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arXiv · 0708.4404

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

Svante Janson
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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 $n^{1/(γ-1)}$. 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.

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Svante Janson. 2008-08-21. The largest component in a subcritical random graph with a power law degree distribution. https://doi.org/10.1214/07-aap490

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