  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.
