The largest component in a subcritical random graph with a power law degree distribution

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.

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)

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