Percolation threshold on planar Euclidean Gabriel Graphs

TL;DR

This paper uses numerical simulations to determine the bond and site percolation thresholds on two-dimensional Gabriel graphs, confirming they belong to the standard 2D percolation universality class.

Contribution

It provides the first detailed numerical analysis of percolation thresholds on Gabriel graphs, a key proximity graph in wireless network modeling.

Findings

Percolation thresholds for Gabriel graphs are identified.

Critical exponents match those of standard 2D percolation.

Gabriel graphs belong to the 2D percolation universality class.

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. 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.