Electronic Communications in Probability

Stationary random graphs on $Z$ with prescribed iid degrees and finite mean connections

Maria Deijfen and Johan Jonasson

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Let $F$ be a probability distribution with support on the non-negative integers. A model is proposed for generating stationary simple graphs on $Z$ with degree distribution $F$ and it is shown for this model that the expected total length of all edges at a given vertex is finite if $F$ has finite second moment. It is not hard to see that any stationary model for generating simple graphs on $Z$ will give infinite mean for the total edge length per vertex if $F$ does not have finite second moment. Hence, finite second moment of $F$ is a necessary and sufficient condition for the existence of a model with finite mean total edge length.

Article information

Electron. Commun. Probab., Volume 11 (2006), paper no. 33, 336-346.

Accepted: 5 December 2006
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C80: Random graphs [See also 60B20]
Secondary: 60G50: Sums of independent random variables; random walks

Random graphs degree distribution stationary model

This work is licensed under aCreative Commons Attribution 3.0 License.


Deijfen, Maria; Jonasson, Johan. Stationary random graphs on $Z$ with prescribed iid degrees and finite mean connections. Electron. Commun. Probab. 11 (2006), paper no. 33, 336--346. doi:10.1214/ECP.v11-1239. https://projecteuclid.org/euclid.ecp/1465058876

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