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Anomalous electrical and frictionless flow conductance in complex networks

López, Eduardo, Carmi, Shai, Havlin, Shlomo, Buldyrev, Sergey and Stanley, Eugene (2006) Anomalous electrical and frictionless flow conductance in complex networks. Physica D: Nonlinear Phenomena, 224 (1-2). pp. 69-76.


We study transport properties such as electrical and frictionless flow conductance on scale-free and Erdős–Rényi networks. We consider the conductance G between two arbitrarily chosen nodes where each link has the same unit resistance. Our theoretical analysis for scale-free networks predicts a broad range of values of G, with a power-law tail distribution , where gG=2λ−1, where λ is the decay exponent for the scale-free network degree distribution. 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 leads to large values of G, thereby significantly improving the transport in scale-free networks, compared to Erdős–Rényi 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 Erdős–Rényi networks can be approximated by ckAkB/(kA+kB) for any pair of nodes A and B with degrees kA and kB. Thus, a single quantity c, which depends on the average degree of the network, characterizes transport on both scale-free and Erdős–Rényi networks. We determine that c tends to 1 for increasing , and it is larger for scale-free networks. We compare the electrical results with a model for frictionless transport, where conductance is defined as the number of link-independent paths between A and B, and find that a similar picture holds. The effects of distance on the value of conductance are considered for both models, and some differences emerge. Finally, we use a recent data set for the AS (autonomous system) level of the Internet and confirm that our results are valid in this real-world example.

Item Type: Article
Keywords: Complex networks; Transport; Diffusion; Conductance; Scaling
Subject(s): Complexity
Centre: CABDyN Complexity Centre
Date Deposited: 25 Feb 2012 21:25
Last Modified: 23 Oct 2015 14:06

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