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ON VERTEX, EDGE, AND VERTEX-EDGE RANDOM GRAPHS (EXTENDED ABSTRACT)

By Elizabeth Beer, James Allen Fill, Svante Janson and Edward R. Scheinerman

Abstract

We consider three classes of random graphs: edge random graphs, vertex random graphs, and vertex-edge random graphs. Edge random graphs are Erdős-Rényi random graphs [7, 8], vertex random graphs are generalizations of geometric random graphs [19], and vertexedge 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

Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.185.4561
Provided by: CiteSeerX
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