Effective dimensions in networks with long-range connections

Cristian F. Moukarzel

Physica A: Statistical Mechanics and its Applications, 2005, vol. 356, issue 1, 157-161

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.

Keywords: Long-range interactions; Power-law; Effective dimension; Chemical dimension; Small-world; Networks; Phase transitions; Graphs (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:356:y:2005:i:1:p:157-161

DOI: 10.1016/j.physa.2005.05.029

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