On the Spread of Innovation in Social Networks

In this paper we analyse different aspects of the diffusion of innovation in social network. Adopting the linear threshold model we firstly propose an algorithm based on the linear programming which takes as input a set of innovators and returns the maximal cohesive subset contained in the complement of the seed set. Then we introduce and formalize with integer programming two problems. The first one is that of finding a seed set of r individual that maximizes the spread of innovation in the network in k step. The second one is that of finding a seed set whose cardinality is minimal which diffuses the innovation to a desired set of adopters in k steps.