Retrieval-Augmented Generation (RAG) enhances large language models by incorporating external knowledge. However, existing vector-based methods often fail on global sensemaking tasks that require reasoning across many documents. GraphRAG addresses this by organizing documents into a knowledge graph with hierarchical communities that can be recursively summarized. Current GraphRAG approaches rely on Leiden clustering for community detection, but we prove that on sparse knowledge graphs, where average degree is constant and most nodes have low degree, modularity optimization admits exponentially many near-optimal partitions, making Leiden-based communities inherently non-reproducible. To address this, we propose replacing Leiden with k-core decomposition, which yields a deterministic, density-aware hierarchy in linear time. We introduce a set of lightweight heuristics that leverage the k-core hierarchy to construct size-bounded, connectivity-preserving communities for retrieval and summarization, along with a token-budget-aware sampling strategy that reduces LLM costs. We evaluate our methods on real-world datasets including financial earnings transcripts, news articles, and podcasts, using three LLMs for answer generation and five independent LLM judges for head-to-head evaluation. Across datasets and models, our approach consistently improves answer comprehensiveness and diversity while reducing token usage, demonstrating that k-core-based GraphRAG is an effective and efficient framework for global sensemaking.

翻译：检索增强生成（RAG）通过整合外部知识来增强大型语言模型。然而，现有的基于向量的方法在处理需要跨多篇文档进行推理的全局语义理解任务时往往失效。GraphRAG通过将文档组织成具有可递归总结的层次化社区的知识图谱来解决这一问题。当前的GraphRAG方法依赖Leiden聚类进行社区检测，但我们证明，在平均度数为常数且大多数节点度数较低的稀疏知识图谱上，模块度优化存在指数级数量的近似最优划分，使得基于Leiden的社区本质上不可复现。为解决此问题，我们提出用k-核分解替代Leiden，该方法可在线性时间内生成确定性的、密度感知的层次结构。我们引入了一组轻量级启发式方法，利用k-核层次结构构建大小受限、保持连通性的社区以用于检索和总结，同时提出一种感知令牌预算的采样策略以降低LLM成本。我们在真实数据集上评估了我们的方法，包括财务收益电话会议记录、新闻文章和播客，使用三种LLM生成答案，并由五个独立的LLM评判员进行直接比较评估。在所有数据集和模型上，我们的方法持续提升了答案的全面性和多样性，同时减少了令牌使用量，证明基于k-核的GraphRAG是一种高效且有效的全局语义理解框架。