Article ID Journal Published Year Pages File Type
4651943 Electronic Notes in Discrete Mathematics 2015 7 Pages PDF
Abstract

In a random graph with a spatial embedding, the probability of linking to a particular vertex v decreases with distance, but the rate of decrease may depend on the particular vertex v, and on the direction in which the distance increases. In this article, we consider the question when the embedding can be chosen to be uniform, so the probability of a link between two vertices depends only on the distance between them. We give necessary and sufficient conditions for the existence of a uniform linear embedding (embedding into a one-dimensional space) for spatial random graphs where the link probability can attain only a finite number of values.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics