Eur. Phys. J. B (2016) 89: 111
https://doi.org/10.1140/epjb/e2016-60728-0

Regular Article

Percolation threshold on planar Euclidean Gabriel graphs

Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany

^a e-mail: christoph.norrenbrock@uni-oldenburg.de

Received: 7 September 2015
Received in final form: 15 February 2016
Published online: 2 May 2016

Abstract

In the present article, numerical simulations have been performed to find the bond and site percolation thresholds on two-dimensional Gabriel graphs (GG) for Poisson point processes. GGs belong to the family of “proximity graphs” and are discussed, e.g., in context of the construction of backbones for wireless ad-hoc networks. Finite-size scaling analyses have been performed to find the critical points and critical exponents ν, β and γ. The critical exponents obtained this way verify that the associated universality class is that of standard 2D percolation.