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.
%0 Journal Article
%1 Cho2009Percolation
%A Cho, Y. S.
%A Kim, J. S.
%A Park, J.
%A Kahng, B.
%A Kim, D.
%D 2009
%I American Physical Society
%J Physical Review Letters
%K percolation explosive-percolation scale-free-networks
%N 13
%P 135702+
%R 10.1103/physrevlett.103.135702
%T Percolation Transitions in Scale-Free Networks under the Achlioptas Process
%U http://dx.doi.org/10.1103/physrevlett.103.135702
%V 103
%X 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.
@article{Cho2009Percolation,
abstract = {{It has been recently shown that the percolation transition is discontinuous in Erd\H{o}s-R\'{e}nyi 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.}},
added-at = {2019-06-10T14:53:09.000+0200},
author = {Cho, Y. S. and Kim, J. S. and Park, J. and Kahng, B. and Kim, D.},
biburl = {https://www.bibsonomy.org/bibtex/29e82a48a94c4f09d2dc2e25166daf657/nonancourt},
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citeulike-linkout-1 = {http://link.aps.org/abstract/PRL/v103/e135702},
citeulike-linkout-2 = {http://dx.doi.org/10.1103/physrevlett.103.135702},
citeulike-linkout-3 = {http://link.aps.org/abstract/PRL/v103/i13/e135702},
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doi = {10.1103/physrevlett.103.135702},
interhash = {883907cf859509a908d43a65d7fc97ca},
intrahash = {9e82a48a94c4f09d2dc2e25166daf657},
journal = {Physical Review Letters},
keywords = {percolation explosive-percolation scale-free-networks},
month = sep,
number = 13,
pages = {135702+},
posted-at = {2009-12-18 11:39:54},
priority = {2},
publisher = {American Physical Society},
timestamp = {2019-08-01T16:13:01.000+0200},
title = {{Percolation Transitions in Scale-Free Networks under the Achlioptas Process}},
url = {http://dx.doi.org/10.1103/physrevlett.103.135702},
volume = 103,
year = 2009
}