This study explores the network formation behaviors of multiple large language models (LLMs) in the context of social and professional settings. By simulating interactions among LLM agents across various model families, the research examines whether these models exhibit key aspects of human network dynamics, such as preferential attachment, triadic closure, homophily, community structure, and the small-world phenomenon. The findings show that LLMs consistently exhibit these social network principles, adapting their strategies based on the characteristics of the network they are forming. For example, in Facebook networks, LLMs prioritize triadic closure and homophily, reflecting close-knit friendships; in phone networks, homophily and preferential attachment dominate, capturing personal and professional connections; and in employment networks, LLMs favor heterophily and high-degree connections, aligning with career advancement dynamics. These results open new avenues for using LLMs in network science research, particularly in agent-based modeling and synthetic network generation. The study also highlights the importance of considering biases and context when employing LLMs in networking scenarios, emphasizing the need for further research to align LLM behavior with human expectations.This study explores the network formation behaviors of multiple large language models (LLMs) in the context of social and professional settings. By simulating interactions among LLM agents across various model families, the research examines whether these models exhibit key aspects of human network dynamics, such as preferential attachment, triadic closure, homophily, community structure, and the small-world phenomenon. The findings show that LLMs consistently exhibit these social network principles, adapting their strategies based on the characteristics of the network they are forming. For example, in Facebook networks, LLMs prioritize triadic closure and homophily, reflecting close-knit friendships; in phone networks, homophily and preferential attachment dominate, capturing personal and professional connections; and in employment networks, LLMs favor heterophily and high-degree connections, aligning with career advancement dynamics. These results open new avenues for using LLMs in network science research, particularly in agent-based modeling and synthetic network generation. The study also highlights the importance of considering biases and context when employing LLMs in networking scenarios, emphasizing the need for further research to align LLM behavior with human expectations.