Inhomogeneous percolation models for spreading phenomena in random graphs

Journal of Statistical Mechanics: Theory and Experiment

Volumn , Issue 8, 2005, Pages 219-256

  Dall'Asta, Luca ^a  

^a UNIVERSITÉ PARIS SUD   (France)

Author keywords

Networks; Percolation problems (theory); Random graphs

Indexed keywords

EID: 24644456070     PISSN: 17425468     EISSN: None     Source Type: Journal    
DOI: 10.1088/1742-5468/2005/08/P08011     Document Type: Article

References (67)

1. Flory P J 1941 Molecular size distribution in three-dimensional gelation I-III J. Am. Chem. Soc. 63 3083
2. Broadbent S R and Hammersley J M 1957 Percolation processes I. Crystals and mazes Proc. Camb. Phil. Soc. 53 629
3. Stauffer D and Aharony A 1994 Introduction to Percolation Theory 2nd edn (London: Taylor and Francis)
4. Essam J W 1980 Percolation theory Rep. Prog. Phys. 43 833
5. Bunde A and Havlin S 1996 'Percolation I' and 'Percolation II' Fractals and Disordered Systems 2nd edn (Berlin: Springer)
6. Kirkpatrick S 1973 Percolation and conduction Rev. Mod. Phys. 45 574
7. Callaway D S, Newman M E J, Strogatz S H and Watts D J 2000 Network robustness and fragility: percolation on random graphs Phys. Rev. Lett. 85 5468
8. Cohen R, ben-Avraham D and Havlin S 2002 Percolation critical exponents in scale-free networks Phys. Rev. E 66 036113
9. Cohen R, Erez K, ben-Avraham D and Havlin S 2000 Resilience of the Internet to random breakdown Phys. Rev. Lett. 85 4626
10. Bollobás B, Janson S and Riordan O 2005 The phase transition in inhomogeneous random graphs Technical Report 18 Uppsala
11. Newman M E J 2002 Assortative mixing in networks Phys. Rev. Lett. 89 208701
12. Newman M E J 2003 Mixing patterns in networks Phys. Rev. E 67 026126
13. Vázquez A and Moreno Y 2003 Resilience to damage of graphs with degree correlations Phys. Rev. E 67 015101
14. Callaway D S, Hopcroft J E, Kleinberg J M, Newman M E J and Strogatz S H 2001 Are randomly grown graphs really random? Phys. Rev. E 64 041219
15. Dorogovtsev S N, Mendes J F F and Samukhin A N 2001 Giant strongly connected component of directed networks Phys. Rev. E 64 025101
16. Schwartz N, Cohen R, ben-Avraham D, Barabási A-L and Havlin S 2002 Percolation in directed scale-free networks Phys. Rev. E 66 015104(R)
17. Bogũá M and Serrano M Á 2005 Generalized percolation in random directed networks Preprint cond-mat/0501533
18. Meyers L A, Newman M E J and Pourbohloul B 2005 Predicting epidemics on directed contact networks J. Math. Biol. submitted
19. Erdös P and Rényi A 1959 On random graphs Publ. Math. 6 290
20. Erdös P and Rényi A 1960 On the evolution of random graphs' Publ. Math. Inst. Hung. Acad. Sci. 5 17
21. Bollobás B 1985 Random Graphs (New York: Academic)
22. Molloy M and Reed B 1995 A critical point for random graphs with a given degree sequence Random Struct. Algorithms 6 161
23. Molloy M and Reed B 1998 The size of the giant component of a random graph with a given degree sequence Comb. Probab. Comput. 7 295
24. Cohen R, Erez K, ben-Avraham D and Havlin S 2001 Breakdown of the Internet under intentional attack Phys. Rev. Lett. 86 3682
25. Holme P 2002 Edge overload breakdown in evolving networks Phys. Rev. E 66 036119
26. Holme P and Kim B J 2002 Vertex overload breakdown in evolving networks Phys. Rev. E 65 066109
27. Motter A E and Lai Y-C 2002 Cascade-based attacks on complex networks Phys. Rev. E 66 065102
28. Watts D J 2002 A simple model of global cascades on random networks Proc. Nat. Acad. Sci. 99 5766
29. Moore C and Newman M E J 2000 Epidemics and percolation in small-world networks Phys. Rev. E 61 5678
30. Moore C and Newman M E J 2000 Exact solution of site and bond percolation on small-world networks Phys. Rev. E 62 7059
31. Newman M E J 2002 Spread of epidemic diseases on networks Phys. Rev. E 64 016128
32. Newman M E J 2005 Contact networks, competing pathogens and the coexistence threshold Preprint cond-mat/0502373
33. Frisch H L and Hammersley J M 1963 Percolation processes and related topics J. SIAM 11 894
