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arXiv · 1005.2504

Explosive percolation via control of the largest cluster

N. A. M. Araújo·H. J. Herrmann
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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 $1.23\pm0.03$, close to that of watersheds.

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N. A. M. Araújo, H. J. Herrmann. 2010-06-16. Explosive percolation via control of the largest cluster. https://doi.org/10.1103/physrevlett.105.035701

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