%0 Journal Article %1 Wu2007Numerical %A Wu, Zhenhua %A Lagorio, Cecilia %A Braunstein, Lidia A. %A Cohen, Reuven %A Havlin, Shlomo %A Stanley, H. Eugene %D 2007 %I American Physical Society %J Physical Review E %K upper-critical-dimension percolation scale-free-networks %N 6 %P 066110+ %R 10.1103/physreve.75.066110 %T Numerical evaluation of the upper critical dimension of percolation in scale-free networks %U http://dx.doi.org/10.1103/physreve.75.066110 %V 75 %X We propose numerical methods to evaluate the upper critical dimension dc of random percolation clusters in Erd\Hos-Rényi networks and in scale-free networks with degree distribution P(k)∼k−λ, where k is the degree of a node and λ is the broadness of the degree distribution. Our results support the theoretical prediction, dc=2(λ−1)∕(λ−3) for scale-free networks with 3<λ<4 and dc=6 for Erd\Hos-Rényi networks and scale-free networks with λ>4. When the removal of nodes is not random but targeted on removing the highest degree nodes we obtain dc=6 for all λ>2. Our method also yields a better numerical evaluation of the critical percolation threshold pc for scale-free networks. Our results suggest that the finite size effects increases when λ approaches 3 from above.

@article{Wu2007Numerical, abstract = {{We propose numerical methods to evaluate the upper critical dimension dc of random percolation clusters in Erd\H{o}s-R\'{e}nyi networks and in scale-free networks with degree distribution P(k)∼k−λ, where k is the degree of a node and λ is the broadness of the degree distribution. Our results support the theoretical prediction, dc=2(λ−1)∕(λ−3) for scale-free networks with 3<λ<4 and dc=6 for Erd\H{o}s-R\'{e}nyi networks and scale-free networks with λ>4. When the removal of nodes is not random but targeted on removing the highest degree nodes we obtain dc=6 for all λ>2. Our method also yields a better numerical evaluation of the critical percolation threshold pc for scale-free networks. Our results suggest that the finite size effects increases when λ approaches 3 from above.}}, added-at = {2019-06-10T14:53:09.000+0200}, author = {Wu, Zhenhua and Lagorio, Cecilia and Braunstein, Lidia A. and Cohen, Reuven and Havlin, Shlomo and Stanley, H. Eugene}, biburl = {https://www.bibsonomy.org/bibtex/2e0392133e4e6d2aa371d2e34de798f3a/nonancourt}, citeulike-article-id = {9023586}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/physreve.75.066110}, citeulike-linkout-1 = {http://link.aps.org/abstract/PRE/v75/i6/e066110}, citeulike-linkout-2 = {http://link.aps.org/pdf/PRE/v75/i6/e066110}, doi = {10.1103/physreve.75.066110}, interhash = {7001dd3372ae77827451e354ce831bf4}, intrahash = {e0392133e4e6d2aa371d2e34de798f3a}, journal = {Physical Review E}, keywords = {upper-critical-dimension percolation scale-free-networks}, month = jun, number = 6, pages = {066110+}, posted-at = {2011-06-24 10:08:10}, priority = {2}, publisher = {American Physical Society}, timestamp = {2019-08-01T16:13:16.000+0200}, title = {{Numerical evaluation of the upper critical dimension of percolation in scale-free networks}}, url = {http://dx.doi.org/10.1103/physreve.75.066110}, volume = 75, year = 2007 }