On the topological Properties of the One Dimensional Exponential Random Geometric Graph

TL;DR

This paper investigates the topological properties of a one-dimensional exponential random geometric graph, deriving exact and limit results for connectivity and related features, and linking truncated exponential distributions to the model.

Contribution

It provides new exact and asymptotic results for the connectivity of exponential random geometric graphs with independently distributed nodes.

Findings

Derived exact formulas for graph connectivity

Established limit theorems for large graphs

Linked truncated exponential distributions to the model

Abstract

In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties associated with this random graph. We show that the asymptotic properties of a graph with a truncated exponential distribution can be obtained using the exponential random geometric graph.