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The Size of the Largest Strongly Connected Component of a Random Digraph with a Given Degree Sequence

Published online by Cambridge University Press:  28 April 2004

COLIN COOPER  and
ALAN FRIEZE
COLIN COOPER
Affiliation:
Department of Mathematical and Computing Sciences, Goldsmiths College, London SW14 6NW, UK (e-mail: cooper@dcs.kcl.ac.uk)
ALAN FRIEZE
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA15213, USA (e-mail: alan@random.math.cmu.edu)
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Abstract

We give results on the strong connectivity for spaces of sparse random digraphs specified by degree sequence. A full characterization is provided, in probability, of the fan-in and fan-out of all vertices including the number of vertices with small ($o(n)$) and large ($cn$) fan-in or fan-out. We also give the size of the giant strongly connected component, if any, and the structure of the bow-tie digraph induced by the vertices with large fan-in or fan-out. Our results follow a direct analogy of the extinction probabilities of classical branching processes.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 13 , Issue 3 , May 2004 , pp. 319 - 337
Copyright
2004 Cambridge University Press

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