Mean-field diffusive dynamics on weighted networks

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

Volumn 82, Issue 1, 2010, Pages

  Baronchelli, Andrea ^a   Pastor Satorras, Romualdo ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX DYNAMICS; DIFFUSIVE DYNAMICS; KEY ELEMENTS; MEAN-FIELD; MEAN-FIELD EQUATIONS; RANDOM WALK PROCESS; SCALE FREE NETWORKS; SOCIAL SYSTEMS; WEIGHTED NETWORKS;

MEAN FIELD THEORY; RELIABILITY THEORY;

DYNAMICS;

EID: 77954511795     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.011111     Document Type: Article

References (52)

1. M. Barthélemy, A. Barrat, R. Pastor-Satorras, and A. Vespignani, Physica A 346, 34 (2005). 10.1016/j.physa.2004.08.047
2. A. Barrat, M. Barthélemy, and A. Vespignani, in Large Scale Structure and Dynamics of Complex Networks: From Information Technology to Finance and Natural sciences, edited by, G. Caldarelli, and, A. Vespignani, (World Scientific, Singapore, 2007), pp. 67-92.
3. S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, Oxford, 2003).
4. R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002). 10.1103/RevModPhys.74.47
5. M. E. J. Newman, Phys. Rev. E 70, 056131 (2004). 10.1103/PhysRevE.70. 056131 (Pubitemid 40086384)
6. A. Barrat, M. Barthélemy, R. Pastor-Satorras, and A. Vespignani, Proc. Natl. Acad. Sci. U.S.A. 101, 3747 (2004). 10.1073/pnas.0400087101 (Pubitemid 38381049)
7. A. Krause, Nature (London) 426, 282 (2003). 10.1038/nature02115 (Pubitemid 37463145)
8. R. Pastor-Satorras and A. Vespignani, Evolution and Structure of the Internet. A Statistical Physics Approach (Cambridge University Press, Cambridge, England, 2004). 10.1017/CBO9780511610905
9. M. A. Serrano, M. Boguñá, and R. Pastor-Satorras, Phys. Rev. E 74, 055101 (2006). 10.1103/PhysRevE.74.055101 (Pubitemid 44748709)
10. S. E. Ahnert, D. Garlaschelli, T. M. A. Fink, and G. Caldarelli, Phys. Rev. E 76, 016101 (2007). 10.1103/PhysRevE.76.016101 (Pubitemid 47146347)
11. D. Garlaschelli and M. I. Loffredo, Phys. Rev. Lett. 102, 038701 (2009). 10.1103/PhysRevLett.102.038701
12. B. J. Kim, C. N. Yoon, S. K. Han, and H. Jeong, Phys. Rev. E 65, 027103 (2002). 10.1103/PhysRevE.65.027103 (Pubitemid 40619540)
13. C. V. Giuraniuc, J. P. L. Hatchett, J. O. Indekeu, M. Leone, I. Perez Castillo, B. Van Schaeybroeck, and C. Vanderzande, Phys. Rev. Lett. 95, 098701 (2005). 10.1103/PhysRevLett.95.098701 (Pubitemid 41505891)
14. A.-C. Wu, X.-J. Xu, Z.-X. Wu, and Y.-H. Wang, Chin. Phys. Lett. 24, 577 (2007). 10.1088/0256-307X/24/2/077
15. M. Karsai, R. Juhász, and F. Iglói, Phys. Rev. E 73, 036116 (2006). 10.1103/PhysRevE.73.036116
16. Y. Gang, Chin. Phys. Lett. 22, 510 (2005). 10.1088/0256-307X/22/2/068
17. V. Colizza and A. Vespignani, Phys. Rev. Lett. 99, 148701 (2007). 10.1103/PhysRevLett.99.148701 (Pubitemid 47549435)
18. C. M. Schneider-Mizell and L. M. Sander, J. Stat. Phys. 136, 59 (2009). 10.1007/s10955-009-9757-6
19. H.-X. Yang, Z. X. Wu, C. Zhou, T. Zhou, and B. H. Wang, Phys. Rev. E 80, 046108 (2009). 10.1103/PhysRevE.80.046108
20. J. Onnela, Proc. Natl. Acad. Sci. U.S.A. 104, 7332 (2007). 10.1073/pnas.0610245104 (Pubitemid 47185905)
21. B. Huberman and R. Lukose, Science 277, 535 (1997). 10.1126/science.277. 5325.535 (Pubitemid 27368996)
22. V. Colizza, A. Barrat, M. Barthélemy, and A. Vespignani, Proc. Natl. Acad. Sci. U.S.A. 103, 2015 (2006). 10.1073/pnas.0510525103 (Pubitemid 43271615)
