HyperGraphRAG: Retrieval-Augmented Generation via Hypergraph-Structured Knowledge Representation
Authors: Haoran Luo
Haihong E
Guanting Chen
Yandan Zheng
Xiaobao Wu
Yikai Guo
Qika Lin
Yu Feng
Zemin Kuang
Meina Song
Yifan Zhu
Anh Tuan Luu
Venue: NeurIPS 2025 poster ()
Keywords: Retrieval-Augumented Generation
Hypergraph
N-ary Relation Extraction
Knowledge Representation
Primary area: machine_learning_for_sciences
TL;DR: HyperGraphRAG introduces hypergraph-based knowledge representation to capture real-world n-ary relations, boosting answer accuracy, retrieval efficiency, and generation quality.

Abstract: Standard Retrieval-Augmented Generation (RAG) relies on chunk-based retrieval, whereas GraphRAG advances this approach by graph-based knowledge representation. However, existing graph-based RAG approaches are constrained by binary relations, as each edge in an ordinary graph connects only two entities, limiting their ability to represent the n-ary relations (n >= 2) in real-world knowledge. In this work, we propose HyperGraphRAG, the first hypergraph-based RAG method that represents n-ary relational facts via hyperedges. HyperGraphRAG consists of a comprehensive pipeline, including knowledge hypergraph construction, retrieval, and generation. Experiments across medicine, agriculture, computer science, and law demonstrate that HyperGraphRAG outperforms both standard RAG and previous graph-based RAG methods in answer accuracy, retrieval efficiency, and generation quality.

HyperGraphRAG: Retrieval-Augmenned Generation via Hypergraph-Structured Knowledge Representation
Haoran Luo!? Haihong E Guanting Chen', Yandan Zheng', Xiaobao Wu', Yikai Guo Qika Lin", Yu Feng', Zemin Kuang', Meina Song', Yifan Zhu', Luu Anh Tuan? 'Beijing University of Posts and Telecommunications ?Nanyang Technological University Beijjng Institute of Computer Technology and Application *National University of Singapore CChina Mobile Research Institute Beijing Anzhen Hospital, Capital Medical University edu. haoran. luo@ieee.... org, ehaihong@bupt. edu. en, anhtuan, luu@ntu. edu.
Abstract
Standard Retrieval-Augmentee Generation (RAG) relies on chunk-basee retrieval, whereas GraphRAG AG advances this approach by graph-based knowledge representa- tion. However, existing graph-based RAG approaches are constrained by binary relations, each edge in an ordinary graph connects only two entities, limiting their ability to represent the n-ary relations (n 2 2) in real-world knowledge. the first hypergraph-baset RAG method
this work, we propose HyperGraphRACK that represents n-ary relational facts via hyperedges. HyperGraphRAG consists comprehensive pipeline, including knowledge hypergraph construction, retrieval, and generation. Experiments across medicine, agriculture, computer science, and law demonstrate that HyperGraphRAG outperforms both standard RAG and pre- vious supph-asedd RAG methods in answer accuracy, retrieval efficiency, and generation quality. Our data and code publicly available!
Introduction
Retrieval- Auggreeted Generation (RAG) 10 has advanced www.leeeinntensive tasks by inte- grating knowledge retrieval with large language models (LLMs) 11 28 thereby enhancing fac- tual awareness and generation accuracy. Stan- dard RAG typically relies on chunk-based re- trieval, segmenting documents into fixed-length text chunks retrieved via dense vector similarity, which overlooks the relationships between en- tities. Recently, GraphRAG 2 has emerged as promising direction that structures knowledge as graph capture inter-entity relations, with the potential to improve retrieval efficiency and knowledge-driven generation
LLM
N-ory Relation Extroction
Domain Knowledge
Knowledge HyperGraph
HyperGraph Retrieval
Knowledgable Generation
User Question
HyperGraph. Guided Generation
However, since each edge in an ordinary graph connects only two entities, existing graph-based
Figure 1: An illustration of HyperGraphRAG.
RAG approaches (2) [ g are all restricted to binary relations, making them insufficient for modeling the n-ary relations among more than entities that are widespread in real-world For example, in the medical domain, as illustrated in Figure 2 representing
domain knowledge
25
Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Domain Knowledge
Main hypertenite with veram creatinine levess betwees 115-133 panel'l aa dioguerd with mild sarum craainine alerationn.
Standard RAG
GraphRAG
HyperGrophäAG
Knowledge Representation
Ordinary Graph Knowledge Represertation
Hypergraph Structured Knowledge Representation
Male lopertaniic pulicats with scruns creaintac levde beineas IiS- 23 panall are diagseoed with nid uram creataite
Mild eerumn creadisine alovation
Hypertonahe patlent
Hypertamaiee palient
Hyperodge_1
Hyperedge 4
Serumi creatiiine levis betnoon 115- 123 proot.
Hyporsigo
Itale
Serum creatiniee levela between 115-133 pmott.
Figure 2: Comparison of knowledge representation: standard RAG uses chunks as units, GraphRAG captures binary relations with graphs, and HyperGraphRAG models n-ary relations with hyperedges.
the fact that "Male hypertensive patients with serum creatinine levels between 115-133 pmol/L are diagnosed with mild serum creatinine elevation" requires decomposing it into several binary relational patient, Male) and Diagnosed_with:n (iypert patient,
triples, such as Gender:(Hypertere Mild serum creatinine elevation), leading representation sparsity during conversion process.
To address these limitations, we propose HyperGraphRAG, as illustrraed Figure [ novel graph- based RAG method built upon hypergraph-structure knowledge representation. In contrast to prior graph-based RAG methods constrained to binary relations, HyperGraphR leverages hyperedges represent n-ary relational facts, where each hyperedge connects entities (n > 2), e.g. eypperedgeeHxypereensvvv patient, Male, Serum creatinine levels between 115-133 pmol/L. Mild serum creatinine elevation), and each hyperedge is expressed through natural language descriptions. This design ensures knowledge completeness, structural expressiveness, and inferential capability, thereby providing more comprehensive support for knowledge-intensive
intensive applications.
Our proposed HyperGraphRAG built upon three key steps. First, we propose knowledge hypergraph construction method, leveraging LLM-based n-ary relation extraction to extract and structure multi-entity relationships. The resulting hypergraph is stored in a bipartite graph database, with separate vector databases for entities and hyperedges to facilitate efficient retrieval. Second, we develop a hypergraph retrieval strategy that employs vector similarity search to retrieve relevant entities and hyperedges, ensuring that the knowledge retrieved is both precise and contextually relevant. Lastly, we introduce a hypergraph-guidee generation mechanism, which combines retrieved n-ary facts with traditional chunk- RAG passages, thereby improving response quality.
To validate the effectiveness, we conduct experiments in multiple knowledge- www.legg-intensive intensive domains (7], in- cluding medicine, agriculture, computer science, and law. Results demonstrate that HyperGraphRAG outperforms standard RAG and previous graph-based RAG methods in answer accuracy, retrieval efficiency, and generation quality, showcasing its strong potential for real-world applications.
2 Related Work
Graph-based RAG. GraphRAG 2 the first graph-based RAG method that improves LLM generation via graph-based retrieval. Based on GraphRAG, several methods 226 22
11 4 23 focus on building graph-baser RAG for different applications. LightRAG [7] enhances efficiency via graph indexing and updates. PathRAG (I] and HippoRAG2 [8] refine retrieval with path pruning and Personalized PageRank. However, all rely on binary relations, limiting knowledge expressiveness. In this work, propose HyperGraphRAG. the first graph-based RAG method via hypergraph-sttuctured knowledge representation. We compare several existing methods with HyperGraphRAG in Table [
Hypergraph Representation. Hypergraph-structure knowledge representation aims to overcome ordinary graph's limitations in modeling n-ary relations [15]. Early methods [25] 27
12
21 employ
various embedding techniques to represent n-ary relational entities. Later methods (5] 24 14 utilize
GNN or attention enhance embedding. However, existing methods mainly focus on link prediction while hypergraphs also show potential for enhancing knowledge representation in graph-based RAG.

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Table 1: Comparison of knowledge construction and retrieval methods for NaiveGeneration, Stan- dardRAG, partial GraphRAG baselines, and our proposed HyperCraphRAG, where K. represents the overall constructed knowledge, and K represents retrieved knowledge when given user question
Method
Knowledge Construction
Knowledge Retrieval
NaiveGencration
K 0. K = te where is a chunk.
K2 0.
StandardRAG
K2 Kaunn Topa K. simiflt ho)
GraphRAG 2
K= = S {sg E Community())),
K Detect(sy S
where 5 the community summary set.
where detected community summaries retrieved.
LightRAG
x= = (V, E),
K Ffe E e. E E g) Kahmnt
where V & É are entity relation sets.
where entities relations are retrieved with chunks. K Prune(p E P. g)-
PathRAG
K = G = (V, E).
where is the same as LightRAG's.
where relational paths are retrieved via pruning.
HippoRAG2
K= = (V U. E).
K. PageRank(m (m E M q).
where V/ & M are phrase & pussuge nodes.
where passages are retrieved Pensonalized PageRank.
HyperGraphRAG (ours)
IC = GH = Ex). where G is structured as hypengraph.
K; (u V 9) U Fale E# | q J Ketunk
where n-ary relational facts retrieved with chunks.
3 Preliminaries
Definition 1: RAG. Given question and domain knowledge K, standard RAG first selects relevant document fragments d from K based on q, and then generates an answer y based on q and d. The probability model is formulated as:
Plyl)) Σ P(ylg, PPPlg, K).
(1)
Definition 2: Graph-based RAG. Graph-based RAG optimizes retrieval by representing knowledge as a graph structure G (V, E), where V is the set of entities and E is the set of relationships between entities. G' consists of facts represented as F (e, Vo)= G, where e the relation and V. is the entity set connected to e. Given question g, the retrieval process is defined as:
P(yl4) = Σ P()lgg))
FEG
Definition 3: Hypergraph. A hypergraph GH = (V, FH) the entity set, Eu is the hyperedge set, and each hyperedge eн En connects 2 or more entities:
29 is a generalized graph, where V is
Ven = (v1, U2, ..., Un).
2 2.
(3)
Unlike ordinary graphs, where relationships are binary V. = (wh, vc), hypergraphs model n-ary relational facts F, (en, Ven) E Gn.
4 Method: HyperGraphRAG
In this section, we introduce the proposed HyperGraphRAG, as shown in Figure 3 including knowledge hypergraph construction, hypergraph retrieval strategy, and hypergraph-guided generation.
4.1
Knowledge Hypergraph Construction
To represent and store knowledge, we propose a knowledge hypergraph construction method that includes n-ary relational extraction, bipartite hypergraph storage, and vector representation storage.
N-ary Relation Extraction. To construct the knowledge hypergraph GH our first step is to extract multiple n-ary relational facts F., from natural language documents d K. Unlike traditional hyper-relations (21, events 13,, or other n-ary relation models [15). in the era of LLMs, to preserve richer and more diverse n-ary relations among entities, we propose
n-ary relation representation F, (eH, Ven ). utilizing natural language descriptions, instead of structured relations, to represent hyperedges eн among multiple entities Vez as follows.
(a) Hyperedge: Given an input text d, it parsed into several independent knowledge fragments, each treated as a hyperedge: Ey = {ei, 6 }. e. Each hyperedge = (eeest e,corr) consists of two parts: a natural language description elext, and a confidence score esoore E (0, 10) indicating the association degree between e and d.
3

