Random intersection graphs when m=ω(n): An equivalence theorem relating the evolution of the G(n, m, p) and G(n, p) models

When the random intersection graph G(n, m, p) proposed by Karoński, 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=n^α 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