Weakly Explosive Percolation in Directed Networks

TL;DR

This paper extends the study of explosive percolation to directed networks, revealing a rapid but not abrupt growth of the giant component using finite-size scaling analysis.

Contribution

It generalizes the explosive percolation process from undirected to directed networks and characterizes its scaling behavior.

Findings

Percolation in directed networks shows rapid growth but is less abrupt than in undirected networks.

Finite-size scaling exponents are identified for directed network percolation.

The phase transition exhibits unique features distinct from undirected cases.

Abstract

Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness of power grids and information networks, the spreading of epidemics and forest fires, and the stability of gene regulatory networks. Recent studies have shown that if network edges are added "competitively" in undirected networks, the onset of percolation is abrupt or "explosive." The unusual qualitative features of this phase transition have been the subject of much recent attention. Here we generalize this previously studied network growth process from undirected networks to directed networks and use finite-size scaling theory to find several scaling exponents. We find that this process is also characterized by a very rapid growth in the giant component, but that this growth is not as sudden as in undirected networks.