\documentclass[12pt]{article}
\usepackage{amsmath,mathrsfs,bbm}
\usepackage{amssymb}
\textwidth=4.825in
\overfullrule=0pt
\thispagestyle{empty}

\begin{document}
\noindent
%
%
{\bf Elizabeth Beer, James Allen Fill, Svante Janson and Edward R. Scheinerman}
%
%

\medskip
\noindent
%
%
{\bf On Vertex, Edge, and Vertex-Edge Random Graphs}
%
%

\vskip 5mm
\noindent
%
%
%
%
We consider three classes of random graphs: edge random graphs, vertex
random graphs, and vertex-edge random graphs. Edge random graphs are
Erd\H{o}s-R\'enyi 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.

\end{document}

.
