# Polarization and Fluctuations in Signed Social Networks

## TL;DR

This paper introduces a new opinion dynamics model for signed social networks that captures polarization and fluctuations, incorporating the boomerang effect and analyzing behavior under structural balance conditions.

## Contribution

It proposes a novel, intuitive model for opinion evolution in signed networks that accounts for psychological effects and analyzes opinion polarization and fluctuations beyond existing models.

## Key findings

- Opinions polarize under structural balance conditions.
- Opinions exhibit persistent fluctuations in unbalanced networks.
- The model captures richer behaviors than previous models.

## Abstract

Much recent research on social networks has focused on the modeling and analysis of how opinions evolve as a function of interpersonal relationships. It is also of great interest to model and understand the implications of friendly and antagonistic relationships. In this paper, we propose a new, simple and intuitive model that incorporates the socio-psychological phenomenon of the boomerang effect in opinion dynamics. We establish that, under certain conditions on the structure of the signed network that corresponds to the so-called structural balance property, the opinions in the network polarize. Compared to other models in the literature, our model displays a richer and perhaps more intuitive behavior of the opinions when the social network does not satisfy structural balance. In particular, we analyze signed networks in which the opinions show persistent fluctuations (including the case of the so-called clustering balance).