The size of the giant component of a random graph with a given degree sequence (1998) [63 citations — 0 self]
by Michael Molloy, Bruce Reed, Equipe Combinatoire
Combin. Probab. Comput
http://www.cs.toronto.edu/~molloy/webpapers/size.ps
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@ARTICLE{Molloy98thesize,author = {Michael Molloy and Bruce Reed and Equipe Combinatoire},
title = {The size of the giant component of a random graph with a given degree sequence},
journal = {Combin. Probab. Comput},
year = {1998},
volume = {7},
pages = {295--305}
}
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Abstract:
Given a sequence of non-negative real numbers 0; 1; : : : which sum to 1, we consider a random graph having approximately i n vertices of degree i. In [12] the authors essentially show that if P i(i \Gamma 2) i? 0 then the graph a.s. has a giant component, while if P i(i \Gamma 2) i! 0 then a.s. all components in the graph are small. In this paper we analyze the size of the giant component in the former case, and the structure of the graph formed by deleting that component. We determine ffl; 0
