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The European Physical Journal B

, Volume 56, Issue 1, pp 71–79 | Cite as

Kinetic-growth self-avoiding walks on small-world networks

  • C. P. HerreroEmail author
Interdisciplinary Physics

Abstract.

Kinetically-grown self-avoiding walks have been studied on Watts-Strogatz small-world networks, rewired from a two-dimensional square lattice. The maximum length L of this kind of walks is limited in regular lattices by an attrition effect, which gives finite values for its mean value 〈L 〉. For random networks, this mean attrition length 〈L 〉 scales as a power of the network size, and diverges in the thermodynamic limit (system size N ↦∞). For small-world networks, we find a behavior that interpolates between those corresponding to regular lattices and randon networks, for rewiring probability p ranging from 0 to 1. For p < 1, the mean self-intersection and attrition length of kinetically-grown walks are finite. For p = 1, 〈L 〉 grows with system size as N1/2, diverging in the thermodynamic limit. In this limit and close to p = 1, the mean attrition length diverges as (1-p)-4. Results of approximate probabilistic calculations agree well with those derived from numerical simulations.

PACS.

89.75.Fb Structures and organization in complex systems 89.75.Hc Networks and genealogical trees 87.23.Ge Dynamics of social systems 05.40.Fb Random walks and Levy flights 

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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Instituto de Ciencia de MaterialesMadridSpain

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