Reputation, Impact, and Relevance in Social Media

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Social Media are used for interaction between users via postings. Postings can have attached topics. Users may follow each other, or may express their special interest in special topics. Furthermore, users can comment on other postings or retweet them. As a consequence, postings will be on the so-called timeline of some users, where the timeline of a user indicates those postings that are visible to that user. These connections between users, postings, topics, and timeline can be used to define how influential users are, what the impact of a posting is, and how relevant a topic is. We extend an existing methodology. We define a model to capture the notions mentioned above and derive a (recursive) system of equations that defines user influence, posting impact, and topic relevancy in terms of each other. Then we present a solution for this set of equations, and a computational approach based on successive substitution.