This paper explores the potential of large language models (LLMs) in graph generation tasks. The authors propose LLM4GraphGen, a framework that systematically evaluates LLMs' abilities in generating graphs with specific structures, distributions, and properties. The study investigates three key aspects: rule-based graph generation, distribution-based graph generation, and property-based graph generation. For rule-based generation, the authors test LLMs' ability to generate graphs following specific structural rules, such as trees, cycles, and bipartite graphs. They find that LLMs, particularly GPT-4, can generate graphs according to simple rules but struggle with more complex ones. The performance of LLMs is influenced by the type of prompt used, with some prompting methods not consistently improving results. In distribution-based generation, the authors assess LLMs' ability to generate graphs based on the distribution of existing graphs. They find that LLMs can understand and generate graphs with simple distributions but perform poorly in complex scenarios. Detailed examples and step-by-step reasoning (CoT) prompts help improve performance in distribution-based tasks. For property-based generation, the authors evaluate LLMs' ability to generate graphs with specific properties, such as molecules that inhibit HIV replication. They use a molecular property prediction dataset and find that LLMs can generate molecules with desired properties, although their performance varies. The results show that LLMs can generate molecules with certain properties, indicating their potential in drug discovery and other applications. The study highlights the potential of LLMs in graph generation, particularly in rule-based and distribution-based tasks. However, it also shows that LLMs have limitations, especially in complex scenarios. The findings suggest that further research is needed to improve LLMs' ability to generate graphs with specific properties and distributions. The results provide valuable insights for future research and practical applications in graph generation.This paper explores the potential of large language models (LLMs) in graph generation tasks. The authors propose LLM4GraphGen, a framework that systematically evaluates LLMs' abilities in generating graphs with specific structures, distributions, and properties. The study investigates three key aspects: rule-based graph generation, distribution-based graph generation, and property-based graph generation. For rule-based generation, the authors test LLMs' ability to generate graphs following specific structural rules, such as trees, cycles, and bipartite graphs. They find that LLMs, particularly GPT-4, can generate graphs according to simple rules but struggle with more complex ones. The performance of LLMs is influenced by the type of prompt used, with some prompting methods not consistently improving results. In distribution-based generation, the authors assess LLMs' ability to generate graphs based on the distribution of existing graphs. They find that LLMs can understand and generate graphs with simple distributions but perform poorly in complex scenarios. Detailed examples and step-by-step reasoning (CoT) prompts help improve performance in distribution-based tasks. For property-based generation, the authors evaluate LLMs' ability to generate graphs with specific properties, such as molecules that inhibit HIV replication. They use a molecular property prediction dataset and find that LLMs can generate molecules with desired properties, although their performance varies. The results show that LLMs can generate molecules with certain properties, indicating their potential in drug discovery and other applications. The study highlights the potential of LLMs in graph generation, particularly in rule-based and distribution-based tasks. However, it also shows that LLMs have limitations, especially in complex scenarios. The findings suggest that further research is needed to improve LLMs' ability to generate graphs with specific properties and distributions. The results provide valuable insights for future research and practical applications in graph generation.