Self-avoiding walks and connective constants in small-world networks.
Phys Rev E Stat Nonlin Soft Matter Phys
; 68(2 Pt 2): 026106, 2003 Aug.
Article
em En
| MEDLINE
| ID: mdl-14525048
ABSTRACT
Long-distance characteristics of small-world networks have been studied by means of self-avoiding walks (SAW's). We consider networks generated by rewiring links in one- and two-dimensional regular lattices. The number of SAW's u(n) was obtained from numerical simulations as a function of the number of steps n on the considered networks. The so-called connective constant, mu=lim(n-->infinity)u(n)/u(n-1), which characterizes the long-distance behavior of the walks, increases continuously with disorder strength (or rewiring probability p). For small p, one has a linear relation mu=mu(0)+ap, mu(0) and a being constants dependent on the underlying lattice. Close to p=1 one finds the behavior expected for random graphs. An analytical approach is given to account for the results derived from numerical simulations. Both methods yield results agreeing with each other for small p, and differ for p close to 1, because of the different connectivity distributions resulting in both cases.
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Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Phys Rev E Stat Nonlin Soft Matter Phys
Assunto da revista:
BIOFISICA
/
FISIOLOGIA
Ano de publicação:
2003
Tipo de documento:
Article
País de afiliação:
Espanha