This paper explores the potential of large language models (LLMs) in graph generation, a task that has received less attention compared to LLMs' success in graph discriminative tasks such as node classification. The authors propose LLM4GraphGen, a systematic approach to evaluate LLMs' abilities in understanding and generating graphs with specific properties. They design several tasks, including rule-based, distribution-based, and property-based graph generation, and conduct extensive experiments using GPT-4. The results show that GPT-4 has preliminary abilities in rule-based and distribution-based graph generation, but the effectiveness of prompting methods like few-shot and chain-of-thought is inconsistent. Additionally, GPT-4 shows potential in generating molecules with specific properties, indicating its ability to leverage domain knowledge. The findings 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, a task that has received less attention compared to LLMs' success in graph discriminative tasks such as node classification. The authors propose LLM4GraphGen, a systematic approach to evaluate LLMs' abilities in understanding and generating graphs with specific properties. They design several tasks, including rule-based, distribution-based, and property-based graph generation, and conduct extensive experiments using GPT-4. The results show that GPT-4 has preliminary abilities in rule-based and distribution-based graph generation, but the effectiveness of prompting methods like few-shot and chain-of-thought is inconsistent. Additionally, GPT-4 shows potential in generating molecules with specific properties, indicating its ability to leverage domain knowledge. The findings provide valuable insights for future research and practical applications in graph generation.