Selfavoiding walks on scalefree networks
Abstract
Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Selfavoiding walks (SAW’s) are expected to be more suitable than unrestricted random walks to explore various kinds of reallife networks. Here we study longrange properties of random SAW’s on scalefree networks, characterized by a degree distribution P (k) ̃ k^{γ} . In the limit of large networks (system size N→∞ ), the average number s_{n} of SAW’s starting from a generic site increases as μ^{n} , with μ= < k^{2} > / <k> 1 . For finite N , s_{n} is reduced due to the presence of loops in the network, which causes the emergence of attrition of the paths. For kinetic growth walks, the average maximum length <L> increases as a power of the system size: <L> ̃ N^{α} , with an exponent α increasing as the parameter γ is raised. We discuss the dependence of α on the minimum allowed degree in the network. A similar powerlaw dependence is found for the mean selfintersection length of nonreversal random walks. Simulation results support our approximate analytical calculations.
 Publication:

Physical Review E
 Pub Date:
 January 2005
 DOI:
 10.1103/PhysRevE.71.016103
 arXiv:
 arXiv:condmat/0412658
 Bibcode:
 2005PhRvE..71a6103H
 Keywords:

 89.75.Fb;
 87.23.Ge;
 05.40.Fb;
 89.75.Da;
 Structures and organization in complex systems;
 Dynamics of social systems;
 Random walks and Levy flights;
 Systems obeying scaling laws;
 Disordered Systems and Neural Networks
 EPrint:
 9 pages, 7 figures