Mathematical Modeling of Advertisement and Influence Spread in Social Networks

We consider the following advertisement problem in social networks. Given a fixed advertisement investment (e.g., provide free samples to small number of users), a company needs to determine the probability that users of a social network will eventually purchase the product. In this paper, we model social networks as scalefree graphs (with or without high clustering coefficient). We then characterize and model various influence mechanisms that govern the influence spreading in large scale social networks. We use the local mean field (LMF) technique to analyze these social networks wherein states of nodes can be changed by various influence mechanisms. Extensive simulations are carried out to validate the accuracy of our model. These results can provide insight in designing efficient advertising strategies in social networks.