Mathematics – Probability
Scientific paper
2007-08-31
Annals of Applied Probability 2008, Vol. 18, No. 4, 1651-1668
Mathematics
Probability
Published in at http://dx.doi.org/10.1214/07-AAP490 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst
Scientific paper
10.1214/07-AAP490
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.
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