Spreading and localization of information in scale-free networks with   communication constraints
  We study localization of information on scale free networks with communication constraints when, for some reason, information can propagate only between ``mutually trusted nodes'' (MTN). We propose an algorithm to construct the MTN network and show that there is a critical value of trusted nodes below which information localizes. This critical value increases drastically if a fraction p of nodes does not transfer information at all. We study the fraction of initial messangers needed to inform a desired fraction of the network as a function of the average number of trusted nodes and discuss possible applications of the model to marketing, to the spreading of risky information and to the spreading of a disease with very short incubation time. 
Kosmas Kosmidis and Armin Bunde