An Analytical Model for the Propagation of Social Influence

Studying the propagation of social influence is critical in the analysis of online social networks. While most existing work focuses on the expected number of users influenced, the detailed probability distribution of users influenced is also significant. However, determining the probability distribution of the final influence propagation state is difficult. Monte-Carlo simulations may be used, but are computationally expensive. In this paper, we develop an analytical model for the influence propagation process in online social networks based on discrete-time Markov chains, and deduce a closed-form equation for the n-step transition probability matrix. We show that given any initial state, the probability distribution of the final influence propagation state may be easily obtained from a matrix product. This provides a powerful tool to further understand social influence propagation.