# Performance Analysis of Online Social Platforms

## TL;DR

This paper presents a mathematical model to analyze how posts spread on online social platforms, deriving probabilities of post visibility and introducing a new influence measure considering platform design and user activity.

## Contribution

The paper introduces a novel mathematical framework for modeling post diffusion and influence ranking that incorporates platform structure, user activity, and competition among posts.

## Key findings

- Derived closed-form probabilities for post visibility between users.
- Validated model accuracy through simulations.
- Proposed a new influence measure accounting for platform and user dynamics.

## Abstract

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.