Can Large Language Models Tackle Graph Partitioning?

Large language models (LLMs) demonstrate remarkable capabilities in understanding complex tasks and have achieved commendable performance in graph-related tasks, such as node classification, link prediction, and subgraph classification. These tasks primarily depend on the local reasoning capabilities of the graph structure. However, research has yet to address the graph partitioning task that requires global perception abilities. Our preliminary findings reveal that vanilla LLMs can only handle graph partitioning on extremely small-scale graphs. To overcome this limitation, we propose a three-phase pipeline to empower LLMs for large-scale graph partitioning: coarsening, reasoning, and refining. The coarsening phase reduces graph complexity. The reasoning phase captures both global and local patterns to generate a coarse partition. The refining phase ensures topological consistency by projecting the coarse-grained partitioning results back to the original graph structure. Extensive experiments demonstrate that our framework enables LLMs to perform graph partitioning across varying graph scales, validating both the effectiveness of LLMs for partitioning tasks and the practical utility of our proposed methodology.