We study scale-free networks constructed via a cooperative Achlioptas growth process. Links between nodes are introduced in order to produce a scale-free graph with given exponent λ for the degree distribution, but the choice of each new link depends on the mass of the clusters that this link will merge. Networks constructed via this biased procedure show a percolation transition which strongly differs from the one observed in standard percolation, where links are introduced just randomly. The different growth process leads to a phase transition with a nonvanishing percolation threshold already for λ>λc∼2.2. More interestingly, the transition is continuous when λ≤3 but becomes discontinuous when λ>3. This may have important consequences for both the structure of networks and for the dynamics of processes taking place on them.
%0 Journal Article
%1 Radicchi2009Explosive
%A Radicchi, Filippo
%A Fortunato, Santo
%D 2009
%I American Physical Society
%J Physical Review Letters
%K critical-phenomena networks explosive-percolation scale-free-networks
%N 16
%P 168701+
%R 10.1103/physrevlett.103.168701
%T Explosive Percolation in Scale-Free Networks
%U http://dx.doi.org/10.1103/physrevlett.103.168701
%V 103
%X We study scale-free networks constructed via a cooperative Achlioptas growth process. Links between nodes are introduced in order to produce a scale-free graph with given exponent λ for the degree distribution, but the choice of each new link depends on the mass of the clusters that this link will merge. Networks constructed via this biased procedure show a percolation transition which strongly differs from the one observed in standard percolation, where links are introduced just randomly. The different growth process leads to a phase transition with a nonvanishing percolation threshold already for λ>λc∼2.2. More interestingly, the transition is continuous when λ≤3 but becomes discontinuous when λ>3. This may have important consequences for both the structure of networks and for the dynamics of processes taking place on them.
@article{Radicchi2009Explosive,
abstract = {{We study scale-free networks constructed via a cooperative Achlioptas growth process. Links between nodes are introduced in order to produce a scale-free graph with given exponent λ for the degree distribution, but the choice of each new link depends on the mass of the clusters that this link will merge. Networks constructed via this biased procedure show a percolation transition which strongly differs from the one observed in standard percolation, where links are introduced just randomly. The different growth process leads to a phase transition with a nonvanishing percolation threshold already for λ>λc∼2.2. More interestingly, the transition is continuous when λ≤3 but becomes discontinuous when λ>3. This may have important consequences for both the structure of networks and for the dynamics of processes taking place on them.}},
added-at = {2019-06-10T14:53:09.000+0200},
author = {Radicchi, Filippo and Fortunato, Santo},
biburl = {https://www.bibsonomy.org/bibtex/22544bb997bb34a50743c2d1099cecaa6/nonancourt},
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doi = {10.1103/physrevlett.103.168701},
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intrahash = {2544bb997bb34a50743c2d1099cecaa6},
journal = {Physical Review Letters},
keywords = {critical-phenomena networks explosive-percolation scale-free-networks},
month = oct,
number = 16,
pages = {168701+},
posted-at = {2009-10-23 11:18:08},
priority = {2},
publisher = {American Physical Society},
timestamp = {2019-08-01T16:13:01.000+0200},
title = {{Explosive Percolation in Scale-Free Networks}},
url = {http://dx.doi.org/10.1103/physrevlett.103.168701},
volume = 103,
year = 2009
}