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The largest component in a subcritical random graph with a power law degree distribution
Svante Janson
Source: Ann. Appl. Probab. Volume 18, Number 4 (2008), 1651-1668.
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.
Primary Subjects: 60C05, 05C80
Keywords: Subcritical random graph; largest component; power law; random multigraph; random multigraph with given vertex degrees
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoap/1216677136
Digital Object Identifier: doi:10.1214/07-AAP490
Mathematical Reviews number (MathSciNet):
MR2434185
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