Propagation of confidential information on scale-free networks

We use Monte Carlo simulations and arguments from percolation theory in order to determine how “confidential” information propagates or localizes on a scale-free network. The basic assumption of our models is that this type of information propagates through the subnetwork of “best friends” which constitute a persons “circle of trust”. We find that there is a sharp percolation transition between a phase where “confidential” information localizes and a phase where “confidential” information propagates. This transition is controlled by the number of best friends m0 that a person is willing to have, and occurs for m0 values higher than intuitively expected from the “small world” property of random networks.