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Title:  The Size of the Giant Component of a Random Graph with a Given Degree Sequence 
Authors:  Molloy, M. Reed, B. 
Keywords:  giant component random sequence 
Issue Date:  1998 
Publisher:  Cambridge University Press 
Citation:  Molloy, M., Reed, B. The Size of the Giant Component of a Random Graph with a Given Degree Sequence. Combin. Probab. Comput. 7(1998), 295306. 
Abstract:  Given a sequence of nonnegative real numbers λ0, λ1,... that sum to 1, we consider a random graph having approximately λin vertices of degree i. In [12] the authors essentially show that if Σ i(i 2)λi > 0 then the graph a.s. has a giant component, while if Σ i(i  2)λi < 0 then a.s. all components in the graph are small. In this paper we analyse the size of the giant component in the former case, and the structure of the graph formed by deleting that component. We determine ∈,λ′0,λ′1... such that a.s. the giant component, C, has en+o(n) vertices, and the structure of the graph remaining after deleting C is basically that of a random graph with n′ = n  C vertices, and with λ′in′ of them of degree i. 
Description:  original source http://www.cambridge.org/journals/journal_catalogue.asp?mnemonic=CPC 
URI:  http://hdl.handle.net/1807/9487 
ISSN:  14692163 
Appears in Collections:  Mathematics

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