It is shown that in a subcritical random graph with given vertex degrees satisfying a power law degree distribution with exponent γ>3, the largest component is of order n1/(γ−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.
Publié le : 2008-08-15
Classification:
Subcritical random graph,
largest component,
power law,
random multigraph,
random multigraph with given vertex degrees,
60C05,
05C80
@article{1216677136,
author = {Janson, Svante},
title = {The largest component in a subcritical random graph with a power law degree distribution},
journal = {Ann. Appl. Probab.},
volume = {18},
number = {1},
year = {2008},
pages = { 1651-1668},
language = {en},
url = {http://dml.mathdoc.fr/item/1216677136}
}
Janson, Svante. The largest component in a subcritical random graph with a power law degree distribution. Ann. Appl. Probab., Tome 18 (2008) no. 1, pp. 1651-1668. http://gdmltest.u-ga.fr/item/1216677136/