Fréchet distribution in geometric graphs for drone networks

Abstract

In this paper, we focus on the link density in random geometric graphs (RGGs) with a distance-based connection function. After deriving the link density in D dimensions, we focus on the two-dimensional (2D) and three-dimensional (3D) space and show that the link density is accurately approximated by the Fréchet distribution, for any rectangular space. We derive expressions, in terms of the link density, for the minimum number of nodes needed in the 2D and 3D spaces to ensure network connectivity. These results provide first-order estimates for, e.g., a swarm of drones to provide coverage in a disaster or crowded area.