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Knowledge HyperGroph
User Question
Knowledge HyperGraph Construction
Knovledge
HyparGnsph
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MypeGGraph-Guldeed
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Figure 3: An overview of HyperGraphRAG, which constructs knowledge hypergraph from domain knowledge, retrieves n-ary facts based on user questions, and generates knowledgeable responses.
(b) Entity: For each hyperedge e,, entity recognition is performed to extract all contained en- tities: Ve, (V1, 12,,,,, ...,, Un ). where Ve, is the entity associated with eş- Each entity By (u.amme,/f) o/Y o geaplain 2i v/oore consists of four parts: entity name 2 S e type o/y explanation oapphin and confidence score 2/ E (0, 100] indicating the extraction certainty.
Following this hypergraph-struccured knowledge representation, we design an n-ary relation extraction prompt Pexa, detailed in Appendix |A.I to enable the LLM perform end-to-end knowledge fragment segmentation and entity recognition, thereby forming the n-ary relational fact set F%
Fr -f fk} ~ ( Pext. d),
where each extracted n-ary relational fact f; = (c;, Ve.) contains information about the corresponding hyperedge e and its associated entity set Ve.- We convert all documents d E K into hyperedges and entities using n-ary relation extraction, forming a complete knowledge hypergraph Gn.
Proposition 1. Hyypergruph-struuturre knowledge representation is more comprehensive than binary.
Proof. We provide experimental results in Section 5.4 and proofs in Appendix B.1
Li
Bipartite Hypergraph Storage. After n-ary relation extraction, we store the constructed knowled knowledge hypergraph Gи in a graph database to support an efficient query. We adopt an ordinary graph database
represented as bipartite graph structure GB (Vn, En) = & (G ), to store the knowledge hypergraph GH = (V, F.H), where & is a transformation function defined as:
VB V EH, EB {(en, v) en E EH, v E Ven),
(5)
where VB is the set of nodes in GB, formed by merging the entity set V and the hyperedge set Eн from GH. The edge set EB captures the connections between each hyperedge ex EH and its associated entities E Venr
Based on GB. can efficiently query all entities associated with hyperedge ен or query all hyperedges linked to a specific entity v, thereby benefiting the optimized query efficiency of an ordinary graph database, well preserving the complete hypergraph--trrucureed knowledge representation.
Moreover, GB allows incremental updates through dynamically expansion: GB + GB ( where Gy represents newly added hypergraph information. The transformation of hyperedges and entities into the bipartite graph storage format enables seamless updates to the graph database.
Proposition 2. bipartite graph can losslessly preserve and query knowledge hypergraph.
Proof. We provide proof's in Appendix B.2

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Vector Representation Storage. To support efficient semantic retrieval, we embed hyperedges en e En and entities v E V using the same embedding model f. ensuring that the vector representation of hyperedges and entities is in the same vector space as questions. Let // be the vector function, then the vector representation storage for the knowledge hypergraph GH is defined as: v(GH) = (En, &v),
where ε is the vector base of hyperedges and yy is the vector base of entities:
v : Eµ (ben ee E Eh}, Ev = {h,
c E EVE
(6)
where each hyperedge eи and entity v in GH is embedded into their vector representations: hag f(en), and h. f()), respectively.
4.2 Hypergraph Retrieval Strategy
After constructing and storing the hypergraph GH. we design an efficient retrieval strategy match user questions with relevant hyperedges and entities.
Entity Retrieval. First, we extract key entities from the question q to facilitate subsequent matching. We design an entity extraction prompt Pq_ext. detailed in Appendix A.2 along with the LLM я to extract the entity set Vz=
Vg ~ ग (VID q).-
After extracting entities, we retrieve the most relevant entities from the entity set V of the knowledge hypergraph Gn. We define the entity retrieval function Ry, which retrieves the most relevant entities from yy using cosine similarity:
Rv argmax (sim(hv, ha) score
(8)
VeV
where hy, = [(V)) is the concatenated text vector representation of the extracted entity set Vg hy E Ey the vector representation of entity v, sim(..-) denotes the similarity function, @ represents clement-wise multiplication between similarity and entity relevance score goror determining the final ranking score, TV is the threshold for the entity retrieval score, and ky is the limit on the number of retrieved entities.
Hyperedge Retrieval. Moreover, to expand the retrieval scope and capture complete n-ary relations within the hyperedge set En of the knowledge hypergraph GH,, we define the hyperedge retrieval function R.,, which retrieves set of hyperedges related q:
ky
R = arrgmax (sim(h, (h,: heg)
@ H >
senre
Eg
where h2 = f()) is the text vector representation of q. hex E EH is the vector representation of the hyperedge eH. @ represents element-wise multiplication between similarity and hyperedge relevance score eccore determining the final ranking score, ти is the threshold for the hyperedge retrieval score, and ky limits the number of retrieved hyperedges.
4.3 Hypergraph-Guide Generation
To fully utilize the structured knowledge in the hypergraph, we propose a Sngeergraph-uuddee Generation mechanism, which consists of hypergraph knowledge fusion and generation augmentation.
Hypergraph Knowledge Fusion. The primary goal of hypergraph knowledge fusion is to expand and reorganize the retrieved n-ary relational knowledge to form comprehensive knowledge input. Since q may only match partial entities or hyperedges, we further expand the retrieval scope. To obtain complete set of n-ary relational facts, we design a bidirectional expansion strategy, that includes expanding hyperedges from retrieved entities and expanding entities from retrieved hyperedges.
First, given the entity set retrieved from denoted as (g) = {U1, U....., Uky }. we retrieve all hyperedges in the knowledge hypergraph GH that connect these entities:
Fv
U
{(eH, Vex) v, E Veg, eh E En}.
(10)
(g)(
Next, we expand the set of entities connected to the retrieved hyperedges RD((g) = {ei, 62, m. Ckw J:
F = U (le,, Ve, CV}
(11)
c.ERx(g)
5

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Finally, we merge the expanded hyperedge set FV with the expanded entity set F to form complete retrieved n-ary relational fact set K FV U.F This contains all necessary n-ary relational knowledge for reasoning and generation, ensuring comprehensive input for the L.M.
Generation Augmentation. Following hypergraph knowledge fusion, augment the generation strategy to improve the accuracy and readability of the responses. We adopt hybrid RAG fusion mechanism, combining hypergraph knowledge K Fr with retrieved chunk-based text fragments Kehunk to form the final knowledge input. We define the final knowledge input K = K U Kehunk, where Kehunk consists of chunk-base based text fragments retrieved using traditional RAG.
Finally, we use a aetrieval-augmentie generation prompt Pgen. detailed in Appendix that combines hypergraph knowledge K and the user question q input LLM to generate hnnll response y":
y т (ylPen: K²
(12)
Reirieving knowledge on knowledge hypergraph improves retrieval efficiency compared methods based on ordinary binary graphs, leading gains in generation quality.
Proposition 3.
Proof. We provide experimental results in Sections 5.5 and 5.6 and proof' in Appendix B.3
5
Experiments
This section presents the experimental setup, main results, and analysis. We answer the following research questions (RQs): RQ1: Does HyperGraphRRAG outperform other methods? RQ2: Does the main component of HyperGraphRAAG work? RQ3: How effective is the knowledge hypergraph con- structed by HyperGraphR across various domains? RQ4: Could the hypergraph retrieval strategy improve retrieval efficiency? RQ5: How effective is the generation quality of HyperGraphRAGG? RQ6: How are the time and cost of HyperGraphRAG in construction and generation phases?
5.1 Experimental Setup
Datasets. To evaluate the performance of HyperGraphRAG across multiple domains, we select four knowledge contexts from UltraDomain [9], as used in LightRAG 77 Agriculture, Computer Science (CS), Legal, and mixed domain (Mix). In addition, we include the latest international hypertension guidelines [16] as the foundational knowledge for the Medicine domain. For each of the five domains, sample knowledge fragments one, two, and three hops away to construct questions with ground-trute truth answers verified by human annotators. We then categorize the questions into Binary Source and N-ary Source, based on whether the sampled knowledge of the question contains facts among n entities (n > 2). More details can be found in Appendix D
Baselines. We compare HyperGraphRAG against six publicly available baseline methods: Naive- Generation [7], which directly generates responses using L.MM: StandardRAG (6) traditional chunk-based RAG approach; GraphRAG (2), LightRAG 7 PathRAG (1) and HippoRAG2 (}) which are four selected available graph- based RAG methods described in Table T To ensure fairness,
we use the same generation prompt, which can be found in Appendix B
Evaluation Metrics. We evaluate the answer accuracy, retrieval efficiency, and generation quality of HyperGraphRAG and its baselines using 3 key metrics: F1, Retrieval Similarity (R-S), and Generation Evaluation (G-E). Fl measures word-level similarity between the generated answer and the ground-truth answer, following FlashRAG [9]. R-S assesses the semantic similarity between the retrieved knowledge and the ground-truth knowledge used to construct the question, in line with RAGAS 33. G-E, inspired by HelloBench (20). is metric that uses LLMM-as-a-judee to evaluate generation quality in 7 dimensions and reports the average score. Details are provided in Appendix E
Implementation Details. We use OpenAl's GPT-4o-mini for extraction and generation, and eexe-dmmbdding-- small for vector. During retrieval, we set the following parameters: entity retrieval ky 60, TV = 50; hyperedge retrieval bH = 60, тH = 5; and chunk retrieval kc = 5, TC 0.5. All experiments were conducted on server with an 80-core CPU and 512GB RAM.
5.2 Main Results (RQ1)
To evaluate the effectiveness of HyperGraphRAG, we compare its performance with various baselines across multiple domains. The results shown in Table 2

