Strongly discontinuous explosive percolation with multiple giant components

Details Strongly discontinuous explosive percolation with multiple giant components Strongly discontinuous explosive percolation with multiple giant components

2010-11-26

arxiv.org/abs/1011.5854v2

Phys. Rev. Lett. 106, 115701 (2011)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Final version appearing in PRL

Scientific paper

10.1103/PhysRevLett.106.115701

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.

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