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The strong giant in a random digraph

Published online by Cambridge University Press:  24 March 2016

Mathew D. Penrose
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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.

Keywords

Semi-homogeneous random digraphgiant componentbranching process
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 1 , March 2016 , pp. 57 - 70
Copyright
Copyright © Applied Probability Trust 2016 

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