Scale-free networks are one of the most famous examples of emergent behavior and are ubiquitous in social systems, especially online social media in which users can follow each other. By analyzing the interactions of multiple generative agents using GPT3.5-turbo as a language model, we demonstrate their ability to not only mimic individual human linguistic behavior but also exhibit collective phenomena intrinsic to human societies, in particular the emergence of scale-free networks. We discovered that this process is disrupted by a skewed token prior distribution of GPT3.5-turbo, which can lead to networks with extreme centralization as a kind of alignment. We show how renaming agents removes these token priors and allows the model to generate a range of networks from random networks to more realistic scale-free networks.