Weighted Scale-Free Networks with Stochastic Weight Assignments

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.