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Percolation in networks with long-range connections

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  • Moukarzel, Cristian F.

Abstract

Two-dimensional lattices of points are connected with long-range links, whose lengths are distributed according to P(r)∼r-α. By changing the decay exponent α one can go from d-dimensional short-range networks to ∞-dimensional networks topologically similar to random graphs. Percolation on these networks is numerically studied for systems of up to 107 sites. The shortest-path, fractal and chemical dimensions are determined at the critical threshold, as a function of the decay exponent α.

Suggested Citation

  • Moukarzel, Cristian F., 2006. "Percolation in networks with long-range connections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 372(2), pages 340-345.
    • Handle: RePEc:eee:phsmap:v:372:y:2006:i:2:p:340-345
    DOI: 10.1016/j.physa.2006.08.049
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    References listed on IDEAS

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    1. Moukarzel, Cristian F., 2005. "Effective dimensions in networks with long-range connections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(1), pages 157-161.
    2. Rego, Henio H.A & Lucena, Liacir S & da Silva, Luciano R & Tsallis, Constantino, 1999. "Crossover from extensive to nonextensive behavior driven by long-range d=1 bond percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 42-48.
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    Cited by:

    1. Sadeghnejad, S. & Masihi, M. & King, P.R., 2013. "Dependency of percolation critical exponents on the exponent of power law size distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6189-6197.
    2. Silveira, Paulo S.P. & Alencar, Adriano M. & Majumdar, Arnab & Lemos, Miriam & Fredberg, Jeffrey J. & Suki, Béla, 2009. "Percolation in a network with long-range connections: Implications for cytoskeletal structure and function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1521-1526.

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