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Table 2: Performance comparison across different domains. Bold indicates the best performance.
Medicine
Agricnlture
Legal
Mix
Method
F1
R-S
G-E
F1
R-S
G-E
R-S
G-E
F1
R-S
G-E
F1
R-S
G-E
Binary Source
NaiveGeneration
12.63
44.70
11.71
18.93
0.00
48.79
22.91
0.00
18.58
0.00
StandardRAG
26.87
61.08
56.24
28.31
42.69
57.58
28.87
49.44
57.10
37.19
52.21
59.85
47.57
46.79
67.42
GraphRAG
17.13
54.56
48.19
20.67
40.90
52.41
23.75
37.65
53.17
31.09
34.26
54.62
23.62
25.01
48.12
LightRAG
12.16
52.38
44.15
17.70
41.24
50.32
22.59
41.86
51.62
33.63
45.54
29.98
34.22
54.50
PathRAG
14.74
52.30
45.36
21.97
42.21
53.13
25.28
41.49
53.28
32.32
43.60
55.45
40.87
33.36
60.75
HippoRAG2
21.12
57.50
51.08
12.60
16.85
44.56
16.94
21.05
47.29
20.10
34.13
46.77
21.10
18.34
45.83
HyperGGrphhRAG (ours)
36.45
69.91
60.65
34.80
61.97
60.94
57.54
44.42
60.87
63.53
51.51
67.34
68.76
N-ary Source
NaiveGeneration
13.15
0.00
41.83
13.78
0.00
47.93
18.37
0.00
48.94
20.37
0.00
48.09
15.29
0.00
45.16
StandardRAG
28.93
64.06
55.08
26.55
48.93
56.62
28.99
47.35
56.69
37.50
51.16
60.09
38.83
47.73
61.82
GraphRAG
18.07
47.09
21.90
41.27
22.90
53.76
29.12
34.11
53.76
24.32
42.32
LightRAG
13.43
54.67
41.86
18.78
42.44
50.92
22.85
41.19
52.20
29.64
44.47
54.65
24.08
33.22
50.83
PathRAG
15.14
54.08
42.77
20.64
42.53
51.83
28.18
42.29
54.97
30.27
44.47
55.26
33.27
34.11
57.47
HippoRAG2
21.56
48.00
12.66
20.32
45.14
17.75
26.92
16.95
34.72
45.09
21.95
18.49
46.87
HyperCiaphRAGG (ours)
34.26
70.48
58.06
32.98
62.58
59.59
31,00
59.25
58.35
43.20
60.07
63.70
45.91
69.09
65.04
Overall
NaiveGeneration
12.89
0.00
43.27
12.74
0.00
46.85
18.65
0.00
48.87
21.64
0.00
49.05
16.93
0.00
45.65
StandardRAG
27.90
62.57
55.66
27.43
45,81
57.10
28.93
48.40
56.89
37.34
51.68
59.97
43.20
47.26
64.62
GraphRAG
17.60
55.89
47.64
21.28
41.08
52.95
23.33
38.11
53.47
34.18
19.27
24.67
45.22
LightRAG
12.79
53.52
43.00
18.24
41.84
50.62
22.72
41.53
51.91
31.64
45.00
55.53
27.03
33.72
$2.67
PathRAG
14.94
53.19
44.06
21.30
42.37
52.48
26.73
41.89
54.13
31.29
44.03
55.36
37.07
33,73
59.11
HippeRAG2
21.34
49.57
12.63
18.58
17.34
23
47.87
18.53
34.42
45.93
21.53
18.42
46.35
HyperCimphRAAG (ours)
35.35
70.19
59.35
33.89
62.27
59.79
31.30
60.09
57.94
43.81
60.47
63.61
48.71
68.21
66.90
Overall Comparison Across Methods. HyperGraphRAG consistently outperforms all baselines F1, R-S, and G-E metries. Compared StandardRAG, it achieves gains of +7.45 (F1), +7.62 (R-S), and 43.69 (G-E), Interestingly, existing graph-based RAG baselines often underperform StandardRAG, as their reliance on binary relational graphs causes knowledge fragmentation, sparsified retrieval, and incomplete context reconstruction during generation.
Comparison Across Source Types. HyperGraphRAG maintains strong gains under both Binary and N-ary settings. For Binary Source, improves F1, R-S, and G-E by +8.6, +8.8, and +4.4; for N-ary Source, the improvements are +5.3, +6.4, and +2.9, confirming its robustness.
Comparison Across Domains. Performance gains are consistent across domains, with the largest improvements in Medicine and Legal (over +7 F1), and stable advantages in Agriculture and CS. HyperGraphRAG adapts well to both highly structured and more general knowledge tasks.
5.3 Ablation Study (RQ2)
As shown in Figure we conduct an ablation study in the Medicine domain by removing entity retrieval (w/o ER), hyperedge retrieval (w/o HR), and their combination (w/o ER HR). We also remove chunk retrieval fusion (w/o CR), and all modules (w/o ER & HR & CR):
Impact of Entity Retrieval (ER). ER is crit- ical for precise retrieval by anchoring key con- cepts. Without ER, F1 falls from 35.4 to 29.8, underscoring its importance in selecting relevant entities for accurate generation.
HyperOmptRRG
HR
Bar
Score
60-
40-
Impact of Hyperedge Retrieval (HR). HR captures n-ary, multi-entity facts necessary for complex reasoning. Removing HR drops from 35.4 4 to 26.4, highlighting its unique role beyond mere entity retrieval.
20*
F1
R-S
G-E
Figure 4: Results of the ablation study.
Impact of Chunk Retrieval Fusion (CR). CR enhances retrieval by integrating unstructured text with hypergraph data. Excluding reduces from 35.4 4 to 29. 2, demonstrating that the fusion leads more complete and fluent generation.

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5.4 Analysis of Hyypergaaph-structured Knowledge Representation (RQ3)
As shown in Figure
we assess HyperGraphRAG's knowledge representation across 5 domains:
(a) Medicine HyperGraph
(b) Agriculture HyperGraph
(c) CS HyperGraph
Med. Agric.
CS
Legal
Mis
4Knowl, Token
1796
580k
7958
940k
127k
GraphRAG
139
1449
225
4Comimuiit
256
505
990
80
LightRAG
9,725
5082
2,270
*Relation
1,304
HyperGrrphiRAG
7,675 19.03
6.201
ntlpperdge
4,188 26,902 18,285 4,356
(d) Legal HyperGraph
(c) Mix HyperGraph
(f) Statistics of Construction
Figure 5: (a-e) Visualizations of knowledge hypergraphs constructed in 5 domains. (f) Statistical comparison highlights HyperGraphRAG's richer expressiveness over GraphRAG and LightRAG.
Visualization of Knowledge Structures. As shown in Figure (aa) 5(e) unlike previous graph-based
RAG methods, which only model binary relations, HyperGraphRAGG connects multiple entities via hyperedges, forming more interconnected and expressive network.
Statistical Analysis. As shown in Figure 5(1) HyperGraphRAG surpasses GraphRAG and LightRAG in all domains. For instance, in CS, it constructs 26,902 hyperedges, whereas GraphRAG has 930 communities and LightRAG 5,632 relations, showing a stronger capacity for capturing knowledge.
5.5 Analysis of Hypergraph Retrieval Efficiency (RQ4)
As shown in Figure to evaluate retrieval efficiency, we conduct two experiments: (a) examining how HyperGraphRAG's retrieval efficiency and token length scales with different top-k values and (b) comparing its Fl scores with other methods under varying retrieval length limits:
100
G-E
*R-Tolen
PaliRAi Hippsttbl
75
70.0
20-3
2011
10000
CoppilaaG LypeRAc
34.3 324
Score
60
8533
8000
#R- -o-Tee
Seore
30
6000
55
364
53.5
4000
152
34
20.0
2000
NaiveGen (StanderdRAG)
k-40
k-8o
k-100
256
1094 409h Pull
(HyperGrrahRAA)
Retrieved Knowledge Length
(a) Impact of Top-k on Retreval Efficency Token Length.
(b) Comparison under Limited Lengths.
Figure Experimental results in the Medicine domain analyzing hypergraph retrieval efficiency.
Impact of Retrieved Hyperedge Quantity. As shown in Figure 6(a)
increasing the top-k hyperedges improves F1, R-S, and G-E along with the rise in token count. Performance saturates around k 60, indicating that HyperGraphRAG achieves strong retrieval quality with limited input.
Performance under Constrained Retrieval Length. As illustrated in Figure 6(b) HyperGraphR outperforms all binary graph-based RAG methods even under retrieval length limits, demonstrating the efficiency of n-ary representations and highlighting the semantic loss inherent in binary structures.

---

5.6 Analysis of Hypergraph-Guidee Generation Quality (RQ5)
As shown in Figure] we evaluate the quality of generation in seven dimensions:
Best Overall Generation Quality. Hyper-
Overall
GraphRAG achieves the highest Overall score (61.5), significantly outprrforning all bascline methods, indicating the comprchensive advan- tage in hypergraph-guit
Factuality
hemeeeensieessss
generation.
53h
Lead on Key Dimensions. HyperGraphRAG achieves notable improvements in Correctness (64.8), Relevance (66.0), and Factuality (64.2), outperforming both standard RAG and binary graph-based methods. These gains indicate its strong capacity to produce accurate, context- aware, and wwwwledee-gronddee responses.
40
35
Logical Coheren
Knowledge-
ability
48
Diversity
Cerrectness
Balanced Performance. Although the Diver- sity score (47.0) is relatively lower than other dimensions, HyperGraphRAG still exceeds all baselines, indicating that it maintains balanced dimension-wir performance, effectively com- bining content richness with structural consis- tency for stable and high-quality generation.
66.0
Relevance
NaiveGmerratik
LightRAG PeebRAG
HippoRAGa
StandrdRRAG
HypeoGophRAG
GruphRAG
Figure 7: Generation Equality Evaluations.
5.7 Analysis of Time and Cost in Construction and Generation Phases (RQ6)
As shown in Table to evaluate the efficiency and cost of HyperGraphRAG, we compare different methods in terms of knowledge construction and generation. We assess time consumption per Ik tokens (TPIKT), cost per 1 tokens (CPIKT), time per query (TPQ),, and cost per 1K query (CP1kQ).
Time & Cost in Construction Phase. Hyper- GraphRAG demonstrates efficient knowledge construction with time cost of 3.084 sec- onds per Ik tokens (TPIKT) and a monetary cost of $0.0063 per 1K tokens (CPIKT). This places it between the faster HippoRAG2 (2.758s, $0.0056) and slower GraphRAG (9.272s, $0.0058). While its cost is slightly higher than GraphRAG, HyperGraphRAG achieves bet- ter balance between speed, expressiveness, and structure, offering more compact yet richer representation of n-ary relational knowledge.
Table 3: Time & Cost Comparisons.
Construction
Generation
Method
TPIKT
CPIKT
TPQ
CPIkQ
NaiveGeneration StandardRAG
Us
U$
0.131
0.059 $
0s
0$
0.147
1.016 $
GraphRAG
9.272
0.0058
0.221
18366
LightRAG
5.168
0.0081 $
0.359
3.359 S
PatRAG
5.168
0.0081
0.436
3.496
HippoRAG2
2.758
0.0056
0.240
3.438 S
HyperGraphRAG
3.084
0.0063 $
0.256
3.184
Time & Cost in Generation Phase. During the generation phase, HyperGraphRAG requires 0.256
seconds per query (TPQ) and incurs a cost of $3.184 per Ik queries (CPIkQ). This is moderately higher than StandardRAG (0.147s, $1.016) but significantly lower than PathRAG (0.436s, $3.496) and LightRAG (0.359s, $3.359). Compared to GraphRAG (0.221s, $1.836). HyperGraphRAG slightly increases time and cost but compensates with better retrieval quality and generation outcomes. The results suggest that HyperGrraphRAC achieves a favorable trade-off between generation efficiency and output quality, suitable for real-world knowledge-intensee intensive applications.
Conclusion
In this work, we present HyperGraphRAGG, satrieval-augmentn generation framework that models knowledge as hypergraphs to capture n-ary relational structures. By introducing novel methods for knowledge hypergraph construction, retrieval, and generation, HyperGraphRACE addresses limitations of binary graph-based RAG methods. Experimental results across diverse domains demonstrate consistent improvements in answer accuracy, retrieval relevance, and generation quality, confirming the effectiveness and generalizability of hypergraph-guite retrieval and generation.

