Percolation of a strongly connected component in simple directed random graphs with a given degree distribution

TL;DR

This paper analyzes how a giant strongly connected component emerges in directed random graphs with specified degree distributions, providing critical percolation thresholds and component size estimates.

Contribution

It derives explicit formulas for the critical percolation probability and the size of the giant strongly connected component in directed graphs with given degree distributions.

Findings

Critical percolation threshold formulas derived

Expressions for the size of the giant component obtained

Applicable to directed graphs with specified degree distributions

Abstract

We study site and bond percolation on directed simple random graphs with a given degree distribution and derive the expressions for the critical value of the percolation probability above which the giant strongly connected component emerges and the fraction of vertices in this component.