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Core-based Hierarchies for Efficient GraphRAG

Jakir Hossain, Ahmet Erdem Sarıyüce

TL;DR

This work introduces 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.

Abstract

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.

Core-based Hierarchies for Efficient GraphRAG

TL;DR

This work introduces 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.

Abstract

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.
Paper Structure (28 sections, 1 theorem, 1 equation, 1 figure, 12 tables, 4 algorithms)

This paper contains 28 sections, 1 theorem, 1 equation, 1 figure, 12 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work and Background
  3. Community-based GraphRAG Overview
  4. Hierarchical $k$-core Decomposition
  5. Why Modularity Optimization is Unreliable on Sparse Knowledge Graphs?
  6. A Robust Alternative: $k$-core Decomposition
  7. Handling Residuals in $k$-core Hierarchy
  8. Handling Small Clusters
  9. Token Efficiency via Sampling
  10. Experimental Setup
  11. Evaluation Criteria
  12. Results and Analysis
  13. Results on Post–Cutoff Data
  14. Evaluation on Full Data by GPT-5-mini
  15. Statistical Analysis
  16. ...and 13 more sections

Key Result

Theorem 1

Let $G$ be a graph with $n$ nodes, $m$ edges, average degree $\bar{k} = 2m/n = O(1)$, and $n_{\mathrm{\le d}} = \Theta(n)$. Then for any $\varepsilon > d(2+\bar{k})/(2m)$, In particular, the number of near-optimal partitions is exponential in $n$, and the tolerance threshold $\varepsilon$ required to trigger this blowup is $O(1/n)$.

Figures (1)

  • Figure 1: $k$-core decomposition (left) and corresponding hierarchy tree produced by RkH (right).

Theorems & Definitions (1)

  • Theorem 1: Modularity Degeneracy in Sparse Graphs