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Cho, Y S; Kim, J S; Park, J; Kahng, B; Kim, D
Physical review letters, 09/2009, Volume: 103, Issue: 13Journal Article
It has been recently shown that the percolation transition is discontinuous in Erdos-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.
