%0 Journal Article %1 Miller2016Equivalence %A Miller, Joel C. %D 2016 %J Physical Review E %K percolation cascades k-core bootstrap bond-percolation %N 3 %P 1837+ %R 10.1103/PhysRevE.94.032313 %T Equivalence of several generalized percolation models on networks %U http://dx.doi.org/10.1103/PhysRevE.94.032313 %V 94 %X Many different concepts of percolation exist for networks. We show that bond percolation, site percolation, \$k\$-core percolation, and bootstrap percolation are all special cases of the Watts Threshold model. We show that the "heterogeneous \$k\$-core" and a corresponding heterogeneous bootstrap model are equivalent to one another and the Watts Threshold Model. A more recent model of a "Generalized Epidemic Process" is also shown to be a special case. Finally, we show that a natural generalization of the Watts Threshold Model is a special case of the Watts Threshold Model, and thus it is equivalent to the Watts Threshold Model as well.

@article{Miller2016Equivalence, abstract = {{Many different concepts of percolation exist for networks. We show that bond percolation, site percolation, \$k\$-core percolation, and bootstrap percolation are all special cases of the Watts Threshold model. We show that the "heterogeneous \$k\$-core" and a corresponding heterogeneous bootstrap model are equivalent to one another and the Watts Threshold Model. A more recent model of a "Generalized Epidemic Process" is also shown to be a special case. Finally, we show that a natural generalization of the Watts Threshold Model is a special case of the Watts Threshold Model, and thus it is equivalent to the Watts Threshold Model as well.}}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {Miller, Joel C.}, biburl = {https://www.bibsonomy.org/bibtex/28602201d5f63d19e506c0218616e7f04/nonancourt}, citeulike-article-id = {13604870}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevE.94.032313}, citeulike-linkout-1 = {http://arxiv.org/abs/1505.01396}, citeulike-linkout-2 = {http://arxiv.org/pdf/1505.01396}, day = 19, doi = {10.1103/PhysRevE.94.032313}, eprint = {1505.01396}, interhash = {d0e192ef18f9b9ede5cfee65414f3aad}, intrahash = {8602201d5f63d19e506c0218616e7f04}, issn = {2470-0053}, journal = {Physical Review E}, keywords = {percolation cascades k-core bootstrap bond-percolation}, month = sep, number = 3, pages = {1837+}, posted-at = {2015-05-07 09:01:01}, priority = {2}, timestamp = {2019-08-23T11:01:11.000+0200}, title = {{Equivalence of several generalized percolation models on networks}}, url = {http://dx.doi.org/10.1103/PhysRevE.94.032313}, volume = 94, year = 2016 }