Random intersection graphs when m= w (n): an equivalence theorem relating the evolution of the G ( n, m, p ) and G ( n,P /italic>) models

When the random intersection graph G(n, m, p) proposed by Karonski, Scheinerman, and Singer-Cohen [Combin Probab Comput 8 (1999), 131–159] is compared with the independent-edge G(n, p), the evolutions are different under some values of m and equivalent under others. In particular, when m=nα and α>6, the total variation distance between the graph random variables has limit 0. ©2000 John Wiley & Sons, Inc. Random Struct. Alg., 16, 156–176, 2000