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| Weighted Gradient Networks on Complex Networks |
| Shuai Zhang, Mangui Liang |
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Abstract This paper reports the finding of a weighted gradient network model
on the unweighted substrate networks, where the edge weight depends
on the degree of the node it connects and a tunable parameter
$\alpha$. With the new definition of the jamming coefficient, the
results of numerical simulations show that in both
Barab\'{a}si-Albert (BA) scale-free networks and Erd\"{o}s-R\'{e}nyi
(ER) random networks, the jamming coefficient becomes larger with
the increase of average degree $\langle k \rangle$ for the same
$\alpha$. Furthermore, there exists a critical value of $\alpha_{c}$
in two networks with the same average degree. For $\alpha <
\alpha_{c}$, the ER random network has a higher level of congestion
than BA scale-free network, while $\alpha > \alpha_{c}$ the opposite
occurs.
DOI: 10.12733/jics20101722
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