Abstract
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.
Citation
Mathew D. Penrose. "The strong giant in a random digraph." J. Appl. Probab. 53 (1) 57 - 70, March 2016.
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