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Random intersection graphs when m =ω( n ): An equivalence theorem relating the evolution of the G ( n , m , p ) and G ( n , p ) models
Author(s) -
Fill James Allen,
Scheinerman Edward R.,
SingerCohen Karen B.
Publication year - 2000
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/(sici)1098-2418(200003)16:2<156::aid-rsa3>3.0.co;2-h
Subject(s) - mathematics , combinatorics , struct , equivalence (formal languages) , random graph , graph , random variable , intersection (aeronautics) , discrete mathematics , intersection graph , central limit theorem , statistics , line graph , computer science , engineering , programming language , aerospace engineering
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