Ranking Online Social Users by Their Influence

We introduce an original mathematical model to analyze the diffusion of posts within a generic online social platform. The main novelty is that each user not simply considered as node on graph, but further equipped with his/her own Wall and Newsfeed, has individual self-posting re-posting activity. As result using our developed model, we derive in closed form probabilities originating from given are found Newsfeed any other. These solution linear system equations, which can be resolved iteratively. In fact, very flexible respect modeling assumptions. Using derived solution, define new measure per-user influence over entire network, $\Psi $ -score, combines position graph (re-)posting homogeneous case where all users have same activity rates, it shown variant -score equal PageRank. Furthermore, compare its against empirical measured large data traces (Twitter, Weibo). results illustrate these tools accurately rank influencers asymmetric for such real world applications.