Percolation transitions in scale-free networks under the Achlioptas process.
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.
Cho
Y S
YS
Center for Theoretical Physics and Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
Kim
J S
JS
Park
J
J
Kahng
B
B
Kim
D
D