Not yet reviewed by Pith; the record is open.

When we integrate factual knowledge from knowledge graphs (KGs) into large language models (LLMs) to enhance their performance, the cost of injection through training increases with the scale of the models. Consequently, there is significant interest in developing prompt strategies that effectively incorporate KG information into LLMs. However, the community has not yet comprehensively understood how LLMs process and interpret KG information in different input formats and organizations within prompts, and researchers often rely on trial and error. To address this gap, we design extensive experiments to empirically study LLMs' comprehension of different KG prompts. At the literal level, we reveal LLMs' preferences for various input formats (from linearized triples to fluent natural language text). At the attention distribution level, we discuss the underlying mechanisms driving these preferences. We then investigate how the organization of structured knowledge impacts LLMs and evaluate LLMs' robustness in processing and utilizing KG information in practical scenarios. Our experiments show that (1) linearized triples are more effective than fluent NL text in helping LLMs understand KG information and answer fact-intensive questions; (2) Different LLMs exhibit varying preferences for different organizational formats of triples; (3) LLMs with larger scales are more susceptible to noisy, incomplete subgraphs.