Social networks influence behaviors, preferences, and relationships and play a crucial role in the dissemination of information and norms within human societies. As large language models (LLMs) increasingly integrate into social and professional environments, understanding their behavior within the context of social networks and interactions becomes essential. Our study analyzes the behaviors of standard network structures and real-world networks to determine whether the dynamics of multiple LLMs align with human social dynamics. We explore various social network principles, including micro-level concepts such as preferential attachment, triadic closure, and homophily, as well as macro-level concepts like community structure and the small-world phenomenon. Our findings suggest that LLMs demonstrate all these principles when they are provided with network structures and asked about their preferences regarding network formation. Furthermore, we investigate LLMs' decision-making based on real-world networks to compare the strengths of these principles. Our results reveal that triadic closure and homophily have a stronger influence than preferential attachment and that LLMs substantially exceed random guessing in the task of network formation predictions. Overall, our study contributes to the development of socially aware LLMs by shedding light on LLMs' network formation behaviors and exploring their impacts on social dynamics and norms.

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