  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.
