An evident peculiarity in real-life debates is polarization, which produces the push of people���s opinions to extreme positions. It is a fundamental task to understand if opinion dynamics models built to understand the opinion formation processes can reproduce them. In this work, we focus on this issue, focusing on the polarization behavior of the popular Friendkin-Johnesn (FJ) model. Despite being this model largely used for studying many aspects of opinion dynamics, the related literature is quite confusing on the definition of both the FJ model and polarization, and mainly ignored the issue of understanding polarization dynamics. In this paper, we fill this gap. First, we make a comprehensive survey on the FJ model emphasizing how it has been proposed in several different forms. Secondly, we have analyzed the polarization definitions given by the literature, deriving the relations among them all. In the end, we focus on the problem of understanding if the FJ can capture polarization, and we proved that this is the case for the largest part of polarization definitions. The results are of paramount importance since they confirm that the FJ model is a realistic instrument to study opinion dynamics. All the theoretical results were validated on real social networks data.

This work is under submission to PNAS journal