A percolation system with extremely long range connections and node dilution

M.L. de Almeida, E.L. Albuquerque, U.L. Fulco and M. Serva

Physica A: Statistical Mechanics and its Applications, 2014, vol. 416, issue C, 273-278

Abstract: We study the very long-range bond-percolation problem on a linear chain with both node and bond dilution. Very long-range means that the probability pij for a connection between two nodes i,j at a distance rij decays as a power-law, i.e. pij=ρ/[rijαN1−α] when α∈[0,1), and pij=ρ/[rijln(N)] when α=1. Node dilution means that the probability that a node is present in a site is ps∈(0,1]. The behavior of this model results from the competition between long-range connectivity which enhances the percolation, and node dilution which weakens percolation. The case α=0 with ps=1 is well-known, being the exactly solvable mean-field model. The percolation order parameter P∞ is investigated numerically for different values of α, ps and ρ. We show that in all range α∈[0,1] the percolation order parameter P∞ depends only on the average connectivity γ of the nodes, which can be explicitly computed in terms of the three parameters α, ps and ρ.

Keywords: Percolation; Node and bond dilution; Long-range; Networks (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:416:y:2014:i:c:p:273-278

DOI: 10.1016/j.physa.2014.08.041

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