Abstract
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.
Citation
Svante Janson. "The largest component in a subcritical random graph with a power law degree distribution." Ann. Appl. Probab. 18 (4) 1651 - 1668, August 2008. https://doi.org/10.1214/07-AAP490
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