Degree Distribution of Unit Disk Graphs with Uniformly Deployed Nodes on a Rectangular Surface

Abstract

Unit disk graphs are a simple model for wireless networks. This paper studies the degree distribution of unit disk graphs for uniformly randomly deployed nodes on rectangular surfaces. Several papers have proposed degree distributions approximating border effects. This paper presents a careful geometric analysis which is used to derive the probability mass function of the degree distribution and its mean. The analysis is validated through simulations which show the accuracy of the proposed distribution.