Properties of weighted structured scale-free networks

A simple model for weighted structured scale-free (WSSF) networks is proposed. The growth dynamics of the network is based on a naive weight-driven deactivation mechanism which couples the establishment of new active vertices and the weights’ dynamical evolution. Simulations show that all the interesting statistical properties of the generated network (vertices degree, vertices strength and links weight) display good right-skewed distribution observed in many realistic systems. Particularly, if the constant bias factor in deactivation probability is appropriately chosen, a power law distribution P(k)∼k<Superscript>- γ</Superscript> for vertices total degree k with the exponent γ=3 is obtained. As a survey of the model, the epidemic spreading process in WSSF networks is studied based on the standard susceptible-infected (SI) model. The spreading velocity reaches a peak very quickly after the infection outbreaks which is similar to the case of infection propagation in other heterogeneous networks; and in the long time propagation it decays approximately with an exponential form. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005