Graph computational tasks are inherently challenging and often demand the development of advanced algorithms for effective solutions. With the emergence of large language models (LLMs), researchers have begun investigating their potential to address these tasks. However, existing approaches are constrained by LLMs' limited capability to comprehend complex graph structures and their high inference costs, rendering them impractical for handling large-scale graphs. Inspired by human approaches to graph problems, we introduce a novel framework, PIE (Pseudocode-Injection-Enhanced LLM Reasoning for Graph Computational Tasks), which consists of three key steps: problem understanding, prompt design, and code generation. In this framework, LLMs are tasked with understanding the problem and extracting relevant information to generate correct code. The responsibility for analyzing the graph structure and executing the code is delegated to the interpreter. We inject task-related pseudocodes into the prompts to further assist the LLMs in generating efficient code. We also employ cost-effective trial-and-error techniques to ensure that the LLM-generated code executes correctly. Unlike other methods that require invoking LLMs for each individual test case, PIE only calls the LLM during the code generation phase, allowing the generated code to be reused and significantly reducing inference costs. Extensive experiments demonstrate that PIE outperforms existing baselines in terms of both accuracy and computational efficiency.

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