Article,
Percolation Transitions in Scale-Free Networks under the Achlioptas Process
Physical Review Letters, 103 (13): 135702+ (September 2009)
DOI: 10.1103/physrevlett.103.135702
Abstract
It has been recently shown that the percolation transition is discontinuous in Erd\Hos-Rényi 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.
