Slight changes in the number of connections within a network that form at random (for example, connections in social networks) can lead to a huge increase in connectivity, a phenomenon termed "explosive percolation." These percolation transitions are often studied with Erdös and Rényi models, in which edges connecting pairs of vertices in a network are added randomly or according to a rule. Whether these transitions are continuous in nature has been the subject of several recent studies. Cho et al. (p. 1185; see the Perspective by Ziff) examined the effect of avoiding bridge bonds that create a spanning cluster (one that completes the percolation path) on the continuity of transitions for a d-dimensional lattice (up to six dimensions). Analytical arguments and numerical studies reveal a critical value for the number of bonds m below which the percolation transition is continuous and above which it is discontinuous. The critical value depends on d and on the fractal dimension of the bridge bonds of the clusters.
%0 Journal Article
%1 Cho2013Avoiding
%A Cho, Y. S.
%A Hwang, S.
%A Herrmann, H. J.
%A Kahng, B.
%D 2013
%I American Association for the Advancement of Science
%J Science
%K percolation critical-phenomena explosive-percolation
%N 6124
%P 1185--1187
%R 10.1126/science.1230813
%T Avoiding a Spanning Cluster in Percolation Models
%U http://dx.doi.org/10.1126/science.1230813
%V 339
%X Slight changes in the number of connections within a network that form at random (for example, connections in social networks) can lead to a huge increase in connectivity, a phenomenon termed "explosive percolation." These percolation transitions are often studied with Erdös and Rényi models, in which edges connecting pairs of vertices in a network are added randomly or according to a rule. Whether these transitions are continuous in nature has been the subject of several recent studies. Cho et al. (p. 1185; see the Perspective by Ziff) examined the effect of avoiding bridge bonds that create a spanning cluster (one that completes the percolation path) on the continuity of transitions for a d-dimensional lattice (up to six dimensions). Analytical arguments and numerical studies reveal a critical value for the number of bonds m below which the percolation transition is continuous and above which it is discontinuous. The critical value depends on d and on the fractal dimension of the bridge bonds of the clusters.
@article{Cho2013Avoiding,
abstract = {{Slight changes in the number of connections within a network that form at random (for example, connections in social networks) can lead to a huge increase in connectivity, a phenomenon termed "explosive percolation." These percolation transitions are often studied with Erd\"{o}s and R\'{e}nyi models, in which edges connecting pairs of vertices in a network are added randomly or according to a rule. Whether these transitions are continuous in nature has been the subject of several recent studies. Cho et al. (p. 1185; see the Perspective by Ziff) examined the effect of avoiding bridge bonds that create a spanning cluster (one that completes the percolation path) on the continuity of transitions for a d-dimensional lattice (up to six dimensions). Analytical arguments and numerical studies reveal a critical value for the number of bonds m below which the percolation transition is continuous and above which it is discontinuous. The critical value depends on d and on the fractal dimension of the bridge bonds of the clusters.}},
added-at = {2019-06-10T14:53:09.000+0200},
author = {Cho, Y. S. and Hwang, S. and Herrmann, H. J. and Kahng, B.},
biburl = {https://www.bibsonomy.org/bibtex/2cd4c163c7ff24ff213a9cb9dede6080e/nonancourt},
citeulike-article-id = {12132090},
citeulike-linkout-0 = {http://dx.doi.org/10.1126/science.1230813},
citeulike-linkout-1 = {http://www.sciencemag.org/content/339/6124/1185.abstract},
citeulike-linkout-2 = {http://www.sciencemag.org/content/339/6124/1185.full.pdf},
citeulike-linkout-3 = {http://www.sciencemag.org/cgi/content/abstract/339/6124/1185},
citeulike-linkout-4 = {http://view.ncbi.nlm.nih.gov/pubmed/23471402},
citeulike-linkout-5 = {http://www.hubmed.org/display.cgi?uids=23471402},
day = 08,
doi = {10.1126/science.1230813},
interhash = {ebb5f8e29f98386728cddc16970498a1},
intrahash = {cd4c163c7ff24ff213a9cb9dede6080e},
issn = {1095-9203},
journal = {Science},
keywords = {percolation critical-phenomena explosive-percolation},
month = mar,
number = 6124,
pages = {1185--1187},
pmid = {23471402},
posted-at = {2013-03-10 12:23:57},
priority = {2},
publisher = {American Association for the Advancement of Science},
timestamp = {2019-08-01T16:09:32.000+0200},
title = {{Avoiding a Spanning Cluster in Percolation Models}},
url = {http://dx.doi.org/10.1126/science.1230813},
volume = 339,
year = 2013
}