Journal of Applied Probability

The strong giant in a random digraph

Mathew D. Penrose

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Consider a random directed graph on n vertices with independent and identically distributed outdegrees with distribution F having mean μ, and destinations of arcs selected uniformly at random. We show that if μ > 1 then for large n there is very likely to be a unique giant strong component with proportionate size given as the product of two branching process survival probabilities, one with offspring distribution F and the other with Poisson offspring distribution with mean μ. If μ ≤ 1 there is very likely to be no giant strong component. We also extend this to allow for F varying with n.

Article information

J. Appl. Probab., Volume 53, Number 1 (2016), 57-70.

First available in Project Euclid: 8 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C80: Random graphs [See also 60B20]
Secondary: 60J85: Applications of branching processes [See also 92Dxx] 92D30: Epidemiology

Semi-homogeneous random digraph giant component branching process


Penrose, Mathew D. The strong giant in a random digraph. J. Appl. Probab. 53 (2016), no. 1, 57--70.

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