We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: f, the fraction of vertices initially activated, and p, the fraction of undamaged vertices in the graph. We observe two transitions: the giant active component appears continuously at a first threshold. There may also be a second, discontinuous, hybrid transition at a higher threshold. Avalanches of activations increase in size as this second critical point is approached, finally diverging at this threshold. We describe the existence of a special critical point at which this second transition first appears. In networks with degree distributions whose second moment diverges (but whose first moment does not), we find a qualitatively different behavior. In this case the giant active component appears for any f>0 and p>0, and the discontinuous transition is absent. This means that the giant active component is robust to damage, and also is very easily activated. We also formulate a generalized bootstrap process in which each vertex can have an arbitrary threshold.
%0 Journal Article
%1 Baxter2010Bootstrap
%A Baxter, G. J.
%A Dorogovtsev, S. N.
%A Goltsev, A. V.
%A Mendes, J. F. F.
%D 2010
%I American Physical Society
%J Physical Review E
%K percolation networks bootstrap
%N 1
%P 011103+
%R 10.1103/physreve.82.011103
%T Bootstrap percolation on complex networks
%U http://dx.doi.org/10.1103/physreve.82.011103
%V 82
%X We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: f, the fraction of vertices initially activated, and p, the fraction of undamaged vertices in the graph. We observe two transitions: the giant active component appears continuously at a first threshold. There may also be a second, discontinuous, hybrid transition at a higher threshold. Avalanches of activations increase in size as this second critical point is approached, finally diverging at this threshold. We describe the existence of a special critical point at which this second transition first appears. In networks with degree distributions whose second moment diverges (but whose first moment does not), we find a qualitatively different behavior. In this case the giant active component appears for any f>0 and p>0, and the discontinuous transition is absent. This means that the giant active component is robust to damage, and also is very easily activated. We also formulate a generalized bootstrap process in which each vertex can have an arbitrary threshold.
@article{Baxter2010Bootstrap,
abstract = {{We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: f, the fraction of vertices initially activated, and p, the fraction of undamaged vertices in the graph. We observe two transitions: the giant active component appears continuously at a first threshold. There may also be a second, discontinuous, hybrid transition at a higher threshold. Avalanches of activations increase in size as this second critical point is approached, finally diverging at this threshold. We describe the existence of a special critical point at which this second transition first appears. In networks with degree distributions whose second moment diverges (but whose first moment does not), we find a qualitatively different behavior. In this case the giant active component appears for any f>0 and p>0, and the discontinuous transition is absent. This means that the giant active component is robust to damage, and also is very easily activated. We also formulate a generalized bootstrap process in which each vertex can have an arbitrary threshold.}},
added-at = {2019-06-10T14:53:09.000+0200},
author = {Baxter, G. J. and Dorogovtsev, S. N. and Goltsev, A. V. and Mendes, J. F. F.},
biburl = {https://www.bibsonomy.org/bibtex/26631bc8539881b10391e56be7f42dcad/nonancourt},
citeulike-article-id = {8240941},
citeulike-linkout-0 = {http://dx.doi.org/10.1103/physreve.82.011103},
citeulike-linkout-1 = {http://link.aps.org/abstract/PRE/v82/i1/e011103},
citeulike-linkout-2 = {http://link.aps.org/pdf/PRE/v82/i1/e011103},
doi = {10.1103/physreve.82.011103},
interhash = {7e0251cbe53d1472025553698652736c},
intrahash = {6631bc8539881b10391e56be7f42dcad},
journal = {Physical Review E},
keywords = {percolation networks bootstrap},
month = jul,
number = 1,
pages = {011103+},
posted-at = {2010-11-12 10:42:12},
priority = {2},
publisher = {American Physical Society},
timestamp = {2019-08-23T10:58:50.000+0200},
title = {{Bootstrap percolation on complex networks}},
url = {http://dx.doi.org/10.1103/physreve.82.011103},
volume = 82,
year = 2010
}