---

Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant No. 62473271, Grant No. 62176026, and Grant No. 62406036) and the Engineering Research Center of Information Networks, Ministry of Education, China.
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Appendix
A Prompts Used in HyperGraphRAG
A.1 N-ary Relation Extraction Prompt
As shown in Figure 8 this prompt is designed for extracting structured n-ary relational facts from raw text. It guides I.L segment the input into coherent knowledge fragments, assign completeness score to each, and identify entities with their names, types, descriptions, and importance scores.
Goal-
Given dooument that is potentaaly relevant to this activty and a tst of entiy tyses, idensiy all endiles of those types from the text and relationshiss among the
identffed entiles.
Use gunge) as output language.
Btops-
1. Dardo the text in several complete knowlocgo segments, For each knoweddee segment, extract the following information:
knowledge, segment: A sentence that describes the contest the know edge segment,
completenese, score: A score from to 10 indicatng the completenees the knowledge engment.
Formal each knowledge segment as (Thyperrebttion (uupee deimeerydrowwddy segments/lupl selmteijsromplleeeees scores)
each lndgeedggg sagmant entity, antiyy hyp: Type entiyy
idently
deniiied writy, extract following informaton::
-aniity name:
language as riput Englin, osplelized the
antiyy description: Comprehersive description anthy's
actiilies.
kay score: soore
100 incicatino importance enthy ontly as l'ontty[lupl: detmitaaeaaaaooo peantty www.e//pmleeeee.ooo htt.l/ppe__llmllllaaaooooo
relationships http:///uuppooolllleeeeeeeeee www.antbyyoocopppoooouuuuuueeeee http:lulll_eimmmeeeeeeoooo scoree)
output (language) dingle
"(record delimterr" delimitrr
(completion delimierr)
4A249B44AAAA204AAAEEEA (examples)
-Real
Text: uinuut
Output:
Figure 8: Prompt for n-ary relation extraction Peu in Equation
A.2 Entity Extraction Prompt
As shown in Figure 9 this prompt is used to extract key entities from user query. LIM is instructed return all identified entities JSON format, ensuring the output is concise, human-readable, and aligned with the language of the input query. This facilitates entity-level retrieval in the hypergraph.
You helpful aesistant tosked with identfying entites
Goal-
Given the all entites.
Instructions-
Output the kaywords JSON lormat.
Examples
#essiiE2n2eRcceev500 (examples)
-Real Data-
Quary: (query)
The Outpur" should be human lext, not unicode characters. Keep the same language as "Querry..
Output:
Figure 9: Prompt for entity extraction Pq_ext Equation
A.3 Retrieval-Augmeented Generation Prompt
To ensure a fair comparison across RAG baselines, we adopt unified Chain-of-Thought Thought (CoT))-based generation prompt Pgen in Equation T2 for all methods. present this prompt together with the
designed evaluation approach in Appendix B
12

---

B Proof
B.1 Proof of Proposition
Proposition 1. Hxpergraph-structured knowledge representation is more comprehensiiv than binary.
Proof. Given a universe of entities V, an n-ary fact with n 2 is denoted as F {U1,.... Un V. For hypergraph representation, we represent it with a single hyperedge:
= F, GH = (V, En).
EH.
(13)
so the representation function ΦH F + eн is naturally injective. For binary graph representation, we connect every pair of entities that co-occur fact. For any collection of facts S S P(V), define the representation function:
(B( =
UB=UP, FES
=
EB = ((u w) u w, FF E S {u, w) S CF), (14)
where EB consists of the binary edges activated by S within the complete graph Kjvj- Each EB is subset of some clique.
Let the random variable X range over all possible fact sets S, with Shannon entropy:
((X) = Σ 1og) log, P(S),
(15)
measuring the total information be represented. For hypergraph representation, since Φн is injective and each fact can be uniquely recovered,
H(X (x)) = O.
(16)
For binary representation, consider any three distinct entities a, b, e E V, and define
S = ((a,b,c) S₂ = {{a.b) {a. c). [b.c]}.
(17)
Clearly, Si # S2, but
Φ = (n()))) = (fa, b, c), {(a, b), (a, c), (b, c)}) = 9.
(18)
since both activate the same set of binary edges. Thus,
0 ((S,)
(d=(()) 2 2,
p(g) < 1,
p(S:)
loga p(S.)
H(X (x(( = -9)= =-
> 0,
(19)
p(g)
p(g)
S.E0g (g)
then, get
H(X ( =
- (())H(( (X) = y) 2 H(g) (x(X) 9) > 0,
(20)
where information is inevitably lost in binary representation.
More generally, as long as there exists at least one n-ary fact (n 2 3) in the knowledge base, we can always construct pair of distinct fact sets that activate the same binary edges through merge-split transformation. Hence,
H(X {B(())> 0, (xX)) = H(X)
H(X dx(X)) < H(),,
(21)
which proves that binary representation is lossy. In contrast, hypergraph representation satisfies [[X (h (X)) 0, so the mutual information reaches its upper bound H/ (X) and all information is preserved. In the special case where no n-ary facts with n 2 3 exist, i.c., all facts are binary, then
Φ (9b) 1, H(X (x)) 0,
(22)
so binary representation becomes injective and equivalent to hypergraph, with no information loss.
In conclusion, as long as the knowledge base contains at least one fact of arity three or higher, hypergraph-structured representation preserves more information with lossless representation, whereas binary representation inevitably loses information. Therefore, hypergraph representation more comprehensive than binary in the information--hherrtte sense.
13

---

B.2 Proof of Proposition 2
Proposition 2. bipartite graph can losslessly preserve and query knowledge hypergraph.
Proof. Let the knowledge hypergraph be denoted G# (V, En); Fu S {en CV |ewr 2 2). Each hyperedge abstracted as a new node, and combined with the set of entity nodes to form a new vertex set VB V U Ен, with edges defined as ÆB (eH, Eн E Eh, t eg). resulting in the incidence bipartite graph & (GH)) = GB = (VB, EB).
Ordering the vertices such that entities come first and hyperedges second, GH can be represented by the binary incidence matrix
M E {0, I
Mu,cH =
eH
(23)
and the adjacency matrix of GB becomes
(10
M
AGn
(24)
MT
0
where M uniquely determines AG., and conversely, M can be recovered from the top-right block of AGa- Therefore, there exists an inverse mapping:
b - GH,
+ (VB, EB) = (V, W (en((e)) en E En)),
(25)
where
NG. (cx) = fv f E V (CH, v) E EB}.
(26)
Clearly,
h-1 o = idg 4 Φ idG
(27)
which means that & is bijection and the encoding is lossless.
The query equivalence can also be derived directly via matrix operations and path counting: the set of hyperedges containing entity y corresponds to the support of the e-th row of M, and in the bipartite graph this is equivalent to the neighborhood NG, (v), given by the right block of
Ag (0, M). Likewise, the entity of hyperedge еμ the support of the ey-th column of M, which matches the left block of f AGg- To determine whether entities u, u co-occur in some hyperedge, it suffices to check whether
(MM) )uv (A2,, Jon + O,
(28)
since (A3 Juy counts all 2-step paths from through hyperedge node to For given subset of entities g
V. hyperedges that contain all of them can be found by summing the corresponding rows Eves Me.* and selecting columns where the sum equals |S]; in the bipartite graph, this corresponds to the intersection
n (v).
(29)
DES
All operations run in time O(EBB)), which matches the complexity of equivalent queries over Gh.
In conclusion, the bijection & guarantees full structural reversibility, while adjacency and path-based reasoning preserve the semantics of all queries involving bipartite graph can losslessly preserve and query knowledge hypergraph.
membership. Therefore,
B.3 Proof of Proposition
Retrieving knowledge on a knowledge hypergraph improves retrieval efficiency compared methody based on ordinary binary graphs, leading gains in generation quality.
Proposition 3.
Proof. Let the ground-truth knowledge set required for query q be modeled as a discrete random variable X P(V), with probability measure μl defined over the measurable space (P(V), B). For any n-ary fact F = (UI,.... en) with n
2 3, we define two encoders:
PH: F eH F. : F - {(v,, 2,)) 1 i<ijjs n).
(30)
Let the encoded knowledge sets be random variables Yи = *H and YB (X). Since р injective, the conditional entropy is zero:
H (X Ya) 0, and hence 1(X;YH) H(X).
(31)
14

---

However, when p([1F] 2 3)) 0, the encoder Pg becomes non-injective. There exist # 22
such that (z(2)) Yn (12), leading to:
H (X YB) Eyn
E
p YB) loga p( YB)
> 0,
(32)
ZEPU (Ya)
[(: H(X) H( YB) < H()).
(33)
To study encoding efficiency, consider encoding Y. (* E {H, BJ) using an optimal prefix code. Let expected code length L. = B(e(Y.)), According to Shannon's 's source coding theorem:
L. (V.)),, HYY)) + 1).
(34)
Define the information efficiency density (information per bit) as:
7/- C.
(35)
This metric quantifies the amount of effective information transmitted per bit. Since T(X; Yn) (X) while YB) < larger outcome space), we have:
(X), and H (YB)) 2 (YH) (as the pairwise representation introduces
H(X) CH
-
NH 7B
8>0, 0, LB CH 2 0,
(36)
CB
which is strictly positive when 8 0. This shows that the hypergraph representation transmits more effective information per bit. Let the maximum retrievable context budget for language model be L, and define the coverage function:
(L) = Pr(I(X;Y.) S #({ n. ((Y()))) S L)),
(37)
(L) is a non-decreasing function of L and is differentiable almost everywhere. Given fjи > B]- the chain rule yields:
do 2 1 ((Yx))L//m de dL J((Y))LL/nB de dL dL
0p de
Op de d do CB(L).
dL Cn(L)=
(38)
which implies CH 2 (L) with strict inequality on intervals where p(()F) 2 3)) > 0. Let generation quality E (e.g., G-E score) differentiable function E (Y): where M. denotes the noise introduced by irrelevant or redundant edges, and satisfies:
0g 01
0g
>00
<.
(39)
ON
Here, noise N, is defined as the set of edges retrieved under budget L that are irrelevant to the ground-truth X1, Under the same bit budget, higher тІи implies fewer edges per bit, and thus:
B[Nn] < B[Wn).
(40)
Treating I. as an independent variable, we apply the chain rule:
dL En (L) Ebb))))
d
0g (0L) a1
d I(x:Ym) dL
d d
((x:Yb)
Ög aa
(0z)
d
No d
d
Nu
dL
dL
dL
(41)
where 0z. is intermediate state between the systems. From Equation 38 and Equation 40 know: (1) The first term is strictly positive if high-arity facts exist; (2) The second term is always non-positive, as higher information density leads lower redundancy. Therefore, the total derivative is strictly positive. Integrating over [0, LJ. we obtain:
(L( EB(L) - '/ d d3
-B) E
d3 > 0, unless u([FF) 2 3)) 0. (42)
Equation 42 formally proves that there exists at least one fact with arity n 2 in the knowledge base, then under any fixed retrieval budget L., the generation quality under hypergraph encoding strictly exceeds that of the binary encoding. In the degenerate case where all facts are binary, both encodings reduce to the same mapping, and the conclusion naturally becomes equality.
D
15

