Explosive percolation via control of the largest cluster

Abstract

We show that only considering the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation our models obtain Gaussian cluster distributions and compact clusters as one would expect at first-order transitions. We also discover that the cluster perimeters are fractal at the transition point, yielding a fractal dimension of $1.23\pm 0.03$, close to that of watersheds.

4 pages, 5 figures, final version

References in corpus (2)

• Explosive percolation in scale-free networks
• New efficient methods to calculate watersheds

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