Numerical evaluation of the upper critical dimension of percolation in scale-free networks TeX Export

@misc{citeulike:1295576, abstract = {We propose a numerical method to evaluate the upper critical dimension \$d\_c\$ of random percolation clusters in Erd\H{o}s-R\'{e}nyi networks and in scale-free networks with degree distribution \${\cal P}(k) \sim k^{-\lambda}\$, where \$k\$ is the degree of a node and \$\lambda\$ is the broadness of the degree distribution. Our results report the theoretical prediction, \$d\_c = 2(\lambda - 1)/(\lambda - 3)\$ for scale-free networks with \$3 \< \lambda \< 4\$ and \$d\_c = 6\$ for Erd\H{o}s-R\'{e}nyi networks and scale-free networks with \$\lambda \> 4\$. When the removal of nodes is not random but targeted on removing the highest degree nodes we obtain \$d\_c = 6\$ for all \$\lambda \> 2\$. Our method also yields a better numerical evaluation of the critical percolation threshold, \$p\_c\$, for scale-free networks. Our results suggest that the finite size effects increases when \$\lambda\$ approaches 3 from above.}, archivePrefix = {arXiv}, author = {Wu, Zhenhua and Lagorio, Cecilia and Braunstein, Lidia A. and Cohen, Reuven and Havlin, Shlomo and Stanley, Eugene H.}, citeulike-article-id = {1295576}, citeulike-linkout-0 = {http://arxiv.org/abs/0705.1547}, citeulike-linkout-1 = {http://arxiv.org/pdf/0705.1547}, day = {10}, eprint = {0705.1547}, keywords = {critical, degree, distribution, free, law, percolation, power, scale, threshold}, month = {May}, posted-at = {2007-05-14 18:07:44}, priority = {2}, title = {Numerical evaluation of the upper critical dimension of percolation in scale-free networks}, url = {http://arxiv.org/abs/0705.1547}, year = {2007} }

TY - ELEC ID - citeulike:1295576 L3 - citeulike-article-id:1295576 N2 - We propose a numerical method to evaluate the upper critical dimension $d_c$ of random percolation clusters in Erd\H{o}s-R\'{e}nyi networks and in scale-free networks with degree distribution ${\cal P}(k) \sim k^{-\lambda}$, where $k$ is the degree of a node and $\lambda$ is the broadness of the degree distribution. Our results report the theoretical prediction, $d_c = 2(\lambda - 1)/(\lambda - 3)$ for scale-free networks with $3 < \lambda < 4$ and $d_c = 6$ for Erd\H{o}s-R\'{e}nyi networks and scale-free networks with $\lambda > 4$. When the removal of nodes is not random but targeted on removing the highest degree nodes we obtain $d_c = 6$ for all $\lambda > 2$. Our method also yields a better numerical evaluation of the critical percolation threshold, $p_c$, for scale-free networks. Our results suggest that the finite size effects increases when $\lambda$ approaches 3 from above. TI - Numerical evaluation of the upper critical dimension of percolation in scale-free networks KW - critical KW - degree KW - distribution KW - free KW - law KW - percolation KW - power KW - scale KW - threshold AU - Wu, Zhenhua AU - Lagorio, Cecilia AU - Braunstein, Lidia AU - Cohen, Reuven AU - Havlin, Shlomo AU - Stanley, Eugene PY - 2007/May/10/ UR - http://arxiv.org/abs/0705.1547 ER -