Strongly discontinuous explosive percolation with multiple giant components

Abstract

We generalize the random graph evolution process of Bohman, Frieze, and Wormald [T. Bohman, A. Frieze, and N. C. Wormald, Random Struct. Algorithms, 25, 432 (2004)]. Potential edges, sampled uniformly at random from the complete graph, are considered one at a time and either added to the graph or rejected provided that the fraction of accepted edges is never smaller than a decreasing function asymptotically approaching the value alpha = 1/2. We show that multiple giant components appear simultaneously in a strongly discontinuous percolation transition and remain distinct. Furthermore, tuning the value of alpha determines the number of such components with smaller alpha leading to an increasingly delayed and more explosive transition. The location of the critical point and strongly discontinuous nature are not affected if only edges which span components are sampled.

Final version appearing in PRL

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• Self-organized adaptation of a simple neural circuit enables complex robot behaviour
• Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
• Explosive percolation in scale-free networks
• Explosive percolation via control of the largest cluster
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Cited by in corpus (3)

• Kinetics of Ring Formation
• Watersheds and Explosive percolation
• Bohman-Frieze processes at criticality and emergence of the giant component