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2006 Stationary random graphs on $Z$ with prescribed iid degrees and finite mean connections
Maria Deijfen, Johan Jonasson
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Electron. Commun. Probab. 11: 336-346 (2006). DOI: 10.1214/ECP.v11-1239


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.


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Maria Deijfen. Johan Jonasson. "Stationary random graphs on $Z$ with prescribed iid degrees and finite mean connections." Electron. Commun. Probab. 11 336 - 346, 2006.


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

zbMATH: 1127.05093
MathSciNet: MR2274528
Digital Object Identifier: 10.1214/ECP.v11-1239

Primary: 05C80
Secondary: 60G50

Keywords: degree distribution , Random graphs , stationary model

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