Nonlinear preferential rewiring in fixed-size networks as a diffusion process

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

Volumn 79, Issue 5, 2009, Pages

  Johnson, Samuel ^a   Torres, Joaquín J ^a   Marro, Joaquín ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CRITICAL REGIMES; DEGREE DISTRIBUTIONS; DIFFUSION PROCESS; EVOLVING NETWORKS; FIXED-SITE; NONLINEAR DIFFUSION EQUATIONS; POWER-LAW; SECOND-ORDER PHASE TRANSITION; STARLIKE STRUCTURES; STATIONARY STATE; TEMPORAL EVOLUTION;

PHASE TRANSITIONS;

NONLINEAR EQUATIONS;

EID: 67549101004     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.050104     Document Type: Article

References (20)

1. S. Boccaletti, Phys. Rep. 424, 175 (2006). 10.1016/j.physrep.2005.10.009
2. A. Arenas, Phys. Rep. 469, 93 (2008). 10.1016/j.physrep.2008.09.002
3. J. Marro, J. J. Torres and J. M. Cortes, J. Stat. Mech.: Theory Exp. (2008) P02017. 10.1088/1742-5468/2008/02/P02017
4. A.-L. Barabási and R. Albert, Science 286, 509 (1999). 10.1126/science.286.5439.509
5. G. Kossinets and D. J. Watts, Science 311, 88 (2006). 10.1126/science.1116869
6. A. Y. Klintsova and W. T. Greenough, Curr. Opin. Neurobiol. 9, 203 (1999). 10.1016/S0959-4388(99)80028-2
7. K. S. Lee, F. Schottler, M. Oliver, and G. Lynch, J. Neurophysiol. 44, 247 (1980).
8. M. De Roo, P. Klauser, P. Mendez, L. Poglia, and D. Muller, Cereb. Cortex 18, 151 (2008). 10.1093/cercor/bhm041
9. R. Albert and A.-L. Barabási, Phys. Rev. Lett. 85, 5234 (2000). 10.1103/PhysRevLett.85.5234
10. S. Thurner, F. Kyriakopoulos, and C. Tsallis, Phys. Rev. E 76, 036111 (2007). 10.1103/PhysRevE.76.036111
11. P. L. Krapivsky, S. Redner, and F. Leyvraz, Phys. Rev. Lett. 85, 4629 (2000). 10.1103/PhysRevLett.85.4629
12. Although all moments of k will diverge unless B=0.
13. There is a finite-size effect not taken into account by the theory-but relevant when α>β -which provides a natural lower cutoff for pst (k): if there are, say, m nodes which are connected to the whole network, then the minimum degree a node can have is m.
14. I. Farkas, I. Derényi, G. Palla, and T. Vicsek, Lect. Notes Phys. 650, 163 (2004).
15. J. Park and M. E. J. Newman, Phys. Rev. E 70, 066117 (2004). 10.1103/PhysRevE.70.066117
16. Z. Burda, J. Jurkiewicz, and A. Krzywicki, Physica A 344, 56 (2004). 10.1016/j.physa.2004.06.087
17. I. Derényi, I. Farkas, G. Palla, and T. Vicsek, Physica A 334, 583 (2004). 10.1016/j.physa.2003.10.083
18. M. E. J. Newman, SIAM Rev. 45, 167 (2003). 10.1137/S003614450342480
19. S. Johnson, J. Marro, and J. J. Torres, EPL 83, 46006 (2008). 10.1209/0295-5075/83/46006
20. M. Barahona and L. M. Pecora, Phys. Rev. Lett. 89, 054101 (2002). 10.1103/PhysRevLett.89.054101