This paper presents a framework for analyzing and comparing the social network formation behavior of large-scale language models (LLMs) with human network dynamics. In both synthetic and real-world settings (e.g., friendship, communication, and employment networks), we demonstrate that LLMs consistently replicate fundamental micro-principles such as preferential connections, triangle closure, and homogeneity, as well as macro-principles such as community structure and the small-world effect. Notably, the relative emphasis of these principles varies across contexts; for example, LLMs favor homogeneity in friendship networks and heterogeneity in organizational settings, reflecting patterns of social mobility. Survey results from human participants confirm a high degree of concordance between LLMs and human participants in link formation decisions. This study demonstrates that LLMs can be a powerful tool for social simulation and synthetic data generation, while also raising important questions about bias, fairness, and the design of AI systems participating in human networks.