Inverting the Achlioptas rule for explosive percolation

Abstract

In the usual Achlioptas processes the smallest clusters of a few randomly chosen ones are selected to merge together at each step. The resulting aggregation process leads to the delayed birth of a giant cluster and the so-called explosive percolation transition showing a set of anomalous features. We explore a process with the opposite selection rule, in which the biggest clusters of the randomly chosen ones merge together. We develop a theory of this kind of percolation based on the Smoluchowski equation, find the percolation threshold, and describe the scaling properties of this continuous transition, namely, the critical exponents and amplitudes, and scaling functions. We show that, qualitatively, this transition is similar to the ordinary percolation one, though occurring in less connected systems.

6 pages, 2 figures

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• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
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• Explosive Phenomena in Complex Networks
• Explosive percolation in finite dimensions
• Product-Sum universality and Rushbrooke inequality in explosive percolation
• Percolation under Noise: Detecting Explosive Percolation Using the Second Largest Component
• Explosive percolation on scale-free multifractal weighted planar stochastic lattice
• Universality class of explosive percolation in Barabási-Albert networks