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1 results

  • The strong giant in a random digraph

  • Mathew D. Penrose
  • Journal:
    Journal of Applied Probability / Volume 53 / Issue 1 / March 2016
    Published online by Cambridge University Press:
    24 March 2016, pp. 57-70
    Print publication:
    March 2016

  • 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.