  We introduce an original mathematical model to analyze the diffusion of posts
within a generic online social platform. Each user of such a platform has his
own Wall and Newsfeed, as well as 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 probabilities are the solution of a linear
system of equations. Conditions of existence of the solution are provided, and
two ways of solving the system are proposed, one using matrix inversion and
another using fixed-point iteration. Comparisons with simulations show the
accuracy of our model and its robustness with respect to the modeling
assumptions. Hence, this article introduces a novel measure which allows to
rank users by their influence on the social platform, by taking into account
not only the social graph structure, but also the platform design, user
activity (self- and re-posting), as well as competition among posts.
