Explosive percolation in graphs

Abstract

Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the same probability. However, alternative rules for the occupation of sites/bonds might affect the order of the transition. A recent set of rules proposed by Achlioptas et al. [Science 323, 1453 (2009)], characterized by competitive link addition, was claimed to lead to a discontinuous connectedness transition, named "explosive percolation". In this work we survey a numerical study of the explosive percolation transition on various types of graphs, from lattices to scale-free networks, and show the consistency of these results with recent analytical work showing that the transition is actually continuous.

10 pages, 7 figures, 1 table. Contribution to the Proceedings of STATPHYS-Kolkata VII, November 26-30, 2010

References in corpus (3)

• Critical phenomena in complex networks
• Explosive percolation in scale-free networks
• Explosive percolation via control of the largest cluster

Cited by in corpus (9)

• Gaussian model of explosive percolation in three and higher dimensions
• Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition
• Solution of the explosive percolation quest. II. Infinite-order transition produced by the initial distributions of clusters
• Identifying vital nodes by Achlioptas process
• Continuous Percolation Phase Transitions of Two-dimensional Lattice Networks under a Generalized Achlioptas Process
• Scaling of percolation transitions on Erdös-Rényi networks under centrality-based attacks
• Explosive percolations on the Bethe Lattice
• Inverting the Achlioptas rule for explosive percolation
• Explosive dismantling of two-dimensional random lattices under betweenness centrality attacks