Social networks shape opinions, behaviors, and information dissemination in human societies. As large language models (LLMs) increasingly integrate into social and professional environments, understanding their behavior within the context of social interactions and networks becomes essential. Our study analyzes LLMs' network formation behavior to examine whether the dynamics of multiple LLMs are similar to or different from human social dynamics. We observe that LLMs exhibit key social network principles, including preferential attachment, triadic closure, homophily, community structure, and the small-world phenomenon, when asked about their preferences in network formation. We also investigate LLMs' decision-making based on real-world networks, revealing that triadic closure and homophily have a stronger influence than preferential attachment and that LLMs perform well in network formation predictions. Overall, our study opens up new possibilities for using LLMs in network science research and helps develop socially aware LLMs by shedding light on their social interaction behaviors and exploring their impacts on social dynamics.
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