Explosive percolation via control of the largest cluster

Nuno A. M. Araujo and Hans J. Herrmann ()

No CCSS-10-005, Working Papers from ETH Zurich, Chair of Systems Design

Abstract: We disclose that only considering the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation our novel models obtain Gaussian cluster distributions and compact clusters as one would expect at first-order transitions. We also discover that, surprisingly, the cluster perimeters are fractal at the transition point yielding a fractal dimension of $1.23\pm0.03$ intriguingly close to that of watersheds.

Keywords: explosive percolation; discontinuous transition (search for similar items in EconPapers)
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