Journal of Applied Probability
- J. Appl. Probab.
- Volume 53, Number 1 (2016), 57-70.
The strong giant in a random digraph
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.
J. Appl. Probab., Volume 53, Number 1 (2016), 57-70.
First available in Project Euclid: 8 March 2016
Permanent link to this document
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
Penrose, Mathew D. The strong giant in a random digraph. J. Appl. Probab. 53 (2016), no. 1, 57--70. https://projecteuclid.org/euclid.jap/1457470558