2 research outputs found
Anomalous electrical and frictionless flow conductance in complex networks
We study transport properties such as electrical and frictionless flow
conductance on scale-free and Erdos-Renyi 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 \Phi_{SF}(G) \sim
G^{g_G}, where g_G = 2\lambda - 1, where \lambda 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 \Phi_{SF}(G) leads
to large values of G, thereby significantly improving the transport in
scale-free networks, compared to Erdos-Renyi 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
Erdos-Renyi networks can be approximated by ck_Ak_B/(k_A+k_B) for any pair of
nodes A and B with degrees k_A and k_B. Thus, a single quantity c, which
depends on the average degree of the network, characterizes transport on
both scale-free and Erdos-Renyi 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.Comment: 8 pages, 11 figure