Percolation Transitions in Scale-Free Networks under Achlioptas Process

Details Percolation Transitions in Scale-Free Networks under Achlioptas Process Percolation Transitions in Scale-Free Networks under Achlioptas Process

2009-07-02

arxiv.org/abs/0907.0309v3

Phys. Rev. Lett. 103, 135702 (2009)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 6 figures

Scientific paper

It has been recently shown that the percolation transition is discontinuous in Erd\H{o}s-R\'enyi networks and square lattices in two dimensions under the Achlioptas Process (AP). Here, we show that when the structure is highly heterogeneous as in scale-free networks, a discontinuous transition does not always occur: a continuous transition is also possible depending on the degree distribution of the scale-free network. This originates from the competition between the AP that discourages the formation of a giant component and the existence of hubs that encourages it. We also estimate the value of the characteristic degree exponent that separates the two transition types.

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