GraphOmni: A Comprehensive and Extensible Benchmark Framework for Large Language Models on Graph-theoretic Tasks

This paper introduces GraphOmni, a comprehensive benchmark designed to evaluate the reasoning capabilities of LLMs on graph-theoretic tasks articulated in natural language. GraphOmni spans diverse graph types, serialization formats, and prompting schemes, substantially extending upon prior efforts in both scope and depth. Through systematic evaluation, we uncover critical interactions among these dimensions, revealing their decisive impact on model performance. Our experiments show that state-of-the-art closed-source models such as Claude-3.5 and o4-mini consistently lead overall, yet still leave considerable headroom, while open-source models display pronounced sensitivity to various design choices. Beyond the standard scope, larger graphs, real-world graphs, and additional NP-hard tasks are further discussed. We further analyze efficiency via output token usage, highlighting cost–accuracy trade-offs, and introduce a reinforcement learning-based optimizer that adaptively selects factor combinations, reducing evaluation cost by 75\% while retaining strong accuracy. This flexible and extensible benchmark not only deepens understanding of LLM performance on structured graph reasoning but also establishes a robust foundation for advancing model design and evaluation. The code and datasets are available at https://anonymous.4open.science/r/ID-14092.