2008/12/08 by Elizabeth Beer, Beer, Elizabeth, James Allen Fill +5 · 1 citation
Mathematics · #05C80 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #math.CO #math.PR #msc:05C80
paper · pdf · doi:10.48550/arxiv.0812.1410
arxiv created 2010/10/13 · arxiv updated 2010/10/14
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.