Open Access
2013 Directed random graphs with given degree distributions
Ningyuan Chen, Mariana Olvera-Cravioto
Stoch. Syst. 3(1): 147-186 (2013). DOI: 10.1214/12-SSY076


Given two distributions $F$ and $G$ on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from $F$ and $G$, respectively, that with high probability will be graphical, that is, from which a simple directed graph can be drawn. We then analyze a directed version of the configuration model and show that, provided that $F$ and $G$ have finite variance, the probability of obtaining a simple graph is bounded away from zero as the number of nodes grows. We show that conditional on the resulting graph being simple, the in- and out-degree distributions are (approximately) $F$ and $G$ for large size graphs. Moreover, when the degree distributions have only finite mean we show that the elimination of self-loops and multiple edges does not significantly change the degree distributions in the resulting simple graph.


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Ningyuan Chen. Mariana Olvera-Cravioto. "Directed random graphs with given degree distributions." Stoch. Syst. 3 (1) 147 - 186, 2013.


Published: 2013
First available in Project Euclid: 24 February 2014

zbMATH: 1297.05212
MathSciNet: MR3353470
Digital Object Identifier: 10.1214/12-SSY076

Primary: 05C80
Secondary: 60C05

Keywords: configuration model , Directed random graphs , prescribed degree distributions , Simple graphs

Rights: Copyright © 2013 INFORMS Applied Probability Society

Vol.3 • No. 1 • 2013
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