Puns are a challenging form of figurative language that exploit phonetic similarity and semantic ambiguity to convey multiple meanings. Although large language models (LLMs) demonstrate strong language understanding capabilities, they still struggle with pun reasoning due to limited phonetic modeling and uncontrolled end-to-end generation. We propose \textbf{PunGraph}, a retrieval-enhanced knowledge graph framework for pun understanding. PunGraph constructs a phonetic-semantic lexical graph using the Unisyn phonetic dictionary, IPA and G2P representations, and WordNet definitions, and retrieves candidate words or senses to constrain LLM reasoning within a structured candidate space. We further introduce \textbf{WebPun}, a new large-scale dataset containing 5,730 annotated heterographic and homographic puns. Experiments on SemEval-2017 and WebPun show that PunGraph consistently improves the performance of small-scale LLMs and achieves competitive results against strong proprietary models. Further analysis shows that retrieval-guided phonetic and semantic constraints effectively reduce common reasoning errors in pun interpretation, highlighting the benefits of integrating structured knowledge with LLMs. We release our code and dataset at https://github.com/ysu132/PunGraph.

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