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Effective dimensions in networks with long-range connections

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  • Moukarzel, Cristian F.

Abstract

One- and two-dimensional lattices of points are connected with long-range links, whose lengths are distributed according to P(r)∼r-μ. By changing the decay exponent μ one can go from d-dimensional short-range networks to ∞-dimensional networks topologically similar to random graphs. An effective dimension dchem(μ) can be defined in terms of the shortest-path properties of these networks. These effective dimensions dchem are calculated here in one and two dimensions, for system sizes of up to 107 points.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:356:y:2005:i:1:p:157-161
    DOI: 10.1016/j.physa.2005.05.029
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    References listed on IDEAS

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    1. Argollo de Menezes, M & Moukarzel, C.F & Penna, T.J.P, 2001. "Geometric phase-transition on systems with sparse long-range connections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 132-139.
    2. Gernot Grabher & Walter W. Powell (ed.), 2004. "Networks," Books, Edward Elgar Publishing, volume 0, number 2771, December.
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    Cited by:

    1. 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.

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