---

C HyperGraphRAG Algorithm Detail
Hypergraph Construction. To provide a clear overview of our system pipeline, we present the detailed procedures of HyperGraphRAG in the form of pseudocode. As shown in Algorithm [ first construct a knowledge hypergraph from raw documents via LLM-based extraction of n-ary relational facts. Each extracted fact forms hyperedge connecting multiple entities, and the resulting hypergraph is stored in a bipartite structure for efficient indexing and retrieval. We further compute dense embeddings for all entities and hyperedges to support semantic retrieval.
Algorithm Hypergraph Construction
Require: Document collection D
Ensure: Knowledge hypergraph Gи = (V, Ei)
I: Initialize entity set V +- 0. hyperedge set Eμ t-
2: for each document d D do
3: Extract n-ary facts: Fa {(e,, Ve.))E=1 ~ T(d)
4: V VV-U Ve,
5: Eн + Eμ He
6: end for
7: Store (V,Ez) FER)) as bipartite graph GB 4(HH)
Compute embeddingg: Ey = (f(u) 8 V). FEg = (f(e) | Fn)
9: return GH = (V, FH))
Complexity Analysis. Given a corpus of D documents, assume each document contains at most relational facts, and each fact involves up to entities. The LLM-based extraction step has complexity O(D) under the assumption of constant time per document prompt. Constructing the hypergraph involves inserting up O(D-r) hyperedges and O n) entities (with deduplication), resulting in a total construction time of O(D-r-n) Embedding all nodes and hyperedges requires O([V+ + || calls the encoder, typically parallelizable.
Hypergraph Retrieval and Generation. Once the hypergraph is constructed, the generation process begins with query input, detailed in Algorithm We first extract relevant entities from the query and perform top-k similarity search to retrieve both entity and hyperedge candidates. bidirectional neighborhood expansion over the hypergraph assemble knowledge set, which may optionally be combined with chunk-level retrieval. Finally, we format the retrieved knowledge into a prompt and generate answer using large language model. This modular pipeline ensures efficient, expressive, and accurate generation grounded in structured knowledge.
then perform
Algorithm 2 Hypergraph Retrieval and Generation
Require: Query q. knowledge hypergraph GH (V, Es)
Ensure: Final answer y
I: Extract query entities: VG ~ ((g)
2: Retrieve top-k entities: V, +- TOPKSIM(V, V., Fv)
3: Retrieve top-k hyperedges: E, +- TOPKSIM(q. EEE)
4: Expand neighbors: FPC = U.ev. Nbr(u), F UcEE. Nbr(e)
5: Assemble retrieved knowledge: KH Fb U F
6: Retrieve additional chunks (optional): K Khunk RETRIEVECHUNKS(Q)
7: Combine all knowledge: K" Kn U Kehunk
Generate answer: y 7(g. K*)
9: return y
Complexity Analysis. Given a query q, entity and hyperedge retrieval involves computing top-k similarity against all entity and hyperedge embeddings. With [V] entities and |EE hyperedges, this results in O(VI + Ex embedding comparisons. The neighborhood expansion step is bounded by the degree of retrieved nodes, i.e., O(k d) where d is average node degree. Finally, generation is treated as a black-box LLM inference, typically OL)) where the prompt length.
In summary, HyperGraphRAAe achieves efficient inference with precomputed indices, and its overall serrivallggenraation time is dominated by vector similarity lookup and prompt generation, both of which scale linearly with hypergraph size and are highly parallclizable in practice.
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D Dataset Construction
D.1 Knowledge Domains
The dataset used for HyperGraphRAG evaluation covers five domains, with data sourced as follows:
Derived from the latest international hypertension guidelines [[6], covering medical diagnosis, treatment plans, and clinical indicators. Agriculture: Extracted from the UltraDomain dataset 19], including knowledge
Medicine:
agricultural production, crop management, and pest control. Computer Science (CS): Sourced from the UltraDomain dataset, encompassing computer architec- ture, algorithms, and machine learning. Legal: Based the UltraDomain dataset, covering legal provisions, judicial precedents, and regulatory interpretations. Mix: A combination of multiple domains the model's generalization ability across interdisciplinary tasks.
D.2 Question Sampling Strategies
To construct fair and comprehensive evaluation benchmark, design uniform sampling strategy for both binary and n-ary sources. Specifically, for each domain, we sample a total 512 questions, consisting of:
Binary Source (256 samples): 128 facts are selected via 1-hop traversal, 64 facts via 2-hop traversal, 64 facts via 3-hop traversal. These facts are composed of binary relations (i.e., pairwise entity connections) and are used to build the binary knowledge source.
N-ary Source (256 samples): 128 facts are sampled via I-hop traversal, 64 facts via 2-hop traversal, 64 facts via 3-hop traversal. These facts involve multi-entity (n 2 3) relational structures and used to construct the n-ary knowledge source.
For each sampled fact, prompt GPT to generate corresponding question and its golden answer. All generated question-answer pairs are manually verified to ensure factual accuracy, relevance, and diversity. This process is repeated independently for every domain to ensure consistent scale and structure across evaluation sets. All datasets undergo manual review to ensure the accuracy of annotated answers and the fairness of model evaluation.
E
Evaluation Details
Unified Generation Prompt. To ensure a fair comparison across all baselines, we adopt a unified generation prompt for all methods, as shown in Figure I0 Specifically, we insert the knowledge retrieved by each method into a fixed prompt template that guides the model to first perform reasoning within <think> block and then provide the final answer within <answer> block, preserving benefits of zero-shot CoT reasoning while maintaining consistency across different retricval strategies.
-Rolee..
You are holpful assistant responding to questions based on given knowlodge.
Knowle dge
-Goel-..
Anower given question.
resscring inside othinno....oh wothinkks
you have answer, you can output answer Inside carswets..ccaneeess
Output answer:
canswoos
(etuestoor]
Figure 10:
The unified prompt for generation Pgen in Equation 12
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We evaluate model performance using three complementary metrics that assess different aspects of retrieval-augmenned generation: factual alignment, retrieval quality, and generation fluency.
(i) F1 Score. Following AG [9], we compute the word-level FI score between each generated answer and its ground-truth reference, and then average all questions. This metric captures reflects factual alignment with the expected answer.
N
2 P: R P: + R
Pred, GT, Pred;
Predd n GT,
FI
P.
R4
(43)
N
GT.
where Pred, and GT, denote the set words the predicted and ground-truth answers for the i-th question, and N is the total number of evaluated questions.
(ii) Retrieval Similarity (R-S). Inspired by RAGAS (3). R-S quantifies the semantic similarity between the retrieved knowledge and the ground-truth knowledge used to construct the question. For each question, concatenate all retrieved knowledge into single string Keer and all golden knowledge into kgoodd then compute the cosine similarity between their embeddings. The final R-S score is the average similarity across the dataset:
1 Σ COs (f(H(E)), f(kgola)) R-S
(44)
where f(.) is the embedding function (e.g., SimCSE), and N is the total number of questions.
(iii) Generation Evaluation (G-E), Adapted from HelloBench [20], G-E uses GPT-4o-mini as an LLM judge to evaluate generation quality along seven dimensions: Correctness, Relevance, Factuality, Comprehensivennss, Knowledgeability, Logical Coherence, and Diversity. For each question, compute the average of the seven dimension scores, then combine it with the question's Fl score by taking their mean. The final G-E score is obtained by averaging this combined score:
N mean
G-E
si,d F1, d=1
Σ
(45)
where 9;,d denotes the score for dimension d on question F1, the word-level F1 score for the i-th question, and N is the total number of evaluated questions. This formulation encourages alignment between LLM-judged quality and factual correctness.
G-E Prompt. Figure 11 and Figure 12 show our generation evaluation prompts. Figure 11 presents the unified prompt used score each dimension on 0-10 scale, while Figure 12] provides the detailed scoring rubric for all seven dimensions, ensuring consistency and fairness across evaluations.
-Role-
You are helpful assistent evalusting "Qitle" generated reporese.
Question
(question)
Answers
(et(anewerss]
"[goal)" using integer stale""
(nubric)
your
integer
lapiaaation
Explain
this
Generatton Evalunted-..
(generation)
Figure 11:
Prompt for G-E.
18

