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On the Strongly Connected Components of Random Directed Graphs with Given Degree Sequences

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Graf_Alessandra.pdf (525.78 KB)

Date

2016-08-24

Authors

Graf, Alessandra

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University of Waterloo

Abstract

A strongly connected component of a directed graph G is a maximal subgraph H of G such that for each pair of vertices u and v in H, there is a directed path from u to v and a directed path from v to u in H. A strongly connected component is said to be giant if it has linear size. We determine the threshold at which a random directed graph with a well-behaved degree sequence asymptotically almost surely contains a giant strongly connected component. This is a new proof of a result by Cooper and Frieze in 2004. In addition, we predict the site percolation threshold for the presence of a giant strongly connected component in a graph with a well-behaved degree sequence.

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Keywords

random graphs, directed graphs, strongly connected components, percolation

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URI

http://hdl.handle.net/10012/10681

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Theses
Combinatorics and Optimization