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

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dc.creatorWu, Zhenhua
dc.creatorLagorio, Cecilia
dc.creatorBraunstein, Lidia A.
dc.creatorCohen, Reuven
dc.creatorHavlin, Shlomo
dc.creatorStanley, H. Eugene
dc.date2007-05-10
dc.date.accessioned2026-07-07T08:34:15Z
dc.date.available2026-07-07T08:34:15Z
dc.descriptionWe propose a numerical method to evaluate the upper critical dimension $d_c$ of random percolation clusters in Erdős-Rényi networks and in scale-free networks with degree distribution ${\cal P}(k) \sim k^{-λ}$, where $k$ is the degree of a node and $λ$ is the broadness of the degree distribution. Our results report the theoretical prediction, $d_c = 2(λ- 1)/(λ- 3)$ for scale-free networks with $3 < λ< 4$ and $d_c = 6$ for Erdős-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 $d_c = 6$ for all $λ> 2$. 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 $λ$ approaches 3 from above.
dc.description10 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/0705.1547
dc.identifierhttp://arxiv.org/abs/0705.1547
dc.identifierPhys. Rev. E 75, 066110 (2007)
dc.identifierdoi:10.1103/PhysRevE.75.066110
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139373
dc.subjectDisordered Systems and Neural Networks
dc.subjectStatistical Mechanics
dc.titleNumerical evaluation of the upper critical dimension of percolation in scale-free networks
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