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The Critical Phase for Random Graphs with a Given Degree Sequence

Published online by Cambridge University Press:  01 January 2008

M. KANG  and
T. G. SEIERSTAD
M. KANG
Affiliation:
Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany (e-mail: [email protected], [email protected])
T. G. SEIERSTAD
Affiliation:
Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany (e-mail: [email protected], [email protected])
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Abstract

We consider random graphs with a fixed degree sequence. Molloy and Reed [11, 12] studied how the size of the giant component changes according to degree conditions. They showed that there is a phase transition and investigated the order of components before and after the critical phase. In this paper we study more closely the order of components at the critical phase, using singularity analysis of a generating function for a branching process which models the random graph with a given degree sequence.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 1 , January 2008 , pp. 67 - 86
Copyright
Copyright © Cambridge University Press 2007

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