The 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 non-trivial 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.