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

Authors
Fill, JA Scheinerman, ER Singer-Cohen, KB
Citation
Ja. Fill et al., Random intersection graphs when m = omega(n): An equivalence theorem relating the evolution of the G(n, m, p) and G(n, p) models, RAND STR AL, 16(2), 2000, pp. 156-176
Citations number
10
Categorie Soggetti
Mathematics
Journal title
RANDOM STRUCTURES & ALGORITHMS
ISSN journal
10429832 → ACNP
Volume
16
Issue
2
Year of publication
2000
Pages
156 - 176
Database
ISI
SICI code
1042-9832(200003)16:2<156:RIGWM=>2.0.ZU;2-8
Abstract
When the random intersection graph G(n,m,p) proposed by Karonski, Scheinerm an, and Singer-Cohen [Combin Probab Comput 8 (1999), 131-159] is compared w ith the independent-edge G(n, p), the evolutions are different under some v alues of m and equivalent under others. In particular, when m = n(alpha) an d alpha > 6, the total variation distance between the graph random variable s has limit 0. (C) 2000 John Wiley & Sons, Inc.