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arXiv · 0907.0309

Percolation Transitions in Scale-Free Networks under Achlioptas Process

Y. S. Cho·J. S. Kim·J. Park·B. Kahng·D. Kim
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Abstract

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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Y. S. Cho, J. S. Kim, J. Park, B. Kahng, D. Kim. 2009-07-02. Percolation Transitions in Scale-Free Networks under Achlioptas Process. https://doi.org/10.1103/physrevlett.103.135702

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