Ranking Online Social Users by their Influence

We introduce an original mathematical model to analyse the diffusion of posts within a generic online social platform. The main novelty is that each user is not simply considered as a node on the social graph, but is further equipped with his own Wall and Newsfeed, and has his own self-posting and re-posting activity. As a main result using our developed model, we derive in closed form the probabilities that posts originating from a given user are found on the Wall and Newsfeed of any other. These are the solution of a linear system of equations. Comparisons with simulations show the accuracy of our model and its robustness with respect to the modelling assumptions. Using the probabilities from the solution we define a new measure of per-user influence over the entire network, the Ψ-score, which combines the user position on the graph with the user (re-)posting activity. Furthermore, we compare the new model and its Ψ-score against the empirical influence measured from very large data traces (Twitter, Weibo). The results illustrate that these new tools can accurately rank influencers for such real world applications.