2008/01/01 by J. Mauricio Campuzano, J. M. Campuzano, James P. Bagrow +2 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · Social Sciences · #Anisotropy #Combinatorics #Complex Network Analysis Techniques #Condensed matter physics #Diffusion and Search Dynamics #Dimension (graph theory) #Exponent #Human Mobility and Location-Based Analysis #Lattice (music) #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Power law #Quantum mechanics #Statistical physics #Statistics #cond-mat.dis-nn
paper · pdf · doi:10.1155/2008/346543
published in Physics Research International 2008(1) (Hindawi Publishing Corporation) · 6 pages, 4 figures, data included with source
openalex publication_date 2008/01/01 · arxiv created 2008/05/06 · arxiv updated 2015/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study the Kleinberg problem of navigation in small‐world networks when the underlying lattice is stretched along a preferred direction. Extensive simulations confirm that maximally efficient navigation is attained when the length r of long‐range links is taken from the distribution P ( r ) ~ r − α , when the exponent α is equal to 2, the dimension of the underlying lattice, regardless of the amount of anisotropy, but only in the limit of infinite lattice size, L → ∞ . For finite size lattices we find an optimal α ( L ) that depends strongly on L . The convergence to α = 2 as L → ∞ shows interesting power‐law dependence on the anisotropy strength.