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.
Original languageEnglish
Pages (from-to)57-70
JournalJournal of Applied Probability
Issue number1
Publication statusPublished - Mar 2016


  • semi-homogeneous random digraph, giant component,branching process


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