On vertex, edge, and vertex-edge random graphs
Combinatorics
2010-10-14 v2 Probability
Abstract
We consider three classes of random graphs: edge random graphs, vertex random graphs, and vertex-edge random graphs. Edge random graphs are Erdos-Renyi random graphs, vertex random graphs are generalizations of geometric random graphs, and vertex-edge random graphs generalize both. The names of these three types of random graphs describe where the randomness in the models lies: in the edges, in the vertices, or in both. We show that vertex-edge random graphs, ostensibly the most general of the three models, can be approximated arbitrarily closely by vertex random graphs, but that the two categories are distinct.
Cite
@article{arxiv.0812.1410,
title = {On vertex, edge, and vertex-edge random graphs},
author = {Elizabeth Beer and James Allen Fill and Svante Janson and Edward R. Scheinerman},
journal= {arXiv preprint arXiv:0812.1410},
year = {2010}
}