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.
Original language | English |
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Pages (from-to) | 57-70 |
Journal | Journal of Applied Probability |
Volume | 53 |
Issue number | 1 |
DOIs | |
Publication status | Published - Mar 2016 |
Keywords
- semi-homogeneous random digraph, giant component,branching process