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Cryptocurrency transaction analysis often relies on black-box machine learning models that achieve high predictive performance but offer limited interpretability of transaction behaviors. This paper investigates the capabilities of large language models (LLMs) in analyzing real-world Bitcoin transaction graphs through a three-level framework: foundational metrics, characteristic overview, and contextual interpretation. To address token constraints, we introduce LLM4TG, a compact, human-readable graph representation, and CETraS, a connectivity-enhanced graph sampling algorithm. Experiments across five LLMs show that node-level information extraction achieves over 98.50% accuracy on most metrics, while meaningful graph characteristics are identified in up to 95.00% of responses. For address classification with limited labeled examples, top-1 accuracy reaches 50.49% using raw graphs, while top-3 accuracy reaches 72.43% using engineered features. These findings demonstrate the potential of LLMs for transaction graph analysis while revealing limitations in global graph reasoning, precise address classification, and explanation reliability.