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

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.