Percolation threshold on planar Euclidean Gabriel Graphs

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. In order to find the critical points, finite-size scaling analyses have been performed for several observables. The critical exponents obtained this way verify that the associated universality class is that of standard $2D$ percolation.