%0 Journal Article %1 Havlin_2005 %A Havlin, Shlomo %A Lopez, Eduardo %A Buldyrev, Sergey V. %A Stanley, H. Eugene %D 2005 %K conductance, diffusion, networks, resistors, scaling %T Anomalous conductance and diffusion in complex networks %X We study transport properties such as conductance and diffusion of complex networks such as scale-free and Erdos-Renyi networks. We consider the equivalent conoductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P (k) ∼ k−λ and Erd˝ s-R´ nyi networks in which each link has the o e same unit resistance. Our theoretical analysis for scale-free networks predicts a broad range of values of G (or the related diffusion constant D), with a power-law tail distribution ΦSF (G) ∼ G−gG , where gG = 2λ − 1. We confirm our predictions by simulations of scale-free networks solving the Kirchhoff equations for the conductance between a pair of nodes. The power-law tail in ΦSF (G) leads to large values of G, thereby significantly improving the transport in scale-free networks, compared to Erd˝ s-R´ nyi o e networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical “transport backbone” picture we suggest that the conductances of scale-free and Erd˝ s-R´ nyi networks can be approximated by ckA kB /(kA + kB ) o e for any pair of nodes A and B with degrees kA and kB . Thus, a single parameter c characterizes transport on both scale-free and Erd˝ s-R´ nyi networks. o e

@article{Havlin_2005, abstract = {We study transport properties such as conductance and diffusion of complex networks such as scale-free and Erdos-Renyi networks. We consider the equivalent conoductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P (k) ∼ k−λ and Erd˝ s-R´ nyi networks in which each link has the o e same unit resistance. Our theoretical analysis for scale-free networks predicts a broad range of values of G (or the related diffusion constant D), with a power-law tail distribution ΦSF (G) ∼ G−gG , where gG = 2λ − 1. We confirm our predictions by simulations of scale-free networks solving the Kirchhoff equations for the conductance between a pair of nodes. The power-law tail in ΦSF (G) leads to large values of G, thereby significantly improving the transport in scale-free networks, compared to Erd˝ s-R´ nyi o e networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical “transport backbone” picture we suggest that the conductances of scale-free and Erd˝ s-R´ nyi networks can be approximated by ckA kB /(kA + kB ) o e for any pair of nodes A and B with degrees kA and kB . Thus, a single parameter c characterizes transport on both scale-free and Erd˝ s-R´ nyi networks. o e}, added-at = {2010-05-10T08:12:01.000+0200}, author = {Havlin, Shlomo and Lopez, Eduardo and Buldyrev, Sergey V. and Stanley, H. Eugene}, biburl = {https://www.bibsonomy.org/bibtex/2ffd0ef8fdf843ea815745fff1194fb15/dhruvbansal}, interhash = {f8f5a32be807ea2f6c03b8b8da4bdaea}, intrahash = {ffd0ef8fdf843ea815745fff1194fb15}, keywords = {conductance, diffusion, networks, resistors, scaling}, optfile = {/home/dhruv/projects/work/papers/papers/Havlin_2005.pdf}, optnumber = {4}, optpages = {1--11}, optread = {nil}, optvolume = {2}, timestamp = {2010-05-10T08:12:03.000+0200}, title = {Anomalous conductance and diffusion in complex networks}, year = 2005 }