Dominance or Fair Play in Social Networks? A Model of Influencer Popularity Dynamic

Abstract: This paper presents a data-driven mean-field approach to model the popularity dynamics of users seeking public attention, i.e., influencers. We propose a novel analytical model that integrates individual activity patterns, expertise in producing viral content, exogenous events, and the platform's role in visibility enhancement, ultimately determining each influencer's success. We analytically derive sufficient conditions for system ergodicity, enabling predictions of popularity distributions. A sensitivity analysis explores various system configurations, highlighting conditions favoring either dominance or fair play among influencers. Our findings offer valuable insights into the potential evolution of social networks towards more equitable or biased influence ecosystems.