Subgraphs in random networks

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

Volumn 68, Issue 2 2, 2003, Pages

  Itzkovitz, S ^a   Milo, R ^a   Kashtan, N ^a   Ziv, G ^a   Alon, U ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL MATERIALS; COMPUTER SIMULATION; LARGE SCALE SYSTEMS; POISSON DISTRIBUTION; RANDOM PROCESSES; TOPOLOGY;

ERDOS NETWORKS; POISSONIAN DEGREE DISTRIBUTION; RANDOM NETWORKS; SUBGRAPHS;

GRAPH THEORY;

EID: 42749099345     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (53)

1. S.H. Strogatz, Nature (London) 410, 268 (2001).
2. R. Albert and A.L. Barabasi, Rev. Mod. Phys. 74, 47 (2002).
3. M. Newman, S. Strogatz, and D. Watts, Phys. Rev. E 6402, 6118 (2001).
4. S.N. Dorogovtsev, J.F.F. Mendes, and A.N. Samukhin, e-print cond-mat/0204111.
5. D. Watts and S. Strogatz, Nature (London) 393, 440 (1998).
6. L. Amaral, A. Scala, M. Bathelemy, and H. Stanley, Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000).
7. S. Shen-Orr, R. Milo, S. Mangan, and U. Alon, Nat. Genet. 31, 64 (2002).
8. R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon, Science 298, 824 (2002).
9. S. Maslov and K. Sneppen, Science 296, 910 (2002)
10. P. Erdós and A. Rényi, Publ. Math. (Debrecen) 6, 290 (1959).
11. P. Erdós and A. Rényi, Publ. Math. Inst. Hungarian Acad. Sci. 5, 17 (1960).
12. P. Erdós and A. Rényi, Acta Math. Acad. Sci. Hung. 12, 261 (1961).
13. B. Bollobas, Random Graphs (Academic Press, New York 1985).
14. P.W. Holland, S.Leinhardt, and D. Heise, Sociological Methodology (Jossey-Bass, San Francisco, 1975), pp. 1-45.
15. J.A. Davis and S. Leinhardt, in Sociological Theories in Progress, edited by Joseph Berger, Morris Zelditch, Jr., and Bo Anderson (Houghton Mifflin, Boston, 1972), Vol. 2, pp. 218-251.
16. P.W. Holland and S. Leinhardt, Am. J. Sociol. 70, 492 (1970).
17. S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications (Cambridge University Press, Cambridge, 1994).
18. A.L. Barabasi and R. Albert, Science 286, 509 (1999).
19. S. Redner, Eur. Phys. J. B 4, 131 (1998).
20. M. Faloutsos, P. Faloutsos, and C. Faloutsos, Comput. Commun. Rev. 29, 251 (1999).
21. B.A. Huberman and L.A. Adamic, Nature (London) 401, 131 (1999).
22. Z. Burda, J.D. Correia, and A. Krzywicki, Phys. Rev. E 64 046118 (2001).
23. A. Krzywicki, e-print cond-mat/0110574.
24. P.L. Krapivsky, G.J. Rodgers, and S. Redner, Phys. Rev. Lett. 86, 5401 (2001).
25. R. Ferrer i Cancho and R.V. Solé, Proc. R. Soc. London, Ser. B 268, 2261 (2001).
26. S. Valverde, R. Ferrer i Cancho, and R. V. Sole, e-print cond-mat/0204344.
27. S.N. Dorogovtsev and J.F.F. Mendes, Adv. Phys. 51, 1079 (2002).
28. S.N. Dorogovtsev and A.N. Samukhin, Phys. Rev. E 67, 037103 (2003).
29. R. Ferrer i Cancho, C. Janssen, and R.V. Sole, Phys. Rev. E 64, 046119 (2001).
30. W. Aiello, F. Chung, and L. Lu, Exp. Math. 10, 53 (2001).
31. M. Molloy and B. Reed, Combinatorics, Probab. Comput. 7, 295 (1998).
32. F. Chung and L. Lu, Proc. Natl. Acad. Sci. U.S.A. 99, 15879 (2002).
33. R. Cohen, D. Ben-Avraham, and S. Havlin, Phys. Rev. E 66, 036113 (2002).
34. R. Cohen, K. Erez, D. ben-Avraham, and S. Havlin, Phys. Rev. Lett. 85, 4626 (2000).
35. M. Newman, Phys. Rev. E 60, 7332 (1999).
36. M. Newman, in Handbook of Graphs and Networks, edited by S. BornHoldt and G. Schuster (Wiley-VCH, Berlin, 2002).
37. S.N. Dorogovtsev, J.F.F. Mendes, and A.N. Samukhin, e-print cond-mat/0206467.
38. E. Ravasz and A.L. Barabasi, Phys. Rev. E 67, 026112 (2003).
39. J. Eckmann and E. Moses, Proc. Natl. Acad. Sci. U.S.A. 99, 5825 (2002).
40. P. Collet and J. Eckmann, J. Stat. Phys. 108, 1107 (2002).
41. S. Maslov, K. Sneppen, and A. Zaliznyak, e-print cond-mat/0205379.
42. C.A. Ouzounis and P.D. Karp, Genome Res. 10, 568 (2000).
43. A. Wagner and D. Fell, Proc. R. Soc. London, Ser. B 268, 1803 (2001).
44. N. Guelzim, S. Bottani, P. Bourgine, and F. Képès, Nat. Genet. 31, 60 (2002).
45. G. Bianconi and A. Capocci, Phys. Rev. Lett. 90, 078701 (2003).
46. J. Berg and M. Lässig, Phys. Rev. Lett. 89, 228701 (2002).
47. M. Molloy and B. Reed, Random Struct. Algorithms 6, 161 (1995).
48. E. Bender and E. Canfield, J. Comb. Theory, Ser. A 24, 296 (1978).
49. J.G. White, E. Southgate, J. N. Thomson, and S. Brenner, Philos. Trans. R. Soc. London, Ser. B 314, 1 (1986).
50. G. Bianconi and A.L. Barabasi, Phys. Rev. Lett. 86, 5632 (2001).
51. 2/N. This gives an incorrect value for the exact number of appearances (compare id14 vs id38 in Table I), but is valid for obtaining scaling relations.
52. F. Harary and H.J. Kommel, J. Math. Sociol. 6, 199 (1979).
53. M. Newman, Phys. Rev. Lett. 89, 208701 (2002).