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"comprehensiveness" {
"comprehentiveness"
"whether thinking considers important aspests thorough",
""Scoring Guide (0-10):
Extramely tharough, covering relevant angles considerations with dopth.
8-3: Oovers most key espects clearly and thoughtfully; only minor omissions.
6-7: Covers some importent espects, but lacks depth or overlooks notable areas.
4 5: Touches
few relevant points, but overall lockss substoncc completeness.
1-3 Sparse or shallww treatment or the topic; misses most key aspects.
0: No compreeenalveness at all; completely superficiel or irrelevant."
"knowledgeabllilt""
eenoledgeabillty
"whether the thinking rich insightfu, domain- relevant knowledgee"
""Sooring (0-10):
10: Demonstrates exosptional depth and insight with strong domain-speciffe knowledge.
Shrws clear domain knowledge good insight; mostly
and relevant.
6-7: Displays some understanding, lacks depth or has notable gaps.
4 4-5: Limited knowledge shown; understancing basic or somewhat flaved.
1-3: Poor grasp relevant knowlodge; superficial mostly Incoreet.
0: No evidence meeningful knowlsdge. -..
"correctness (
"corractness""
"whether the reasoning and answer are logically and factually correct",
""Soorrng Guide (0-10):
Fully accurate logically sound: tlaws reasoning tacts.
8-9: Mostly correct with minor inacorrccees or small logical gaps.
Partially
key
inconsistancles present.
4-5: Noticeable incerrect reasoning or factual errors throughout.
1-3: Largely incorrect, misleading, or illogical.
0: Entrraly wrong nonsensical." s.
"relovance":
"ralevance",
"whether the reasoning and answer are highly relevant helpful question",
""Scoring Guide (0-10):
Fully focused the question; highly relevant and helpful.
8-9: Mostly an point; minor digressions but overall useful.
6-7: Generally relevant, but includes distractions or less helpful parts.
Limited relevance:
of response off-topic unhelptul.
1-3: Barely related to the question or largely unhelpfu.
0: Entirely inrelvant."
"diversity": (
"diversity",
"whether the reasoning thought-proooking, ottering varied perspectives',
""Sooring Cuide (0-10):
- 10: Exceptionally rich and original; demonstrates multiple fresh and Brougght-proooiigg ideus. novel anglos interesting perspectives.
8-9: Contains
6-7: Some varicty, but genurally safe or conventional.
4-3 Mostly standard thinking, minimal diversity.
Very predictable
0: No diversity or originality at all."
"logical_ccherennc" coherence
"loiiall coherence".
"whether the reasoning is internalyy consistent, clear, and well
""Sooring
(0-10)
Highly logical, clear, and easy to follow throughout.
8-9: Well structured with minor lapses in flow or clarity.
structure logic,
confusing or weekly connected parts.
4-5: Often disorganized or uncicar; logic hard to follow.
1-3: Poorty structured and incoherent.
Entirely lllogical
...
"factuality": (
"factuality":
"whether the reasoning and answer are based on sccurate and verifibble facts",
""Searing Guide (0-10):
8-3: Mostly accurate; only minor factual issues.
6-7: Contains some factual inacouracies unvorified claime.
significant factual errors.
1-3: Mostly false or misloading.
0: Completely fsbricsted factually wrong throughout." ...
Figure 12: Seven Evaluation Dimensions for Generation Quality.
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Baseline Details
We compare HyperGraphRAG against six representative baselines that cover retrieval-free, chunk- based, and binary graph-based RAG paradigms:
NaiveGeneration is retrieval-free baseline where the LLM directly answers questions without any external knowledge input. This serves lower bound for auugenel generation.
StandardRAG follows the original RAG design, retrieving top-k text chunks from a flat corpus using dense vector similarity and feeding them into the generator.
GraphRAG 2 constructs a binary relational graph and retrieves community- summaries linked to query-relevant entities. It uses entity overlap to detect relevant subgraphs.
LightRAG 7 enhances retrieval efficiency by using graph indexing and lightweight entity-relation matching over the binary graph, and then combines results with chunk-level retrieval.
improves graph-based retrieval by selecting paths through the graph that are semanti- cally relevant to the query, using path pruning strategies to reduce redundancy.
PathRAG 1
HippoRAG2 g introduces a high-precision multi-hop retrieval mechanism over binary graphs, using Personalized PageRank to select passage-level nodes connected to query.
To ensure fairness, all baselines use the same generation prompt (Figure 10) and are evaluated under identical conditions. with retrieved knowledge constrained to equivalent token budgets. Each method's construction and retrieval mechanism is summarized in Table
G Hyperparameter Settings
For all methods, adopt unified set of hyperparameters for all models across both the main evaluation in Table the time/cost experiments in table ensure fair and consistent comparison. retrieve the top-5 chunks using dense similarity.
For chunk-based methods (c.g.. StandardRAG), For graph-based methods, including GraphRAG, LightRAG, PathRAG, and HippoRAG2, we retrieve the top-60 relevant elements according to their respective retrieval strategies. HyperGraphRAG performs dual top-60 retrieval over entities and hyperedges, followed by neighborhood expansion. using 16 parallel cores and the same generation model (GPT-40-mini) with
All methods temperature 1.0 and a maximum generation length of 32k tokens. Table 4 summarizes the detailed hyperparameter configurations used throughout experiments.
Table Hyperparameter settings for all methods.
Method
Retrieval Type
Top-k Units
Parallel Cores
Generation Model
NaiveGeneration
None
16
GPT-4o-mini
StandardRAG
Chunk
chunks
16
GPT-4o-mini
GraphRAG
Entity Community
60
16
GPT-4o-mini
LightRAG
Entity Relation
60
16
GPT-4o-mini
PathRAG
Graph Path
60
16
GPT-4o-mini
HippoRAG2
PageRank over Graph
60
16
GPT-4o-mini
HyperGraphRAG (ours)
Entity + Hyperedge
60
16
GPT-4o-mini
H
Case Study
To better understand how different methods perform in complex, knowledge-intensive scenarios, present a case study on the question: "What type of renal denervation has been shown to demonstrate BP BP-lowering efficacy over 24 hours in several randomized, shan-controlled trials, particularly for resistant hypertension?" As shown in Table this question requires synthesizing clinical evidence and distinguishing between treatment modalities (e.g., ultrasound vs. catheter-based techniques).
HyperGraphRAG provides the most comprehensive and accurate response, clearly identifying ultrasound renal denervation the answer, and justifying it with domain-relevant reasoning and structured knowledge. achieves the highest scores across all dimensions, including Correctness (10.00), Factuality (9.50), and Knowledgeability (10.00), resulting in overall G-E score of 92.86.
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Table 5: Case study comparing RAG methods on a complex medical question. The reported metrics reflect the actual scores for this specific example. HyperCraphR generates the most accurate and comprehensive answer, achieving the highest scores across all evaluation metrics, while other baselines exhibit factual omissions or ambiguity.
Query
Whar type of meall dimerattoon has been shous in famonetrate Hi-inweeitg affracy one sq beem seceral randorited, ebar-conindled trals paziedaayy for reaiiiaaa Iepertanios?
Doldin Arswer
"ULTRASOUND BENAL DENERVATION
R-S
Comprahen
-hhennsx
Knowledge labliity
Correttness
Relevance
Divaraity
Goharance
Logical
Factuaity
<tf niol denervation a procedure used tn neaitart by on dirupting the rerves near arteries, which are bellased contribut ute regulation blod presourn, Beveral tooleiiquee car perlod
donervation, ng indofroceency by, uirosound. rigeruslly
athiacy
Genwarinn
valious randorized sham-oontrdeed and has snown cint persisiance blood pressure redlucioon particuarlyy putants with rosistatt roler Tharslone, rackotocuentyy merhod stands nut smong the mosi shie tnchnity une wnw.iinnntiinnneneee...o conowrrrri Reditrequency renal denervation has been shown to demonstrato BP lowering efficecy over 24 hours in several randomized, sham- controllodd trids, particularly for resistant hypartemalonn (nclammssee
eddleeguenyy renal denercation. This approach
IntowGrranntinn
Breluation Soore
18.00
00.00
<dhink-inihh tost mentiono sceeral dovices baeed renal denervation tecing the most exdeece BiP-oowwiig arteasy, netex that both axcitecuennyy and trasound nensl denarvation have been domonsthated to lowar blood pressure over 24 hours in broad spectrum of typortansion cases. including resiiant hyporension. Thus, both rackolnccuanc and ulbraound nenal denervation seem be sflective bussc on the trals rularer cad in-ottenconnnaanneeee cansvarrin Cuthefer-bua buas---aaeddd renal denervation, particutarly by radiot equenny and ultrasound renal denervation, has been shown demonetrate BP-Krweriing efficaay over S4 hours several randomizzsi, shan controlled trials for reaistant hypertemaion inclaswerr
ieeetigatedd treatig recistant Toperten but specifoaly hight oathetor
Gerwodonn
Evntustion Soore
60.00
55.00
65.00
63.00
RP Anowwing Renal deneraation
trot
hypreteevtion diespping
signnll
which can isad long tamm reductions blood presuurs. virieverul clinccll bias. such is the SYMPL CITY HTN and those inchiing catholer based ullmooudd tacheiguue, hawe wos intt the efwcctuaress ses of nece devenation for twering rederant hypattensss.. Mive spacthollyy some tride have shown a sustained blood pressure lovering offect over 8 hour serod, which essentall for patients sulloring form rosstartt
Gonevotin
@raphRAB
pypameentinn trinktte esing connect provieed cath basedd recd denemaaion sposers bes the speciic type that tree shown sag thoen trese trish, partiulatyy targeting patients pecohhireeoecarreweeee randomized, controled trials, particularly resistant hypertension, inolnswerr
offeacy
not respond tradtional and typo tonsiie
SP-lowering afficacy
Evntustion Soore
67.55
00
36.9 00
atrinna-lttturll di deniniztion is procedura simod at reducing High bro pressura J301 by cianppting runal nerve activty. The document diacussss vantuus fyrws of meol deneoust on, parteaaterly high ligtingg cathwee-hsee methods Theee methode use aelebeeuenry and istreeound lochnoloogis to denervata nond arteria. trabs merrioned demonstrato lovering offeacy over D4 poloo these approaches. Ginan ettectvell
hypederaion, redorrqueeey tooh wuuss///hhkkksssee chokkkkkaaaaa Culheterr rendl denervation using radiolequeenyy ultroound shown demonstrate BP -i--wwwring efficacy hours several randomized, sham- contr Iypertension Veclrdwers
LigHAAG
contrelled elled traae, particutarly resabant
Besuution Soore
24
<thrakc///TTe quaetton is abouut nensi der denwnstion specttrally tocroding on In type then ahown wfticeyy in blood preesum (IP) inwering. Rierall der denarcation is proced.n ze thet invobres meciyynn narve agras in the lodnny to help contecl hypeteraion. The trai: mamtioned speciiially perter to rendemtined, sham cant stuties which exatame the aftectiarmss of dthenet techriquuss devices durig prosedure, The arnoorr denovattion" is common reehhd used Ieey Viatheeer toparteraio itn.ttreoolsscaaeeeeeee
PahhRAG
Ocnortton
triis, several have reporedd hes offectveness in hours several randomized, con--contoolled trials, particulerly resistant hypertansion. tnclantawr
BP-lowering
Sreluatinn Score
16.00
60.44
G7
48,00
30.00
48.00
68:00
38.00
48,00
E6 20.00
<th niccinn The provaded fect mentone that cathwaar based nanal denemvstinn has been stuched sagritsarlyy in tharthng resitant hypertenson ln, with Iscua on two tectnallogaa:: raderheuuenyy and uttrasund nenal derevatten. The senteros ind cates that thers avatable dencs hom several nandem aed, sham cor troked vius wtrcch contimed liwering atheacy for these methecs over 24 hour pario, Thensons, answer should pariiulatyy rediobecuanty radiofrequency partcularly
Genevation
HopoRAGe
been
shown demonatrate BP loweriieg effeaey hours several rundomizod, sham contrelio efedd trials, particularty resislant hypartanaion. inclerasser
Siclutton Score
19.85
66.15
58.25
$4.58
68
$4.58
59 19:88
30.68
$4.68
54 68
wtth Tho ei mettin seko abour a type ol nenil der reveraatinn than has demonelatted rEPaawering afticay now 24 hours specttically in the connect of seyoral randoriizdd, sham corno led trick related to recktonn hyportoniion Bascd on the provided knowlodgg, both uhrosound ronal denercation racuttee enzy meaal ceneraation hace been ment aned to show EiP-oseetng ettiaay. The typaredgae alse state that several shom contro secognized
Goneration
been publ demonstratin effeacy these two mothods. Thorefores essentaa to icently type that
denevation flwned conjunction with aandmmited tpaa poterisily cuality,
condiatee wiThus, ultsouud denervation mithod thut tia ortanis the question www.://eooooeeeoeeeeeeeeeoeooe Ultrasound renal denervation iollnswers
Svstustion Score
100.00
70.07
52.08
90.50
05.00
100.00
100.00
75,00
93.00
$6.00
In contrast, baseline methods like NaiveGeneration and StandardRAG produce factually plausible but imprecise or overly generic answers (e.g., mentioning radiofrequency denervation instead), leading to lower scores, particularly in Correctness and Factuality. Graph-based baselines such as GraphRAG. LightRAG, and PathRAG improve coherence but still fall short in domain specificity. Even the best-performing baseline, HGpp fails to precisely isolate the correct answer, with reduced clarity and comprehensiveness compared to HyperGraphR This case highlights the strength of HyperGraphRAAC in integrating multi-entity clinical knowledge through hyperedges, enabling more precise, interpretable, and fact-grounded responses in real-world expert-level tasks.
21

