%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 }