Role of second trials in cascades of information over networks.

We study the propagation of information in social networks. To do so, we focus on a cascade model where nodes are infected with probability p_{1} after their first contact with the information and with probability p_{2} at all subsequent contacts. The diffusion starts from one random node and leads to a cascade of infection. It is shown that first and subsequent trials play different roles in the propagation and that the size of the cascade depends in a nontrivial way on p_{1} , p_{2} , and on the network structure. Second trials are shown to amplify the propagation in dense parts of the network while first trials are dominant for the exploration of new parts of the network and launching new seeds of infection.