  We study two kinds of weighted networks, weighted small-world (WSW) and
weighted scale-free (WSF). The weight $w_{ij}$ of a link between nodes $i$ and
$j$ in the network is defined as the product of endpoint node degrees; that is
$w_{ij}=(k_{i}k_{j})^{\theta}$. In contrast to adding weights to links during
networks being constructed, we only consider weights depending on the ``
popularity\rq\rq of the nodes represented by their connectivity. It was found
that the both weighted networks have broad distributions on characterization
the link weight, vertex strength, and average shortest path length.
Furthermore, as a survey of the model, the epidemic spreading process in both
weighted networks was studied based on the standard \emph{susceptible-infected}
(SI) model. The spreading velocity reaches a peak very quickly after the
infection outbreaks and an exponential decay was found in the long time
propagation.
