The largest component in a subcritical random graph with a power law
degree distribution
S. Janson. (2007)cite arxiv:0708.4404
Comment: 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).
Аннотация
It is shown that in a subcritical random graph with given vertex degrees
satisfying a power law degree distribution with exponent $\gamma>3$, the
largest component is of order $n^1/(\gamma-1)$. 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.
Описание
The largest component in a subcritical random graph with a power law
degree distribution
cite arxiv:0708.4404
Comment: 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)
%0 Generic
%1 Janson2007
%A Janson, Svante
%D 2007
%K 2009 2010 ai bookmarking graph graphs ipipan java jure kdd social tools toread
%T The largest component in a subcritical random graph with a power law
degree distribution
%U http://arxiv.org/abs/0708.4404
%X It is shown that in a subcritical random graph with given vertex degrees
satisfying a power law degree distribution with exponent $\gamma>3$, the
largest component is of order $n^1/(\gamma-1)$. 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.
@misc{Janson2007,
abstract = { It is shown that in a subcritical random graph with given vertex degrees
satisfying a power law degree distribution with exponent $\gamma>3$, the
largest component is of order $n^{1/(\gamma-1)}$. 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.
},
added-at = {2010-05-26T11:15:46.000+0200},
author = {Janson, Svante},
biburl = {https://www.bibsonomy.org/bibtex/2ca3fedee4f6a922e77f12fa94c865dcc/bdas_demo},
description = {The largest component in a subcritical random graph with a power law
degree distribution},
interhash = {05f4fd8011389b8b2f11e6c06d376e82},
intrahash = {ca3fedee4f6a922e77f12fa94c865dcc},
keywords = {2009 2010 ai bookmarking graph graphs ipipan java jure kdd social tools toread},
note = {cite arxiv:0708.4404
Comment: 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)},
timestamp = {2010-05-31T08:00:40.000+0200},
title = {The largest component in a subcritical random graph with a power law
degree distribution},
url = {http://arxiv.org/abs/0708.4404},
year = 2007
}