Asymptotic critical transmission radii in random geometry graphs over three-dimensional regions

TL;DR

This paper derives the exact asymptotic distribution of critical transmission radii related to k-connectivity and minimum vertex degree in 3D random geometric graphs, advancing understanding of network connectivity thresholds.

Contribution

It provides the first precise asymptotic distribution results for critical transmission radii in 3D random geometric graphs, focusing on k-connectivity and vertex degree.

Findings

Asymptotic distribution formulas for critical radii in 3D.

Insights into connectivity thresholds in 3D geometric networks.

Enhanced understanding of network robustness in three-dimensional spaces.

Abstract

This article presents the precise asymptotical distribution of two types of critical transmission radii, defined in terms of k-connectivity and the minimum vertex degree, for random geometry graphs distributed over three-dimensional regions.