A trust model for spreading gossip in social networks: a multi-type bootstrap percolation model

We introduce here a multi-type bootstrap percolation model, which we call $$ -Bootstrap Percolation ( $$ -BP), and apply it to study information propagation in social networks. In this model, a social network is represented by a graph G whose vertices have different labels corresponding to the type of role the person plays in the network (e.g. a student, an educator etc.). Once an initial set of vertices of G is randomly selected to be carrying a gossip (e.g. to be infected), the gossip propagates to a new vertex provided it is transmitted by a minimum threshold of vertices with different labels. By considering random graphs, which have been shown to closely represent social networks, we study different properties of the $$ -BP model through numerical simulations, and describe its implications when applied to rumour spread, fake news and marketing strategies.