23. E. Berlow, Nature (London) 398, 330 (1999). 10.1038/18672 (Pubitemid 29161686)
24. S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Rev. Mod. Phys. 80, 1275 (2008). 10.1103/RevModPhys.80.1275
25. A. Barrat, M. Barthélemy, and A. Vespignani, Dynamical Processes on Complex Networks (Cambridge University Press, Cambridge, England, 2008).
26. C. Castellano and R. Pastor-Satorras, Phys. Rev. Lett. 96, 038701 (2006). 10.1103/PhysRevLett.96.038701 (Pubitemid 43248187)
27. M. Ha, H. Hong, and H. Park, Phys. Rev. Lett. 98, 029801 (2007). 10.1103/PhysRevLett.98.029801 (Pubitemid 46135149)
28. C. Castellano and R. Pastor-Satorras, Phys. Rev. Lett. 98, 029802 (2007). 10.1103/PhysRevLett.98.029802 (Pubitemid 46135148)
29. C. Castellano and R. Pastor-Satorras, Phys. Rev. Lett. 100, 148701 (2008). 10.1103/PhysRevLett.100.148701 (Pubitemid 351514255)
30. M. Boguñá, C. Castellano, and R. Pastor-Satorras, Phys. Rev. E 79, 036110 (2009). 10.1103/PhysRevE.79.036110
31. R. Pastor-Satorras, A. Vázquez, and A. Vespignani, Phys. Rev. Lett. 87, 258701 (2001). 10.1103/PhysRevLett.87.258701
32. S. Gil and D. Zanette, Eur. Phys. J. B 47, 265 (2005). 10.1140/epjb/e2005-00319-8 (Pubitemid 41436924)
33. S. Weber and M. Porto, Phys. Rev. E 76, 046111 (2007). 10.1103/PhysRevE.76.046111 (Pubitemid 47613369)
34. D. Stauffer and M. Sahimi, Phys. Rev. E 72, 046128 (2005). 10.1103/PhysRevE.72.046128 (Pubitemid 41777938)
35. We do not consider here the case of complex trees, that would deserve a dedicated analysis due to its specificity.
36. J. D. Noh and H. Rieger, Phys. Rev. Lett. 92, 118701 (2004). 10.1103/PhysRevLett.92.118701
37. A. Fronczak and P. Fronczak, Phys. Rev. E 80, 016107 (2009). 10.1103/PhysRevE.80.016107
38. R. Durret, Essentials of Stochastic Processes (Springer-Verlag, New York, 1999).
39. M. Boguñá and R. Pastor-Satorras, Phys. Rev. E 66, 047104 (2002). 10.1103/PhysRevE.66.047104 (Pubitemid 40606348)
40. E. W. Montroll and G. H. Weiss, J. Math. Phys. 6, 167 (1965). 10.1063/1.1704269
41. A. Baronchelli, M. Catanzaro, and R. Pastor-Satorras, Phys. Rev. E 78, 011114 (2008). 10.1103/PhysRevE.78.011114
42. J. Saramäki and K. Kaski, Physica A 341, 80 (2004). 10.1016/j.physa.2004.04.110
43. A. Baronchelli and V. Loreto, Phys. Rev. E 73, 026103 (2006). 10.1103/PhysRevE.73.026103 (Pubitemid 43287721)
44. C. Castellano and R. Pastor-Satorras, J. Stat. Mech. (2006), P05001. 10.1088/1742-5468/2006/05/P05001
45. Remember that in an annealed network the interaction of a vertex i with itself is allowed.
46. M. Catanzaro, M. Boguñá, and R. Pastor-Satorras, Phys. Rev. E 71, 027103 (2005). 10.1103/PhysRevE.71.027103 (Pubitemid 40607082)
47. Of course, in numerical simulations the ensemble average of Eq. is substituted with the network average performed on the generated networks.
48. S. Carmi, P. L. Krapivsky, and D. ben-Avraham, Phys. Rev. E 78, 066111 (2008). 10.1103/PhysRevE.78.066111
49. L. A. Adamic, R. M. Lukose, A. R. Puniyani, and B. A. Huberman, Phys. Rev. E 64, 046135 (2001). 10.1103/PhysRevE.64.046135
50. J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, England, 1999). 10.1017/CBO9780511524288
51. M. Boguñá, R. Pastor-Satorras, and A. Vespignani, in Statistical Mechanics of Complex Networks, Lecture Notes in Physics Vol. 625, edited by, R. Pastor-Satorras,,, J. M. Rubí,, and, A. Díaz-Guilera, (Springer-Verlag, Berlin, 2003).
52. J.-D. Bancal and R. Pastor-Satorras, Eur. Phys. J. B 76, 109 (2010). 10.1140/epjb/e2010-00165-7