Large Language Models (LLMs) can be deployed in situations where they process positive/negative interactions with other agents. We study how this is done under the sociological framework of social balance, which explains the emergence of one faction or multiple antagonistic ones among agents. Across different LLM models, we find that balance depends on the (i) type of interaction, (ii) update mechanism, and (iii) population size. Across (i)-(iii), we characterize the frequency at which social balance is achieved, the justifications for the social dynamics, and the diversity and stability of interactions. Finally, we explain how our findings inform the deployment of agentic systems.