## Stochastic Systems

### Directed random graphs with given degree distributions

#### Abstract

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.

#### Article information

Source
Stoch. Syst., Volume 3, Number 1 (2013), 147-186.

Dates
First available in Project Euclid: 24 February 2014

https://projecteuclid.org/euclid.ssy/1393251983

Digital Object Identifier
doi:10.1214/12-SSY076

Mathematical Reviews number (MathSciNet)
MR3353470

Zentralblatt MATH identifier
1297.05212

Subjects
Secondary: 60C05: Combinatorial probability

#### Citation

Chen, Ningyuan; Olvera-Cravioto, Mariana. Directed random graphs with given degree distributions. Stoch. Syst. 3 (2013), no. 1, 147--186. doi:10.1214/12-SSY076. https://projecteuclid.org/euclid.ssy/1393251983

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