The largest component in a subcritical random graph with a power law degree distribution
Probability
2008-08-21 v2 Combinatorics
Abstract
It is shown that in a subcritical random graph with given vertex degrees satisfying a power law degree distribution with exponent , the largest component is of order . More precisely, the order of the largest component is approximatively given by a simple constant times the largest vertex degree. These results are extended to several other random graph models with power law degree distributions. This proves a conjecture by Durrett.
Cite
@article{arxiv.0708.4404,
title = {The largest component in a subcritical random graph with a power law degree distribution},
author = {Svante Janson},
journal= {arXiv preprint arXiv:0708.4404},
year = {2008}
}
Comments
Published in at http://dx.doi.org/10.1214/07-AAP490 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)