Adaptive random walks on the class of Web graphs

European Physical Journal B

Volumn 23, Issue 2, 2001, Pages 221-228

  Tadic B ^a  

^a JO EF STEFAN INSTITUTE   (Slovenia)

Author keywords

05.40.Fb Random walks and Levy flights; 89.20.Hh World Wide Web, Internet; 89.75.Da Systems obeying scaling laws

Indexed keywords

EID: 0000575260     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100510170071     Document Type: Article

References (30)

1. S.H. Strogatz, Nature 410, 268 (2001).
2. R. Albert, A.-L. Barabasi, Statistical Mechanics of Complex Networks, Rev. Mod. Phys. (in press).
3. P.M. Gleiss, P.F. Stadler, A. Wagner, D.A. Fell, cond-mat/0009124; H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, A. Barabasi, Nature 407, 651 (2000).
4. P.M. Gleiss, P.F. Stadler, A. Wagner, D.A. Fell, cond-mat/0009124; H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, A. Barabasi, Nature 407, 651 (2000).
5. A. Scala, L.A.N. Amaral, M. Barthélémy, cond-mat/ 0004380.
6. J.M. Montoya, R.V. Solé, cond-mat/0011195.
7. M.E.J. Newman, Proc. Natl. Acad. Sci. 98, 404 (2001).
8. S. Redner, Eur. Phys. J. B 4, 131 (1998).
9. A. Broder, R. Kumar, F. Maghoul, P. Raghavan, R. Sridhar, R. Stata, A. Tomkins, J. Wiener, Computer Networks 33, 209 (2000).
10. D. Dhar, Physica A 263, 4 (1999).
11. B. Tadić, Physica A 293, 273 (2001); cond-mat/0011442.
12. Other mechanisms, for instance in the Internet growth, may also involve local optimization of supply, see A. Capocci et al., cond-mat/0106084.
13. A.-L. Barabasi, R. Albert, H. Jeong, Physica A 272, 173 (1999).
14. H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford Univ. Press, New York, 1971).
15. S.N. Dorogovtsev, J.F.F. Mendes, A.N. Samukhin, Phys. Rev. Lett. 85, 4633 (2000).
16. S.N. Dorogovtsev, J.F.F. Mendes, Phys. Rev. E 62, 1824 (2000).
17. L.P. Krapivsky, G.J. Rodgers, S. Redner, Phys. Rev. Lett. 86, 5401 (2001).
18. G. Ergün, G.J. Rodgers, cond-mat/0103423.
19. A special type of aiging, fitness and other constraints on the microscopic dynamic level are shown to affect the emergent behavior in the preference attachment model, see discussion in reference [2].
20. B. Tadić, cond-mat/0104029.
21. Such a reaction in which the reactants are added with a given rate and the products constantly removed was proposed recently to study work produced by molecular DNA motors, B. Yurke et al., Nature 406, 605 (2000).
22. The actual number of links in the Web exceeds number of nodes suggesting that a larger M would be more realistic. In the model the universal properties of the network in the scaling region are not affected when M is varied.
23. Technically, in order to simulate large graphs we preserve out-and in-degrees at each node from the growth phase and search links by once again using the rule in equation (2). The potential differences are minimized with increasing size of the ensemble.
24. V.B. Priezzhev, privat communication.
25. 1/τ.
26. A different mechanism of desease spreading on hierarchical graphs was considered in reference R. Pastor-Satorras, A. Vespignani, cond-mat/0102028.
27. It was shown recently that search time scales sublinearly with the network size in several other search algorithms that utilize local information in a power-law graph with symmetric links, see L.A. Adamic, R.M. Lukose, A.R. Puniyani, B.A. Huberman, cs.NI/0103016.
28. J. Keener, J. Sneiyd, Mathematical Physiology (Springer, Berlin, 1998).
29. B. Bollobás, Modern Graph Theory (Springer-Verlag, New York, 1998).
30. A. Arenas, A. Díaz-Guilera, R. Guimerà, cond-mat/ 0009395.