Social balance is a concept in sociology which states that if every three individuals in a population achieve certain structures of positive or negative interactions, then the whole population ends up in one faction of positive interactions or divided between two or more antagonistic factions. In this paper, we consider a group of interacting large language models (LLMs) and study how, after continuous interactions, they can achieve social balance. Across three different LLM models, we found that social balance depends on (i) whether interactions are updated based on "relationships", "appraisals", or "opinions"; (ii) whether agents update their interactions based on homophily or influence from their peers; and (iii) the number of simultaneous interactions the LLMs consider. When social balance is achieved, its particular structure of positive or negative interactions depends on these three conditions and are different across LLM models and sizes. The stability of interactions and the justification for their update also vary across models. Thus, social balance is driven by the pre-training and alignment particular to each LLM model.

Signed Graph Neural Networks (SGNNs) have recently gained attention as an effective tool for several learning tasks on signed networks, i.e., graphs where edges have an associated polarity. One of these tasks is to predict the polarity of the links for which this information is missing, starting from the network structure and the other available polarities. However, when the available polarities are few and potentially noisy, such a task becomes challenging. In this work, we devise a semi-supervised learning framework that builds around the novel concept of \emph{multiscale social balance} to improve the prediction of link polarities in settings characterized by limited data quantity and quality. Our model-agnostic approach can seamlessly integrate with any SGNN architecture, dynamically reweighting the importance of each data sample while making strategic use of the structural information from unlabeled edges combined with social balance theory. Empirical validation demonstrates that our approach outperforms established baseline models, effectively addressing the limitations imposed by noisy and sparse data. This result underlines the benefits of incorporating multiscale social balance into SGNNs, opening new avenues for robust and accurate predictions in signed network analysis.