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I Limitations and Future Work
L1 Multimodal HyperGraphRAG
While our current framework focuses on textual knowledge, real-world information often spans multiple modalities, including images, tables, and structured metadata. promising direction is to extend HyperGraphRAG to the multimodal setting by constructing hypergraphs that integrate both textual and non-textual entities (e.g., medical images, diagrams, or structured EHR fields). This would allow the model to reason over complex multimodal relationships, such as "image + report + diagnosis" "chart claim textual guideline," and enable broader deployment in domains like medicine, science, and law. Future work will explore how to encode, align, and retrieve multimodal hyperedges effectively, while maintaining the structural advantages of hypergraph representations.
I.2 HyperGraphRAG with Reinforcement Learning
Another important extension lies in incorporating reinforcement learning (RL) to guide both retrieval and generation. In our current setup, retrieval is driven by fixed similarity metrics, which may not fully capture downstream utility. By formulating hypergraph-bart decision-make manonn process, we can apply RL to optimize entity and hyperedge selection policies based on long-term generation rewards- such as factuality, coherence, user feedback. This would allow HyperGraphRRA to dynamically adapt retrieval strategies to different tasks and domains, leading to more efficient and effective use of structured knowledge.
retrieval as sequential
L.3 Federated HyperGraphRAG for Privacy- Preserving Retrieval
Many real-world applications involve sensitive or distributed data that cannot be centralized due to privacy constraints. To address this, we propose to integrate HyperGraphRAGG with federated learning techniques, allowing hypergraph construction, retrieval, and generation to occur across decentralized data silos. Each local client can construct its own partial hypergraph and share only anonymized or encrypted embeddings, preserving privacy while contributing to global retrieval. This federated HyperGraphRAGG would be particularly beneficial in domains like healthcare or finance, where data sharing is restricted but collective knowledge crucial for robust decision-making.
1.4 Toward Foundation Model for HyperGraph- Retrieval
As large language models continue to scale and generalize across domains, natural extension is to explore the development of foundation model for HyperGraphRAG. Rather than constructing and retrieving from hypergraphs on a per-task or per-domain basis, we envision pretrained hypergraph reasoning model that jointly learns representations of entities, relations, and higher-order hyperedges across diverse corpora. This model would encode structural, semantic, and contextual signals in unified way, and could be adapted to new domains via lightweight fine-tuning. Such foundation model could also enable transfer learning across showledge-intensive tasks, reducing the need for specific engineering and improving the sample efficiency retrieval and generation pipelines. Building this requires scalable hypergraph pretraining objectives, efficient storage formats, and robust generalization strategics, which we leave as future work.
1.5 Sealing to Harder Tasks and Broader Applications
Finally, we plan to evaluate HyperGraphRAG on more challenging tasks and diverse real-world applications. This includes settings that require deeper compositional reasoning, such as multi-hop question answering, legal argument generation, or complex scientific synthesis. Additionally, we aim to apply HyperGraphRAGG to broader domains beyond the current benchmarks, including policy analysis, education, and open-domain dialogue. These tasks will test the framework's 's ability to generalize across domains, handle larger and more diverse knowledge bases, and maintain high-quality generation under increasingly demanding conditions.
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Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification:
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Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core of the paper level of detail that is necessary to appreciate the results and make sense of them.
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Reviews:
[{"review_id": "byqUcKGCtG", "reviewer": "Reviewer_pQR1", "summary": "This paper introduces HyperGraphRAG, a novel retrieval-augmented generation framework leveraging hypergraph-structured knowledge representation to effectively model n-ary relationships involving multiple entities, thus overcoming the limitations of chunk-based and traditional binary graph-based methods. It consists of three key components: (1) knowledge hypergraph construction, which employs LLM-based extraction of multi-entity relational facts; (2) hypergraph retrieval, using semantic similarity to efficiently fetch relevant entities and hyperedges; and (3) hypergraph-guided generation, integrating structured hypergraph knowledge with traditional retrieval methods to enhance response accuracy and informativeness. The authors demonstrate through experiments across diverse domains—including medicine, agriculture, computer science, law, and a mixed domain—that HyperGraphRAG consistently outperforms existing retrieval methods in answer accuracy, retrieval relevance, and generation quality. These results confirm its practical effectiveness and broad applicability.", "questions": "1. In HyperGraphRAG, hypergraphs are stored in a standard graph database using bipartite graph structures(sec 4.1). While this ensures compatibility with existing graph databases, it potentially introduces additional complexity or inefficiency in querying and maintaining high-order relationships. Could the authors elaborate on the rationale behind choosing a standard graph database instead of a native hypergraph database[1], and discuss any trade-offs or limitations (e.g., information loss, query efficiency, scalability)? Moreover, under what circumstances would the use of a native hypergraph database be beneficial or recommended for HyperGraphRAG?\n2.Does HyperGraphRAG have the potential to generalize to multi-hop reasoning scenarios?\n3.How does the N-ary Relation Extraction Prompt handle extremely long documents?\n4.How can one address failure cases caused by unstable structured output?\n5.What about using a long-CoT reasoning LLM (e.g. DeepSeek-R1 or its distilled version) as the QA model, since those are better at thinking through complex reasoning before answering?\n\n\n[1] Feng, Y., Hu, H., Hou, X., Liu, S., Ying, S., Du, S., ... & Gao, Y. (2025). Hyper-RAG: Combating LLM Hallucinations using Hypergraph-Driven Retrieval-Augmented Generation. arXiv preprint arXiv:2504.08758.", "limitations": "Yes. The authors have thoroughly addressed key limitations, clearly highlighting areas for potential improvement.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths：\nQuality: The method rigorously addresses the key limitation of binary graph-based representations by introducing hypergraph structures, effectively capturing complex multi-entity relationships. The comprehensive theoretical justification, including formal proofs, strengthens the technical validity.\n\nClarity: The paper is clearly written, well-structured, and effectively communicates complex ideas with detailed explanations and illustrative figures. The step-by-step breakdown of methodology and experiments greatly enhances readability.\n\nSignificance: HyperGraphRAG addresses a meaningful and significant gap in current retrieval-augmented generation methods. By modeling n-ary relations, it substantially improves the completeness and informativeness of retrieved knowledge, which is critical for knowledge-intensive applications.\n\nOriginality: HyperGraphRAG is innovative, clearly differentiated from existing chunk-based and binary graph-based methods. The introduction of a hypergraph-guided generation strategy is particularly novel and practical.\n\n\nWeaknesses: \n1. Scalability concerns for complex reasoning tasks. HyperGraphRAG’s hypergraph structure, at inference time, only retrieves the vector-matched nodes and hyperedges plus their 1-hop neighbors, so direct entity-to-entity interactions are missing.\n2. Heavy workload for very long documents. In Appendix A.1, the N-ary relation extraction prompt asks the LLM to segment the input into coherent knowledge fragments and identify entities—but when documents become extremely long there is no post-processing to ensure that the model’s structured outputs remain well-formed.\n3. Questionable summarization and abstraction ability. In Algorithm 1, HyperGraphRAG handles each document independently before merging into a single hypergraph. However, because knowledge segments are extracted in isolation, it lacks GraphRAG’s community-based graph structuring and hierarchical summarization.\n4. Evaluation setup concerns. In section E, the Unified Generation Prompt requires GPT-4o-mini to “think” inside a <think> block before giving its answer in an <answer> block—but GPT-4o-mini is a short-CoT model, not a long-CoT reasoning LLM like DeepSeek-R1, which is designed to perform more extensive chain-of-thought before answering.\n5. The ablation studies were conducted primarily within the medicine domain. Providing additional ablation results in other domains would strengthen the empirical validation and generalizability claims.", "was_revised": true, "final_justification": "The author has addressed my concerns and supplemented the corresponding experiments, so I consider rasing the score to 5.", "rebuttal": "Thank you very much for your time and effort in reviewing our paper. We sincerely appreciate your feedback. Below, we respectfully provide our detailed responses to address your concerns.\n\n---\n**W1: \"Scalability concerns for complex reasoning tasks. Direct entity-to-entity interactions are missing.\"**\n- We thank the reviewer for raising this important point.\n- Although HyperGraphRAG retrieves vector-matched entities and hyperedges along with their 1-hop neighbors, this process **implicitly preserves rich entity-to-entity interactions** via its **n-ary relational structure**:\n  - An entity’s 1-hop neighbor is a hyperedge, whose 1-hop neighbors are other participating entities.\n  - Thus, retrieving one entity leads to retrieving **all related entities** co-involved in the same hyperedge.\n- The retrieved knowledge consists of **complete multi-entity facts**, naturally encoding **entity-to-entity semantics** through shared hyperedges. We also provide a detailed proof in **Appendix B.2** that our hyperedge and one-hop entity-to-entity interaction are equivalent.\n- Unlike binary graphs that require multiple hops to recover latent connections, HyperGraphRAG captures **multi-entity semantics in a single hop**, offering both **efficiency and expressiveness**.\n- We hope this clarifies how HyperGraphRAG inherently supports rich entity-level retrieval while remaining scalable.\n---\n**W2&Q3&Q4: \"Heavy workload for very long documents. How does the N-ary Relation Extraction Prompt handle extremely long documents? How can one address failure cases caused by unstable structured output?\"**\n- We thank the reviewer for pointing out the potential challenge of handling very long documents during n-ary relation extraction.\n- To clarify, as shown in Equation4, our implementation **segments long documents into shorter, coherent fragments** $d$ before feeding them into the LLM for relation extraction. This segmentation step ensures that the model input remains within length limits. After extraction, we perform **entity-level merging across different fragments**, with identical names. This process yields a **well-connected hypergraph**, where entities are shared across multiple hyperedges derived from different document segments. This strategy is consistent with prior GraphRAG methods such as **LightRAG** and **PathRAG**, which also operate on chunked inputs for knowledge graph construction.\n- During retrieval, we leverage this interconnected structure to support **global entity-level knowledge retrieval**, ensuring that even when documents are long, the retrieved knowledge maintains structural integrity, rich connectivity, and semantic consistency, enabling robust retrieval and generation performance.\n- For structured output stability, we use several structured examples to prompt the LLM, which helps mitigate variability in structured outputs. Additionally, we write **post-processing code** to validate and correct the output string, ensuring that it remains well-formed and semantically coherent. You can refer to the code for more details on the implementation.\n---\n**W3: \"Questionable summarization and abstraction ability.\"**\n- We appreciate the reviewer’s observation regarding the lack of community-based graph structuring and hierarchical summarization in HyperGraphRAG, as seen in GraphRAG.\n- Indeed, the community detection and summarization mechanisms in GraphRAG are valuable for some applications. However, these features come with notable limitations: \n  1) They typically incur **higher API costs** due to the extra summarization stage; \n  2) The summarization process may introduce **hallucinations** or semantic drift from the original content, especially when compressing complex knowledge into coarse-grained summaries.\n- In contrast, HyperGraphRAG adopts a different design philosophy. Our goal is to construct a **minimal-loss, structurally rich index** over the source knowledge through **hypergraph-based representation**, which explicitly encodes **n-ary relations among entities**. This allows for a faithful reconstruction of the original document structure through **fine-grained, semantically grounded hyperedges**.\n- At inference time, the retrieval is performed over this hypergraph structure, enabling access to **precise and contextually grounded knowledge segments**, closer to the original content than abstracted summaries. This design delivers **higher retrieval efficiency than StandardRAG**, and **more expressive knowledge representation than traditional binary GraphRAG methods**, striking a practical balance between fidelity, structure, and scalability.\n- Such capabilities make HyperGraphRAG particularly well-suited for domains like **medicine** and **law**, where semantic precision and interpretability in knowledge construction are crucial.\n---\n**W4: \"GPT-4o-mini is a short-CoT model, not a long-CoT reasoning LLM like DeepSeek-R1, which is designed to perform more extensive chain-of-thought before answering.\"**\n- We thank the reviewer for this insightful observation.\n- We found that **GraphRAG evaluation is highly sensitive to the final generation prompt**. To ensure fair and stable comparison, we adopted a **unified prompt format across all methods**, reducing the confounding effects of prompt engineering.\n- The `[THINK]...[/THINK]` and `[ANSWER]...[/ANSWER]` tags serve as a **zero-shot CoT strategy**, encouraging lightweight reasoning even in short-CoT models like GPT-4o-mini. We **intentionally avoided long-CoT models** such as DeepSeek-R1 to **minimize prompt-specific biases** and ensure a **level playing field**.\n- Our goal was to **isolate the effects of structured knowledge representation**, not to amplify performance via model-specific prompt tuning.\n---\n**W5: \"The ablation studies were conducted primarily within the medicine domain.\"**\n- We thank the reviewer for the constructive suggestion.\n- We initially focused on the **medicine domain** because it aligns with our motivation—where **structured, high-precision knowledge representation and retrieval are critical**. This also enabled **fine-grained qualitative evaluation** in collaboration with clinical experts.