The Semi-definite Programming Model for Optimizing Information Propagation Rate on Social Network Based on the Spectral Graph Theory.

In the study of online collaboration, one of the important aspects to optimize information propagation among users is to improve the rate of the propagation besides extending the propagation range, e.g., to deliver the advertisements to given target customers in shortest time or to inform a community in limited time. Due to the global optimization requirement, it is often challenging to optimize the propagation rate on a social network efficiently. Concerning the transition probability on each interpersonal relationship, we define information propagation as a random walk on a weighted directed graph, and indicate the propagation rate with the convergence rate of the random walk. Based on spectral graph theory, we further connect the convergence rate with the second smallest eigenvalue of the graph. Finally, by increasing the , a semi-definite programming model is proposed to globally optimize the information propagation rate more easily. Experimental results on real social network shows that the proposed solution can optimize the information propagation rate and further benefit the effectiveness of different typical influence diffusion models.