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