The structural properties of naturally arising social graphs are extensively studied to understand their evolution. Prior approaches for modeling network dynamics typically rely on rule-based models, which lack realism and generalizability, or deep learning-based models, which require large-scale training datasets. As abstract graph representations of entity-wise interactions, social graphs present an opportunity to explore network evolution mechanisms through realistic simulations of human-item interactions. Leveraging the pre-trained social consensus knowledge embedded in large language models (LLMs), we present GraphAgent-Generator (GAG), a novel simulation-based framework for dynamic, text-attributed social graph generation. GAG simulates the temporal node and edge generation processes for zero-shot social graph generation. The resulting graphs adhere to seven key macroscopic network properties, achieving an 11% improvement in microscopic graph structure metrics. Through the node classification benchmarking task, we validate that GAG effectively captures the intricate text-structure correlations in graph generation. Furthermore, GAG supports generating graphs with up to nearly 100,000 nodes or 10 million edges through large-scale LLM-based agent simulation with parallel acceleration, achieving a minimum speed-up of 90.4%. The source code is available at https://github.com/Ji-Cather/GraphAgent.