Generalized percolation in random directed networks

TL;DR

This paper develops a comprehensive theory for percolation in directed random networks with complex features like correlations and bidirectional edges, providing new insights and validated by simulations.

Contribution

It introduces a general theoretical framework for percolation in directed networks with correlations and bidirectional edges, extending previous models.

Findings

Derived equations for percolation threshold and giant component sizes

Validated theoretical predictions with simulation results

Extended understanding of percolation phenomena in complex networks

Abstract

We develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges, that is, edges pointing in both directions simultaneously. These two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena. Equations for the percolation threshold and the sizes of the giant components are derived in the most general case. We also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions.