Gibbs entropy of network ensembles by cavity methods

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

Volumn 82, Issue 1, 2010, Pages

  Anand, Kartik ^a   Bianconi, Ginestra ^b  

^a ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

^b NORTHEASTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CANONICAL ENSEMBLE; CAVITY METHOD; COMMUNITY STRUCTURES; CONFIGURATION MODEL; DEGREE SEQUENCE; GIBBS ENTROPY; HARD CONSTRAINTS; LARGE DEVIATIONS; NETWORK CONFIGURATION; NETWORK ENSEMBLE; REAL NETWORKS;

ALGEBRA;

ENTROPY;

EID: 77954823947     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.011116     Document Type: Article

References (35)

1. R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002). 10.1103/RevModPhys.74.47
2. S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks: From Biological Nets to the Internet and the WWW (Oxford University Press, Oxford, 2003)
3. M. E. J. Newman, SIAM Rev. 45, 167 (2003). 10.1137/S003614450342480
4. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D. U. Hwang, Phys. Rep. 424, 175 (2006). 10.1016/j.physrep.2005.10.009
5. S. N. Dorogovtsev, Lectures on Complex Networks (Oxford University Press, Oxford, 2010). 10.1093/acprof:oso/9780199548927.001.0001
6. M. E. J. Newman, Networks (Oxford University Press, Oxford, 2010).
7. S. Fortunato, Phys. Rep. 486, 75 (2010). 10.1016/j.physrep.2009.11.002
8. S. N. Dorogovtsev, A. Goltsev, and J. F. F. Mendes, Rev. Mod. Phys. 80, 1275 (2008). 10.1103/RevModPhys.80.1275
9. A. Barrat, M. Barthélemy, and A. Vespignani, Dynamics Processes on Complex Networks (Cambridge University Press, Cambridge, England, 2008).
10. D. Gfeller, J.-C. Chappelier, and P. De Los Rios, Phys. Rev. E 72, 056135 (2005). 10.1103/PhysRevE.72.056135
11. G. Bianconi, P. Pin, and M. Marsili, Proc. Natl. Acad. Sci. U.S.A. 106, 11433 (2009). 10.1073/pnas.0811511106
12. S. Johnson, J. J. Torres, J. Marro, and M. A. Muñoz, Phys. Rev. Lett. 104, 108702 (2010). 10.1103/PhysRevLett.104.108702
13. G. Bianconi, EPL 81, 28005 (2008). 10.1209/0295-5075/81/28005
14. G. Bianconi, Phys. Rev. E 79, 036114 (2009). 10.1103/PhysRevE.79.036114
15. G. Bianconi, A. C. C. Coolen, and C. J. Perez Vicente, Phys. Rev. E 78, 016114 (2008). 10.1103/PhysRevE.78.016114
16. K. Anand and G. Bianconi, Phys. Rev. E 80, 045102 (R) (2009). 10.1103/PhysRevE.80.045102
17. A. Annibale, A. C. C. Coolen, L. Fernandes, F. Fraternali, and J. Kleinjung, e-print arXiv:0908.1759.
18. B. Karrer and M. E. J. Newman, Phys. Rev. Lett. 102, 128701 (2009). 10.1103/PhysRevLett.102.128701
19. M. E. J. Newman, Phys. Rev. Lett. 103, 058701 (2009). 10.1103/PhysRevLett.103.058701
20. B. Karrer and M. Newman, e-print arXiv:1005.1659.
21. S. Janson, T. Luczak, and A. Rucínski, Random Graphs (John Wiley & Sons, New York, 2000).
22. M. Molloy and B. Reed, Random Struct. Algorithms 6, 161 (1995). 10.1002/rsa.3240060204
23. G. Caldarelli, A. Capocci, P. De Los Rios, and M. A. Muñoz, Phys. Rev. Lett. 89, 258702 (2002). 10.1103/PhysRevLett.89.258702
24. J. Park and M. E. J. Newman, Phys. Rev. E 70, 066146 (2004). 10.1103/PhysRevE.70.066146
25. M. Boguñá and R. Pastor-Satorras, Phys. Rev. E 68, 036112 (2003). 10.1103/PhysRevE.68.036112
26. T. A. B. Snijders, P. E. Pattison, G. L. Robins, and M. S. Handcock, Sociol. Methodol. 36, 99 (2006). 10.1111/j.1467-9531.2006.00176.x
27. J. S. Yedidia, W. T. Freeman, and Y. Weiss, Exploring Artificial Intelligence in the New Millennium (Morgan Kaufman, San Mateo, CA, 2003), Chap..
28. M. Mézard and A. Montanari, Information, Physics and Computation (Oxford University Press, Oxford, 2009). 10.1093/acprof:oso/9780198570837.001. 0001
29. E. T. Jaynes, Phys. Rev. 108, 171 (1957). 10.1103/PhysRev.108.171
30. E. Marinari and G. Semerijian, J. Stat. Mech.: Theory Exp. (2006), P06019. 10.1088/1742-5468/2006/06/P06019
31. E. Marinari, R. Monasson, and S. Semerjian, EPL 73, 8 (2006). 10.1209/epl/i2005-10355-0
32. K. Tanaka and V. Van Kerrebroeck, Interdisciplinary Information Sciences 15, 301 (2009). 10.4036/iis.2009.301
33. S. L. Braunstein, S. Gosh, and S. Severini, Ann. Comb. 10, 291 (2006) 10.1007/s00026-006-0289-3
34. F. Passerini and S. Severini, e-print arXiv:0812.2597.
35. While extensions for directed networks are straightforward we shall focus, for the sake of clarity, on undirected networks only.