RM/baran.list.html.
8. B. A. Huberman, P. L. T. Pirolli, J. E. Pitkow, and R. J. Lukose, Science 280, 95 (1998).
9. J. Lahererre and D. Sornette, Eur. Phys. J. B 2, 525 (1998).
10. S. Redner, Eur. Phys. J. B 4, 131 (1998).
11. L. A. N. Amaral, A. Scala, M. Barthelemy, and H. E. Stanley, Proc. Natl. Acad. Sci. U.S.A. 97, 11 149 (2000).
12. M. E. J. Newman, Proc. Natl. Acad. Sci. USA 98, 404 (2001).
13. M. E. J. Newman, e-print cond-mat/0011144.
14. H. Jeong, B. Tombor, R. Albert, Z. N. Oltvai, and A.-L. Barabási, Nature (London) 407, 651 (2000).
15. In the recent physical literatute, the term “connectivity” was frequently used for a number of connections of a node. This term has quite a different meaning in mathematical language. Here, stimulated by one of our previous referees, we use the mathematically correct term degree.
16. R. Cohen, K. Erez, D. ben-Avraham, and S. Havlin, Phys. Rev. Lett. 85, 4626 (2000).
17. P. L. Krapivsky, S. Redner, and F. Leyvraz, Phys. Rev. Lett. 85, 4629 (2000).
18. S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, Phys. Rev. Lett. 85, 4633 (2000).
19. A.-L. Barabási, R. Albert, and H. Jeong, Physica A 272, 173 (1999).
20. S. N. Dorogovtsev and J. F. F. Mendes, Phys. Rev. E 62, 1842 (2000).
21. H. A. Simon, Biometrika 42, 425 (1955);Models of Man (Wiley, New York, 1957).
22. S. Solomon and M. Levy, Int. J. Mod. Phys. C 7, 745 (1996);
23. D. Sornette and R. Cont, J. Phys. I 7, 431 (1997);
24. H. Takayasu, A.-H. Sato, and M. Takayasu, Phys. Rev. Lett. 79, 966 (1997);
25. M. Marsili, S. Maslov, and Y.-C. Zhang, Physica A 253, 403 (1998).
26. G. Bianconi and A.-L. Barabási, e-print cond-mat/0011224.
27. S. M. Maurer and B. A. Huberman, e-print nlin.CD/0003041.
28. R. Albert, H. Jeong, and A.-L. Barabási, Nature (London) 406, 378 (2000);
29. R. Albert and A.-L. Barabási, Phys. Rev. Lett. 85, 5234 (2000).
30. C. Moore and M. E. J. Newman, Phys. Rev. E 61, 5678 (2000).
31. D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. Lett. 85, 5468 (2000).
32. R. Cohen, K. Erez, D. ben-Avraham, and S. Havlin, e-print cond-mat/0010251.
33. S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, e-print cond-mat/0011115.
34. P. Erdös and A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960).
35. B. Bollobás, Modern Graph Theory (Springer, New York, 1998).
36. J. Kleinberg, R. Kumar, P. Raphavan, S. Rajagopalan, and Tomkins (unpublished).
37. S. Bornholdt and H. Ebel, e-print cond-mat/0008465.
38. S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, e-print cond-mat/0009090.
39. S. N. Dorogovtsev and J. F. F. Mendes, Europhys. Lett. 52, 33 (2000).
40. S. N. Dorogovtsev and J. F. F. Mendes, Phys. Rev. E 63, 025101 (2001);e-print cond-mat/0009065.
41. G. Bianconi and A.-L. Barabási, e-print cond-mat/0011029.
42. P. L. Krapivsky and S. Redner, e-print cond-mat/0011094.
43. L. A. Adamic and B. A. Huberman, Science 287, 2115a (2000).