# Transport between multiple users in complex networks

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- 15 Citations

## Abstract.

We study the transport properties of model networks such as
scale-free and Erdös-Rényi networks as well as a real
network. We consider few possibilities for the trnasport problem.
We start by studying 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
$\Phi_{\rm SF}(G)\sim G^{-g_G}$
, where g_{G}=2λ-1, and
λ is the decay exponent for the scale-free network degree
distribution. The power-law tail in Φ_{SF}(G) leads to
large values of G, thereby significantly improving the transport
in scale-free networks, compared to Erdös-Rényi networks
where the tail of the conductivity distribution decays
exponentially. We develop a simple physical picture of the
transport to account for the results. The other model for
transport is the *max-flow* model, where conductance is defined
as the number of link-independent paths between the two nodes, 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. We then extend our study to the case of
multiple sources ans sinks, where the transport is defined between two
*groups* of nodes. We find a fundamental difference between
the two forms of flow when considering the quality of the
transport with respect to the number of sources, and find an
optimal number of sources, or users, for the max-flow case. A
qualitative (and partially quantitative) explanation is also
given.

## PACS.

89.75.Hc Networks and genealogical trees 05.60.Cd Classical transport## Preview

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