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arXiv · 1101.3567

Explosive percolation in graphs

Santo Fortunato·Filippo Radicchi
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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.

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Santo Fortunato, Filippo Radicchi. 2011-01-18. Explosive percolation in graphs. https://doi.org/10.1088/1742-6596%2F297%2F1%2F012009

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