The critical phase for random graphs with a given degree sequence

Authors:
M. Kang;T. g. Seierstad
Affiliations:
Institut für informatik, humboldt-universität zu berlin, unter den linden 6, 10099 berlin, germany (e-mail: kang@informatik.hu-berlin.de, seiersta@informatik.hu-berlin.de);Institut für informatik, humboldt-universität zu berlin, unter den linden 6, 10099 berlin, germany (e-mail: kang@informatik.hu-berlin.de, seiersta@informatik.hu-berlin.de)
Venue:
Combinatorics, Probability and Computing
Year:
2008

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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.