Opinion dynamics and network balance in social systems under external perturbations

In modern societies, political debate happens largely on social networks, which makes opinion dynamics models especially valuable for their descriptive and predictive power. Understanding how opinions form and change online can help keep public discourse healthy and protect the democratic foundations of our increasingly digital societies. This master's thesis explores opinion dynamics in complex social systems, with a particular focus on the role of leaders and their interaction with external events. To this end, we based our approach on Heider’s social balance theory. This latter is well documented in the literature, but the connection between micro-level balancing processes and broader network dynamics has received limited attention in existing research. To address this gap, we start from an opinion dynamics model that incorporates agreement dynamics and external information effects and we extend the model by introducing two new elements: Heider reputation heuristics, a structural property that leads to social balance, and leader–follower dynamics, essential to reproduce real interaction patterns. To connect theoretical modelling with empirical analysis, we examined whether real-world networks follow Heider reputation heuristics and how their features respond to external perturbations. We analysed interactions between normal users and Italian politicians on Twitter/X over five years, focusing on the Covid-19 pandemic as an external perturbation. The empirical analysis reveals significant pandemic-related changes: network balancedness decreased, cross-community retweet flows increased, and average triadic coherence diminished. We characterized triadic configurations based on leader-follower composition, identifying different stability patterns across different triadic types. Once the observables affected by the external event had been identified in the data, we sought to study these same observables within the model to validate its robustness. These findings establish that structural properties coming from triadic relations can be connected to emergent collective phenomena such as opinion polarization and leader cooperation dynamics. The extended model effectively captures how opinion formation and network stability evolve under external perturbations, linking micro-level structural network configurations with macro-level collective responses to crisis events.