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This paper studies Large Language Models (LLMs) augmented with structureddata--particularly graphs--a crucial data modality that remains underexploredin the LLM literature. We aim to understand when and why the incorporation ofstructural information inherent in graph data can improve the predictionperformance of LLMs on node classification tasks with textual features. Toaddress the ``when'' question, we examine a variety of prompting methods forencoding structural information, in settings where textual node features areeither rich or scarce. For the ``why'' questions, we probe into two potentialcontributing factors to the LLM performance: data leakage and homophily. Ourexploration of these questions reveals that (i) LLMs can benefit fromstructural information, especially when textual node features are scarce; (ii)there is no substantial evidence indicating that the performance of LLMs issignificantly attributed to data leakage; and (iii) the performance of LLMs ona target node is strongly positively related to the local homophily ratio ofthe node\footnote{Codes and datasets are at:\url{https://github.com/TRAIS-Lab/LLM-Structured-Data}}.

Can LLMs Effectively Leverage Graph Structural Information: When and Why