Epidemic spread in weighted networks
  We study the detailed epidemic spreading process in scale-free networks with weight that denote familiarity between two people or computers. The result shows that spreading velocity reaches a peak quickly then decays representing power-law time behavior, and comparing to non-weighted networks, precise hierarchical dynamics is not found although the nodes with larger strength is preferential to be infected. 
G. Yan, Tao Zhou, Jie Wang, Zhongqian Fu, Binghong Wang