This study explores how multiple large language models (LLMs) form networks and whether their behaviors align with human social network dynamics. By simulating interactions among LLM agents across various model families, the research reveals that these models consistently exhibit key patterns associated with human network dynamics, including preferential attachment, triadic closure, homophily, community structure, and the small-world phenomenon. LLMs adapt their network formation strategies based on the context of the network, reflecting the context-dependent nature of human behavior. For example, in Facebook networks, LLMs prioritize triadic closure and homophily, mirroring 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 findings open new avenues for using LLMs in network science research, with potential applications in agent-based modeling and synthetic network generation. The study also highlights the potential of LLMs for synthetic dataset generation, which is critical in network science, especially in scenarios where privacy concerns limit access to real-world data. The results demonstrate that LLMs can simulate complex networks, such as social, economic, or biological systems, by leveraging their ability to simulate preferential attachment and scale-free distributions. These models can be used to study real-world phenomena like information diffusion, hub formation, or connectivity patterns under varying conditions. Additionally, the sensitivity of network structures to parameters like temperature and context underscores the importance of prompt design in steering outcomes, making LLMs versatile tools for tailored simulations. The study also finds that LLMs exhibit homophily, triadic closure, and preferential attachment in network formation, with homophily being the dominant factor. The results suggest that LLMs can be used to simulate realistic social and structural networks, aligning with social principles observed in real-world communities. The study also investigates the behavior of LLMs in real-world network formation contexts with four datasets in two differing real-world domains. The findings indicate that LLMs prioritize homophily in network formation, with coefficients for homophily being consistently the largest and highly significant across all datasets and models. The study also highlights the need for researchers to provide oversight and ensure that LLM behaviors align with human expectations when employing them in scientific research methods, such as agent-based modeling. The study suggests that LLMs may not necessarily need to mirror human networking behaviors and could be personalized to promote more equitable and efficient information dissemination. Future research directions include investigating LLM behavior in more complex interactions, exploring how LLMs can be integrated into real-world settings, and using our methods to create realistic synthetic networks.This study explores how multiple large language models (LLMs) form networks and whether their behaviors align with human social network dynamics. By simulating interactions among LLM agents across various model families, the research reveals that these models consistently exhibit key patterns associated with human network dynamics, including preferential attachment, triadic closure, homophily, community structure, and the small-world phenomenon. LLMs adapt their network formation strategies based on the context of the network, reflecting the context-dependent nature of human behavior. For example, in Facebook networks, LLMs prioritize triadic closure and homophily, mirroring 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 findings open new avenues for using LLMs in network science research, with potential applications in agent-based modeling and synthetic network generation. The study also highlights the potential of LLMs for synthetic dataset generation, which is critical in network science, especially in scenarios where privacy concerns limit access to real-world data. The results demonstrate that LLMs can simulate complex networks, such as social, economic, or biological systems, by leveraging their ability to simulate preferential attachment and scale-free distributions. These models can be used to study real-world phenomena like information diffusion, hub formation, or connectivity patterns under varying conditions. Additionally, the sensitivity of network structures to parameters like temperature and context underscores the importance of prompt design in steering outcomes, making LLMs versatile tools for tailored simulations. The study also finds that LLMs exhibit homophily, triadic closure, and preferential attachment in network formation, with homophily being the dominant factor. The results suggest that LLMs can be used to simulate realistic social and structural networks, aligning with social principles observed in real-world communities. The study also investigates the behavior of LLMs in real-world network formation contexts with four datasets in two differing real-world domains. The findings indicate that LLMs prioritize homophily in network formation, with coefficients for homophily being consistently the largest and highly significant across all datasets and models. The study also highlights the need for researchers to provide oversight and ensure that LLM behaviors align with human expectations when employing them in scientific research methods, such as agent-based modeling. The study suggests that LLMs may not necessarily need to mirror human networking behaviors and could be personalized to promote more equitable and efficient information dissemination. Future research directions include investigating LLM behavior in more complex interactions, exploring how LLMs can be integrated into real-world settings, and using our methods to create realistic synthetic networks.