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Large language models (LLMs) have achieved remarkable success in natural language processing (NLP), demonstrating significant capabilities in processing and understanding text data. However, recent studies have identified limitations in LLMs’ ability to manipulate, program, and reason about structured data, especially graphs. We introduce GraphEval36K1 , the first comprehensive graph dataset, comprising 40 graph coding problems and 36,900 test cases to evaluate the ability of LLMs on graph problem solving. Our dataset is categorized into eight primary and four sub-categories to ensure a thorough evaluation across different types of graphs. We benchmark ten LLMs, finding that private models outperform open-source ones, though the gap is narrowing. We also analyze the performance of LLMs across directed vs undirected graphs, different kinds of graph concepts, and network models. Furthermore, to improve the usability of our evaluation framework, we propose Structured Symbolic Decomposition (SSD), an instruction-based method designed to enhance LLM performance on complex graph tasks. Results show that SSD improves the average passing rate of GPT-4, GPT4o, Gemini-Pro and Claude-3-Sonnet by 8.38%, 6.78%, 29.28% and 25.28%, respectively. 

This paper studies the problem of unconstrained (e.g. not orthogonal or unit) symmetric frame field design in volumes. Our principal contribution is a novel (and theoretically well‐founded) local integrability condition for frame fields represented as a triplet of symmetric tensors of second, fourth, and sixth order. We also formulate a novel smoothness energy for this representation. To validate our discritization, we study the problem of seamless parameterization of volumetric objects. We compare against baseline approaches by formulating a smooth, integrable, and approximately octahedral frame objective in our discritization. Our method is the first to solve these problems with automatic placement of singularities while also enforcing a symmetric proxy for local integrability as a hard constraint, achieving significantly higher quality parameterizations, in expectation, relative to other frame field design based approaches.