Anastasios Giovanidis, Bruno Baynat, Clémence Magnien & Antoine Vendeville
IEEE/ACM Transactions on Networking ( Early Access ) (2021)
This work introduces an original mathematical model to analyze 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/her own Wall and Newsfeed, and has his/her own individual self-posting and re-posting activity. As a main result using the developed model, the probabilities that posts originating from a given user are found on the Wall and Newsfeed of any other can be derived in closed form. These are the solution of a linear system of equations, which can be resolved iteratively. In fact, the new model is very flexible with respect to the modeling assumptions. Using the probabilities derived from the solution, a new measure of per-user influence over the entire network is defined, named the Ψ-score, which combines the user position on the graph with user (re-)posting activity. In the homogeneous case where all users have the same activity rates, it is shown that a variant of the Ψ-score is equal to PageRank. Furthermore, the new model and its Ψ-score are compared against the empirical influence measured from very large data traces (Twitter, Weibo). The results illustrate that these new tools can accurately rank influencers with asymmetric (re-)posting activity for such real world applications.
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