The critical phase for random graphs with a given degree sequence
By Mihyun Kang and Taral Guldahl SeierstadCombinatorics, Probability and Computing, 17 (2008), 67-86.
Abstract
We consider random graphs with a fixed degree sequence. Molloy and Reed studied how the size of the giant component changes according to degree conditions. They showed that there is a phase transition and investigated the size of components before and after the critical phase. In this paper we study more closely the size of components at the critical phase, using singularity analysis of generating function for a branching process which models the random graph with a given degree sequence.
Download
- pdf - givendeg.pdf
