Spectra of complex networks

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

Volumn 68, Issue 4, 2003, Pages

  Dorogovtsev, S N ^a   Goltsev, A V ^a   Mendes, J F F ^b,c   Samukhin, A N ^a  

^a UNIVERSITY OF PORTO   (Portugal)

^b UNIVERSITY OF AVEIRO   (Portugal)

^c IOFFE INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84863710296     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.68.046109     Document Type: Article

References (53)

1. A.-L. Barabási and R. Albert, Science 286, 509 (1999).
2. S.H. Strogatz, Nature (London) 401, 268 (2001).
3. R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002).
4. S.N. Dorogovtsev and J.F.F. Mendes, Adv. Phys. 51, 4 (2002).
5. M.E.J. Newman, SIAM Rev. 45, 167 (2003).
6. D.J. Watts, Small Worlds: The Dynamics of Networks between Order and Randomness (Princeton University Press, Princeton, NJ, 1999).
7. S.N. Dorogovtsev and J.F.F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, Oxford, 2003).
8. D. Cvetković, M. Domb, and H. Sachs, Spectra of Graphs: Theory and Applications (Johann Ambrosius Barth, Heidelberg, 1995).
9. D. Cvetković, P. Rowlinson, and S. Simić, Eigenspaces of Graphs (Cambridge University Press, Cambridge, 1997).
10. F.R.K. Chung, Spectral Graph Theory (American Mathematical Society, Providence, RI, 1997).
11. M. Faloutsos, P. Faloutsos, and C. Faloutsos, Comput. Commun. Rev. 29, 251 (1999).
12. G. Siganos, M. Faloutsos, P. Faloutsos, and C. Faloutsos, IEEE-ACM T. Network. 11 514(2003).
13. R. Monasson, Eur. Phys. J. B 12, 555 (1999).
14. I.J. Farkas, I. Derényi, A.-L. Barabási, and T. Vicsek, Phys. Rev. E 64, 026704 (2001);
15. I. Farkas, I. Derenyi, H. Jeong, Z. Neda, Z.N. Oltvai, E. Ravasz, A. Schubert, A.-L. Barabási, and T. Vicsek, Physica A 314, 25 (2002).
16. K.-I. Goh, B. Kahng, and D. Kim, Phys. Rev. E 64, 051903 (2001).
17. K.A. Eriksen, I. Simonsen, S. Maslov, and K. Sneppen, Phys. Rev. Lett. 90, 148701 (2003).
18. D. Vukadinović, P. Huang, and T. Erlebach, Lect. Notes Comput. Sci. 2346, 83 (2002).
19. O. Golinelli, e-print cond-mat/0301437.
20. Th. Guhr, A. Müller-Groeling, and H.A. Weidenmüller, Phys. Rep. 299, 189 (1998);
21. Phys. Rep.A.D. Mirlin, 326, 259 (2000).
22. A.J. Bray and G.J. Rodgers, Phys. Rev. B 38, 11 461 (1988).
23. E.P. Wigner, Ann. Math. 62, 548 (1955);
24. Ann. Math.E.P. Wigner65, 203 (1957);
25. Ann. Math.E.P. Wigner67, 325 (1958).
26. G.J. Rodgers and A.J. Bray, Phys. Rev. B 37, 3557 (1988).
27. G. Semerjian and L.F. Cugliandolo, J. Phys. A 35, 4837 (2002).
28. A. Bekessy, P. Bekessy, and J. Komlos, Stud. Sci. Math. Hungar. 7, 343 (1972);
29. E.A. Bender and E.R. Canfield, J. Comb. Theory, Ser. A 24, 296 (1978);
30. B. Bollobás, Eur. J. Comb. 1, 311 (1980);
31. N.C. Wormald, J. Comb. Theory, Ser. B 31, 156 168 (1981);
32. J. Comb. Theory, Ser. BN.C. Wormald31, 168 (1981);
33. M. Molloy and B. Reed, Random Struct. Algorithms 6, 161 (1995).
34. S.N. Dorogovtsev, J.F.F. Mendes, and A.N. Samukhin, Nucl. Phys. B 666, 396 (2003).
35. M.E.J. Newman, Phys. Rev. Lett. 89, 208701 (2002);
36. Phys. Rev. Lett.J. Berg and M. Lässig, 89, 228701 (2002);
37. S.N. Dorogovtsev, J.F.F. Mendes, and A.N. Samukhin, e-print cond-mat/0206467.
38. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, Cambridge, 2001).
39. M. Mihail and C. Papadimitriou, Lect. Notes Comput. Sci. 254, 2483 (2002).
40. R. Solomonoff and A. Rapoport, Bull. Math. Biophys. 13, 107 (1951).
41. P. Erdős and A. Rényi, Publ. Math. (Debrecen) 6, 290 (1959);
42. P. ErdősA. RényiPubl. Math. Inst. Hung. Acad. Sci. 5, 17 (1960).
43. One should note that the position of the cutoff may depend on details of the ensemble of random graphs. In particular, Z. Burda and A. Krzywicki, Phys. Rev. E 67, 046118 (2003). showed that the exclusion of multiple connections in a network may diminish (Formula presented)
44. M. Krivelevich and B. Sudakov, Combinatorics, Probab. Comput. 12, 61 (2003).
45. R. Pastor-Satorras, A. Vázquez, and A. Vespignani, Phys. Rev. Lett. 87, 258701 (2001).
46. S. Maslov and K. Sneppen, Science 296, 910 (2002).
47. E. Ravasz, A.L. Somera, D.A. Mongru, Z.N. Oltvai, and A.-L. Barabási, Science 297, 1551 (2002).
48. A. Vázquez, R. Pastor-Satorras, and A. Vespignani, Phys. Rev. E 65, 066130 (2002).
49. S.N. Dorogovtsev, A.V. Goltsev, and J.F.F. Mendes, Phys. Rev. E 65, 066122 (2002).
50. S. Kirkpatrick and T.P. Eggarter, Phys. Rev. B 6, 3598 (1972).
51. L. He, X. Liu, and G. Strang, Stud. Appl. Math. 110, 123 (2003).
52. A. Vázquez, e-print cond-mat/0211528.
53. F. Chung, L. Lu, and V. Vu, Ann. Comb. 7, 21 (2003).