Network Growth Rule Dependency of Percolation Criticality -- Generalized Explosive Percolation

Details Network Growth Rule Dependency of Percolation Criticality -- Generalized Explosive Percolation Network Growth Rule Dependency of Percolation Criticality -- Generalized Explosive Percolation

2011-11-08

arxiv.org/abs/1111.2005v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 4 figures

Scientific paper

To consider percolation criticality in the evolving network model exhaustively, we propose a general network-growth rule. Our proposed rule includes the conventional network-growth rule and the rule introduced by Achlioptas et al. in 2009 [Science 323, 1453 (2009)]. We introduce the generalized parameter $q$ which characterizes the method of time development of network growth. We calculate size-dependency of percolation step and fractal dimension of percolated cluster at the percolation step for several $q$. The strong size-dependency of percolation step is observed for intermediate $q$. Moreover, we find that fractal dimension obviously changes at the point between the conventional rule and the Achlioptas rule.

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