Can LLMs perform structured graph reasoning?

Pretrained Large Language Models (LLMs) have demonstrated various reasoning capabilities through language-based prompts alone, particularly in unstructured task settings (tasks purely based on language semantics). However, LLMs often struggle with structured tasks, because of the inherent incompatibility of input representation. Reducing structured tasks to uni-dimensional language semantics often renders the problem trivial. Keeping the trade-off between LLM compatibility and structure complexity in mind, we design various graph reasoning tasks as a proxy to semi-structured tasks in this paper, in order to test the ability to navigate through representations beyond plain text in various LLMs. Particularly, we design 10 distinct problems of graph traversal, each representing increasing levels of complexity, and benchmark 5 different instruct-finetuned LLMs (GPT-4, GPT-3.5, Claude-2, Llama-2 and Palm-2) on the aforementioned tasks. Further, we analyse the performance of models across various settings such as varying sizes of graphs as well as different forms of k-shot prompting. We highlight various limitations, biases and properties of LLMs through this benchmarking process, such as an inverse relation to the average degrees of freedom of traversal per node in graphs, the overall negative impact of k-shot prompting on graph reasoning tasks, and a positive response bias which prevents LLMs from identifying the absence of a valid solution. Finally, we introduce a new prompting technique specially designed for graph traversal tasks (PathCompare), which demonstrates a notable increase in the performance of LLMs in comparison to standard prompting techniques such as Chain-of-Thought (CoT).