  We propose and study a model of weighted scale-free networks incorporating a
stochastic scheme for weight assignments to the links, taking into account both
the popularity and fitness of a node. As the network grows the weights of links
are driven either by the connectivity with probability $p$ or by the fitness
with probability $1-p$. Results of numerical simulations show that the total
weight associated with a selected node exhibits a power law distribution with
an exponent $\sigma$, the value of which depends on the probability $p$. The
exponent $\sigma$ decreases continuously as $p$ increases. For $p=0$, the total
weight distribution displays the same scaling behavior as that of the
connectivity distribution with $\sigma= \gamma = 3$, where $\gamma$ is the
exponent characterizing the connectivity distribution. An analytical expression
for the total weight is derived so as to explain the features observed in the
numerical results. Numerical results are also presented for a generalized model
with a fitness-dependent link formation mechanism.