34. Grassberger P 1983 On the critical behaviour of the general epidemic process and dynamical percolation Math. Biosci. 63 157
35. Warren C P, Sander L M and Sokolov I M 2003 Firewalls, disorder, and percolation in epidemics Physica A 325 1
36. Sander L M, Warren C P, Sokolov I M, Simon C and Koopman J 2002 Percolation on disordered networks as a model for epidemics Math. Biosci. 180 293
37. May R M and Lloyd A L 2001 Infection dynamics on scale-free networks Phys. Rev. E 64 066112
38. Pastor-Satorras R and Vespignani A 2001 Epidemic spreading in scale-free networks Phys. Rev. Lett. 86 3200
39. Pastor-Satorras R and Vespignani A 2001 Epidemic dynamics and endemic states in complex networks Phys. Rev. E 63 066117
40. Bogũá M, Pastor-Satorras R and Vespignani A 2003 Absence of epidemic threshold in scale-free networks with degree correlations Phys. Rev. Lett. 90 08701
41. Bogũá M and Pastor-Satorras R 2002 Epidemic spreading in correlated complex networks Phys. Rev. E 66 047104
42. Moreno Y, Pastor-Satorras R and Vespignani A 2002 Epidemic outbreaks in complex heterogeneous networks Eur. Phys. J. B 26 521
43. Moreno Y and Vázquez A 2003 Disease spreading in structured scale-free networks Eur. Phys. J. B 31 265
44. Pastor-Satorras R and Vespignani A 2001 Immunization of complex networks Phys. Rev. E 65 036104
45. Bogũá M, Pastor-Satorras R and Vespignani A 2003 Epidemic spreading in complex networks with degree correlations Lect. Notes Phys. 625 127
46. Bruggeman D A G 1935 The calculation of various physical constants of heterogeneous substances. I. The dielectric constants and conductivities of mixtures composed of isotropic substances Ann. Phys. Lpz. 24 636
47. Landauer R 1952 The electrical resistance of binary metallic mixtures J. Appl. Phys. 24 779
48. Garet O 2004 Percolation transition for some excursion sets Electron. J. Probab. 9 255
49. Zhang Y 1994 A note on inhomogeneous percolation Ann. Probab. 22 803
50. Georgii H-O, Häggström O and Maes C 2001 The random geometry of equilibrium phases Phase Transitions and Critical Phenomena vol 14 ed C Domb and J Lebowitz (New York: Academic) pp 1-142
51. Grimmett G R 1999 Percolation 2nd edn (Berlin: Springer)
52. Kesten H 1982 Percolation Theory for Mathematicians (Boston, MA: Birkhäuser)
53. Dorogovtsev S N and Mendes J F F 2003 Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford: Oxford University Press)
54. Pastor-Satorras R and Vespignani A 2004 Evolution and Structure of the Internet: a Statistical Physics Approach (Cambridge: Cambridge University Press)
55. Albert R and Barabási A-L 2002 Statistical mechanics of complex networks Rev. Mod. Phys. 74 47
56. Newman M E J 2003 The structure and function of complex networks SIAM Rev. 45 167
57. Franceschetti M, Booth L, Cook M, Bruck J and Meester R 2005 Continuum percolation with unreliable and spread out connections J. Stat. Phys. 118 721
58. Wilf H S 1994 Generatingfunctionology 2nd edn (London: Academic)
59. Dorogovtsev S N and Mendes J F F 2002 Evolution of networks Adv. Phys. 51 1079
60. Newman M E J and Ziff R M 2001 A fast Monte Carlo algorithm for site or bond percolation Phys. Rev. E 64 016706
61. Barrat A, Barthélemy M, Pastor-Satorras R and Vespignani A 2004 The architecture of complex weighted networks Proc. Nat. Acad. Sci. 101 3747
62. Serrano M Á and Bogũá M 2005 Weighted configuration model Preprint cond-mat/0501750
63. Almaas E, Krapivsky P L and Redner S 2004 Statistics of weighted tree-like networks Preprint cond-mat/0408295
64. Abramowitz M and Stegun I 1965 Handbook of Mathematical Functions (New York: Dover)
65. Dorogovtsev S N and Mendes J F F 2001 Comment on breakdown of the Internet under intentional attack Phys. Rev. Lett. 87 219801
66. Gallos L K, Argyrakis P, Bunde A, Cohen R and Havlin S 2004 Tolerance of scale-free networks: from friendly to intentional attack strategies Physica A 344 504
67. Gallos L K, Argyrakis P, Bunde A, Cohen R and Havlin S 2005 Stability and topology of scale-free networks under attack and defense strategies Phys. Rev. Lett. 94 188701