The Annals of Applied Probability

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 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.

Article information

Source
Ann. Appl. Probab., Volume 18, Number 4 (2008), 1651-1668.

Dates
First available in Project Euclid: 21 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1216677136

Digital Object Identifier
doi:10.1214/07-AAP490

Mathematical Reviews number (MathSciNet)
MR2434185

Zentralblatt MATH identifier
1149.60007

Subjects
Primary: 60C05: Combinatorial probability 05C80: Random graphs [See also 60B20]

Keywords
Subcritical random graph largest component power law random multigraph random multigraph with given vertex degrees

Citation

Janson, Svante. The largest component in a subcritical random graph with a power law degree distribution. Ann. Appl. Probab. 18 (2008), no. 4, 1651--1668. doi:10.1214/07-AAP490. https://projecteuclid.org/euclid.aoap/1216677136


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