Weakly Explosive Percolation in Directed Networks

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.

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Cited by in corpus (7)

• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Explosive Phenomena in Complex Networks
• Explosive Percolation: Novel critical and supercritical phenomena
• Explosive Percolation: Unusual Transitions of a Simple Model
• Sensitivity of directed networks to the addition and pruning of edges and vertices
• Unstable supercritical discontinuous percolation transitions
• Explosive Percolation on Directed Networks Due to Monotonic Flow of Activity