Degree Distribution of Delaunay Triangulations

TL;DR

This paper investigates the degree distribution of Delaunay triangulations viewed as complex networks, revealing that they generally follow a Gaussian distribution, contrasting with other well-known network types.

Contribution

It is the first to statistically analyze the degree distribution of Delaunay triangulation networks, showing they predominantly follow a Gaussian distribution.

Findings

Degree distribution of DT networks follows Gaussian distribution

Contrasts with Poisson and Power-Law distributions in other networks

Provides new insights into the structure of Delaunay triangulations

Abstract

Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional Delaunay Triangulations (DTs) as a type of complex networks, and term it as DT networks. Then we statistically investigate the degree distribution of DT networks. We find that the degree distribution of DT networks well follows the Gaussian distribution in most cases, which differs from the Poisson distribution and the Power-Law distribution for the well-known Small-World networks and Scale-Free networks.