Spectra of sparse regular graphs with loops

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

Volumn 84, Issue 5, 2011, Pages

  Metz, F L ^a   Neri, I ^b   Bolle D ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b UNIVERSITÉ MONTPELLIER 2   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL FORMULAS; DYNAMICAL PROPERTIES; NETWORK MODELS; REGULAR GRAPHS; SPECTRAL GAP;

CONDENSED MATTER PHYSICS; PHYSICS;

GRAPH THEORY;

EID: 83255193032     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.055101     Document Type: Article

References (44)

1. A. Barrat, M. Barthélemy, and A. Vespignani, Dynamical Processes on Networks (Cambridge University Press, Cambridge, UK, 2008)
2. M. E. J. Newman, Networks, An Introduction (Oxford University Press, Oxford, 2010).
3. S. Hoory, N. Linial, and A. Wigderson, Bull. Amer. Math. Soc. 0273-0979 10.1090/S0273-0979-06-01126-8 43, 439 (2006). (Pubitemid 44448254)
4. M. R. Murty, J. Ramanujan Math. Soc. 18, 1 (2003).
5. M. Barahona and L. M. Pecora, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.054101 89, 054101 (2002).
6. L. Donetti, P. I. Hurtado, and M. A. Muñoz, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.95.188701 95, 188701 (2005); (Pubitemid 41777326)
7. T. Nishikawa and A. E. Motter, Phys. Rev. E 1539-3755 10.1103/PhysRevE.73.065106 73, 065106 (2006). (Pubitemid 43980055)
8. L. Lovász and P. Winkler, Mixing of Random Walks and Other Diffusions on a Graph (Cambridge University Press, Cambridge, UK, 1995), pp. 119-154.
9. F. R. K. Chung, Spectral Graph Theory (American Mathematical Society, Providence, 1997);
10. B. Georgeot, O. Giraud, and D. L. Shepelyansky, Phys. Rev. E 1539-3755 10.1103/PhysRevE.81.056109 81, 056109 (2010);
11. Z. Wang, A. Scaglione, and R. Thomas, IEEE Trans. Smart Grid 1, 1949 (2010).
12. B. Bollobás, Random Graphs (Cambridge University Press, Cambridge, UK, 2001).
13. H. Kesten, Trans. Amer. Math. Soc. 10.1090/S0002-9947-1959-0109367-6 92, 336354 (1959);
14. B. D. McKay, Linear Algebra Appl. LAAPAW 0024-3795 10.1016/0024-3795(81) 90150-6 40, 203 (1981).
15. J. Friedman and J. Tillich, SIAM J. Discrete Math. 19, 3 (2002).
16. T. Rogers, I. P. Castillo, R. Kühn, and K. Takeda, Phys. Rev. E 1539-3755 10.1103/PhysRevE.78.031116 78, 031116 (2008);
17. R. Kühn, J. Phys. A: Math. Theor. 1751-8113 10.1088/1751-8113/41/29/ 295002 41, 295002 (2008).
18. C. Bordenave and M. Lelarge, Random Struct. Algorithms RSALFD 1042-9832 10.1002/rsa.20313 37, 332 (2010).
19. J. Fortin, J. Phys. A 0305-4470 10.1088/0305-4470/38/5/L02 38, L57 (2005); (Pubitemid 40239724)
20. A. N. Samukhin, S. N. Dorogovtsev, and J. F. F. Mendes, Phys. Rev. E 1539-3755 10.1103/PhysRevE.77.036115 77, 036115 (2008); (Pubitemid 351431339)
21. I. J. Farkas, I. Derényi, A.-L. Barabási, and T. Vicsek, Phys. Rev. E 1539-3755 10.1103/PhysRevE.64.026704 64, 026704 (2001);
22. R. Kühn and J. Mourik, J. Phys. A: Math. Theor. 1751-8113 10.1088/1751-8113/44/16/165205 44, 165205 (2011).
23. P. M. Gleiss, e-print arXiv: cond-mat/0009124;
24. G. Bianconi, G. Caldarelli, and A. Capocci, Phys. Rev. E PRESCM 1539-3755 10.1103/PhysRevE.71.066116 71, 066116 (2005). (Pubitemid 41663831)
25. G. Bianconi, N. Gulbahce, and A. E. Motter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.118701 100, 118701 (2008). (Pubitemid 351457211)
26. K. Husimi, J. Chem. Phys. 0021-9606 10.1063/1.1747725 18, 682 (1950);
27. F. Harary and G. Uhlenbeck, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.39.4.315 39, 315 (1953).
28. M. Eckstein, M. Kollar, K. Byczuk, and D. Vollhardt, Phys. Rev. B 1098-0121 10.1103/PhysRevB.71.235119 71, 235119 (2005); (Pubitemid 41717840)
29. M. Galiceanu and A. Blumen, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2787005 127, 134904 (2007). (Pubitemid 47531641)
30. M. Molloy and B. Reed, Random Struct. Algorithms 1042-9832 10.1002/rsa.3240060204 6, 161 (1995);
31. M. Molloy and B. Reed, Combinatorics, Probab. Comput. CPCOFG 0963-5483 10.1017/S0963548398003526 7, 295 (1998).
32. F. L. Metz, I. Neri, and D. Bollé (unpublished).
33. Y. Huang and W. F. McColl, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/30/22/026 30, 7919 (1997). (Pubitemid 127150631)
34. Z. D. Bai and J. W. Silverstein, Spectral Analysis of Large Dimensional Random Matrices (Springer Science, New York, 2009).
35. P. Fazekas, Lecture Notes on Electron Correlation and Magnetism (World Scientific, Singapore, 1999).
36. J. Feinberg and A. Zee, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(97)00502-6 504, 579 (1997).
37. T. Rogers and I. P. Castillo, Phys. Rev. E PRESCM 1539-3755 10.1103/PhysRevE.79.012101 79, 012101 (2009).
38. T. Rogers, Ph. D. thesis, King's College London, 2010.
39. N. Alon, Combinatorica 0209-9683 10.1007/BF02579166 6, 83 (1986);
40. J. Friedman, Mem. Amer. Math. Soc 195, 910 (2008).
41. J. R. Norris, Markov Chains, Statistical and Probabilistic Mathematics (Cambridge University Press, Cambridge, UK, 1998).
42. G. Semerjian and L. F. Cugliandolo, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-00226-8 61, 247 (2003). (Pubitemid 36185159)
43. G. Biroli, G. Semerjian, and M. Tarzia, Prog. Theor. Phys. Suppl. 0375-9687 10.1143/PTPS.184.187 184, 187 (2010);
44. F. L. Metz, I. Neri, and D. Bollé, Phys. Rev. E PRESCM 1539-3755 10.1103/PhysRevE.82.031135 82, 031135 (2010).