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{\bf Elizabeth Beer, James Allen Fill, Svante Janson and Edward R. Scheinerman}
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{\bf On Vertex, Edge, and Vertex-Edge Random Graphs}
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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.
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