%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 }