\n- We appreciate the reviewer’s feedback to strengthen the generalizability and empirical validation of our work. We will include ablation results from additional domains in the final version to enhance completeness and robustness.\n---\n**Q1: Could the authors elaborate on the rationale behind choosing a standard graph database instead of a native hypergraph database[1], and discuss any trade-offs or limitations (e.g., information loss, query efficiency, scalability)?**\n- We thank the reviewer for this thoughtful and technically insightful question. During the review period, we have also noticed related work Hyper-RAG, which is also a wonderful work that employs a **native hypergraph database**.\n- However, as you have noted, **our primary motivation for choosing a bipartite graph structure** is to ensure **broad compatibility with existing standard graph databases and infrastructure**, such as **Neo4j**, **RDF** stores, **TuGraph**, and even in-memory graph structures like **NetworkX**. These platforms are widely adopted in industry and research, and thus enable easier deployment and integration.\n- The bipartite transformation corresponds to the **star expansion** in hypergraph theory and is **lossless and theoretically equivalent** to native hypergraphs. We formally discuss this in **Appendix B.2**, demonstrating how **n-ary relational semantics** are fully preserved via **hyperedge-entity linking**.\n- Regarding **query efficiency**, the typical one-hop query in native hypergraphs is equivalent to a **two-hop traversal** in the bipartite graph (entity → hyperedge → entity). Since bipartite edges are non-informative, the actual **time complexity remains unchanged**.\n- Moreover, our schema is **representation-agnostic**, and HyperGraphRAG can be **ported to native hypergraph databases easily** with no fundamental changes.\n- In summary, we adopt bipartite structures to achieve **interoperability and scalability** while preserving **semantic fidelity and efficiency**, making our method practical and extensible for real-world applications.\n---\n**Q2&Q5: Does HyperGraphRAG have the potential to generalize to multi-hop reasoning scenarios? What about using a long-CoT reasoning LLM as the QA model, since those are better at thinking through complex reasoning before answering?**\n- We thank the reviewer for this forward-looking question. In the current work, we focus on isolating the effects of **hypergraph-based knowledge representation** under single-turn QA and non-RL models to ensure fair comparison.\n- That said, we **strongly believe HyperGraphRAG is well-suited for multi-hop reasoning**. As discussed in **Appendix I**, we are actively extending HyperGraphRAG with **end-to-end reinforcement learning (RL)** via the GRPO framework. This enables an agent to iteratively explore the hypergraph, retrieving intermediate nodes before final answer generation.\n- Our **preliminary results** from this follow-up system—HyperGraphRAG+GRPO—show strong gains over **Search-R1** (a StandardRAG + GRPO baseline) using **Qwen2.5-7B** as the base model:\n\n| Model| F1 (Avg.) | G-E Score (Avg.) |\n|-|-|-|\n| Search-R1             | 46.19     | 68.60            |\n| **HyperGraphRAG+GRPO** | **57.82** | **76.23**        |\n\n- These results suggest that **RL amplifies the strengths of hypergraph representations**, enabling more effective navigation and reasoning over structured knowledge.\n- In conclusion, HyperGraphRAG not only generalizes to multi-hop settings, but also provides a robust foundation for **agentic QA and long-CoT reasoning systems**.\n---\nAt last, we sincerely appreciate your valuable feedback, and we will carefully consider all your suggestions to further improve our paper. We would be deeply grateful if you could kindly reconsider raising the score further. Thank you very much!"}, {"review_id": "4oIHdjsAMf", "reviewer": "Reviewer_hXZP", "summary": "This paper identifies a key limitation in existing RAG paradigms: standard methods ignore relational structure, while graph-based approaches are confined to binary relationships. This work assumes that such models are insufficient for capturing the complex, n-ary facts prevalent in real-world knowledge domains.\n\nTo address this limitation, the paper introduces HyperGraphRAG, a novel framework that leverages hypergraphs for knowledge representation. The core contribution is the modeling of n-ary facts as single hyperedges, each connecting multiple entities, thereby preserving the contextual integrity of complex information that would otherwise be fragmented. The authors present a complete methodology that includes an LLM-driven process for knowledge hypergraph construction, a dual-retrieval strategy for both entities and hyperedges, and a final hypergraph-guided generation stage.\n\nThe effectiveness of HyperGraphRAG is validated through extensive experiments across 5 distinct domains. The results demonstrate significant improvements over both standard RAG and existing graph-based baselines across multiple metrics, including answer accuracy and retrieval quality.", "questions": "see weakness", "limitations": "see weakness", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "# Strength\n\n1. **Novelty of the Idea:** The paper's primary contribution is the application of hypergraphs to RAG, directly addressing a critical shortcoming of prior methods. By modeling complex facts as single hyperedges described in natural language, the approach preserves the contextual integrity of information. This is a significant conceptual advance, offering a new paradigm for knowledge representation.\n\n2. **Experiments:** The validation across five distinct domains and a fair comparison against a comprehensive suite of strong baselines provides compelling evidence for the method's superiority and generalizability.\n\n# Weakness\n\n1. **Systemic Risks Arising from the Method:** While conceptually novel, the proposed method makes a significant trade-off: it sacrifices the structural rigor, query precision, and inferential capabilities of traditional knowledge engineering for the flexibility of automated context extraction. This dependency on unstable LLM-based extraction introduces a systemic risk to the knowledge base's quality and consistency. Consequently, the system functions more as a sophisticated context retriever than as a knowledge base with precise and logical representations.\n\n2. **Challenges in Engineering Feasibility and Scalability:** The end-to-end pipeline is complex, and the associated costs of construction and maintenance are substantial. The heavy reliance on expensive LLMs for extraction and the long, multi-stage processing chain present significant challenges to scalability.\n\n3. **Limitations in Representational Capabilities:** The model's flat hyperedge structure is unsuitable for representing hierarchical or interdependent knowledge. While effective at bundling a single **event**, it struggles to model the complex logical relationships (e.g., causality, dependency, conditionality) that often connect these events in domains like law or science. This limits its applicability for tasks requiring deep, multi-step reasoning.\n\n4. **Absence of Knowledge Discovery Capabilities:** The framework's definition of knowledge is confined to explicit statements within the source text. It tends to reproduce existing information rather than discovering implicit patterns or latent relationships that are not explicitly stated. The resulting knowledge base is effectively a structured recombination of text snippets, not a higher-level abstraction of the underlying knowledge, thereby missing a key value proposition of traditional knowledge graphs: data mining and insight discovery.", "was_revised": true, "final_justification": "The authors have adequately addressed my concerns, and I am raising my score to 4.", "rebuttal": "Thank you very much for your time and effort in reviewing our paper. We sincerely appreciate your feedback. Below, we respectfully provide our detailed responses to address your concerns.\n\n---\n**Q1: \"Systemic Risks Arising from the Method: While conceptually novel, the proposed method makes a significant trade-off. The system functions more as a sophisticated context retriever than as a knowledge base with precise and logical representations.\"**\n- We sincerely thank the reviewer for this insightful comment. We would like to clarify that HyperGraphRAG is **not a significant trade-off** but aims to **combine both advantages** of **the structural rigor of traditional knowledge graphs** and **the contextual flexibility of RAG systems**, while **overcoming the limitations of both**. \n- On the one hand, traditional knowledge graphs, typically based on binary (head, relation, tail) triples, often fail to represent **n-ary relations** naturally. For example, a fact like  \n  *\"Drug X lowers blood pressure in elderly patients with chronic kidney disease\"*  \n  must be split into several disconnected triples, potentially losing contextual integrity.\n- On the other hand, RAG methods that retrieve raw text chunks lack an explicit structural representation and cannot model relationships between entities, leading to **redundant or semantically incoherent retrievals**.\n- **HyperGraphRAG addresses both limitations by encoding each multi-entity fact as a natural language hyperedge**, forming a **hypergraph** where nodes are entities and edges are complete n-ary semantic units. This preserves **semantic completeness** while maintaining a structured representation.\n- As shown in **Appendix B.1**, we formally prove that our hypergraph representation is both **semantically lossless and structurally grounded**. For example, a clinical statement like:\n  *\"In patients with resistant hypertension, ultrasound renal denervation reduces 24-hour BP.\"*  \n  becomes a hyperedge connecting `treatment`, `patient`, and `effect`, fully modeling the medical fact as a **3-ary connected and queryable unit**.\n- Moreover, the use of LLMs for n-ary relation extraction enables efficient and scalable construction. This approach has shown strong consistency in prior work and significantly reduces the overhead of **manual annotation**. Importantly, our system with **human-in-the-loop validation** ensures that risks associated with automated knowledge extraction can be effectively mitigated.\n- In summary, **HyperGraphRAG is not merely a “context retriever” but a semantically rich and graph-structural knowledge system**, bridging the gap between symbolic reasoning and scalable generation. We believe this novel design offers a promising direction for future retrieval-augmented systems in complex domains.\n---\n**Q2: \"Challenges in Engineering Feasibility and Scalability: The end-to-end pipeline is complex. The heavy reliance on expensive LLMs for extraction and the long, multi-stage processing chain present significant challenges to scalability.\"**\n- We thank the reviewer for raising important concerns regarding the engineering feasibility and scalability of our system. While it is true that constructing high-quality structured knowledge representations typically incurs certain complexity and computational cost, we would like to clarify several key points that demonstrate the practical viability of HyperGraphRAG.\n- Although HyperGraphRAG consists of three components: knowledge construction, structured retrieval, and generation, its pipeline design closely aligns with standard GraphRAG frameworks widely adopted in industrial settings. It follows a modular and stable structure rather than a lengthy or ad hoc multi-stage pipeline.\n- In real-world deployment, the hypergraph can be **pre-constructed**, enabling efficient and real-time querying, and supports **cache-based updates and incremental maintenance** (see **Section 4.1**), showcasing the scalability of the system.\n- As shown in **Section 5.7**, we provide a detailed cost and time analysis for both construction and inference phases. The results show that HyperGraphRAG delivers stronger performance while keeping the overall engineering cost within a practical and acceptable range. Its cost profile is **superior to most graph-based systems (e.g., GraphRAG, LightRAG)** and **comparable to StandardRAG**, indicating that the system is resource-efficient and scalable.\n- Concretely, as shown in **Table 3**, constructing a knowledge base from 1,000 tokens of text costs only **\\$0.0063** using HyperGraphRAG. This implies that for a 1 million-token corpus, the total construction cost would be approximately **\\$6.30** only. Furthermore, for the inference phase, answering **1,000 queries** only costs **\\$3.184**. We believe these costs are acceptable for real-world applications, especially in high-stakes, knowledge-intensive domains such as **medicine and law**, where HyperGraphRAG offers substantial improvements in knowledge quality, generation accuracy, and reliability.\n- In summary, HyperGraphRAG is carefully designed with scalability and real-world deployment in mind. It offers a strong balance between construction cost, runtime efficiency, and deployment flexibility, and does not pose a fundamental scalability bottleneck. \n---\n**Q3: \"Limitations in Representational Capabilities: It struggles to model the complex logical relationships (e.g., causality, dependency, conditionality) that often connect these events in domains like law or science. This limits its applicability for tasks requiring deep, multi-step reasoning.\"**\n- We sincerely thank the reviewer for this insightful comment. We fully agree that capturing complex logical relationships and supporting multi-step reasoning are crucial, especially in domains like law and science. Below, we clarify our design choices and the representational potential of HyperGraphRAG.\n- **First**, HyperGraphRAG is designed to enhance **structural expressiveness** and **semantic integrity**. Unlike binary knowledge graphs that encode relations as fixed triples (e.g., (A, causes, B)), we adopt **semantic hyperedges** expressed in natural language. This allows us to capture rich, high-order logic like:\n  - *\"Excessive sodium intake increases blood pressure in hypertensive patients.\"* → causal + conditional.\n  - *\"The contract is void if either party breaches the agreement.\"* → dependency + conditionality.\n  - *\"If a gene is mutated, it may lead to protein dysfunction and cause disease.\"* → causal chain with nested conditions.\n- These semantic hyperedges enable **flexible representation of causality, dependency, and conditionality** across multiple entities within a single edge—capabilities that binary graphs typically struggle to achieve without complex multi-hop construction.\n- **Second**, we acknowledge that this paper focuses on **single-hop retrieval**, aligned with prior works such as GraphRAG and LightRAG, to **isolate and evaluate the expressiveness and efficiency** of the hypergraph representation itself (see Figure 6). We intentionally exclude complex multi-step reasoning components to avoid confounding effects.\n- That said, **HyperGraphRAG is fully compatible with advanced reasoning mechanisms** such as:\n  - Chain-of-Thought prompting over structured knowledge,\n  - Path-based traversal or agent-style step-wise interaction,\n  - Reinforcement Learning, which we discuss as future work in Appendix I.\n- As demonstrated in **Section 5.6**, hypergraph retrieval is **more efficient** than binary graphs and can resolve certain multi-hop logical chains in a **single-hop**, thanks to n-ary modeling.\n- In conclusion, this work aims to establish **hypergraphs as a stronger foundation** for structured knowledge in LLMs. While we begin with single-hop evaluation, we believe the **semantic flexibility and multi-entity capacity of hyperedges make HyperGraphRAG inherently well-suited** for modeling complex logical relationships and future multi-step reasoning integration.\n---\n**Q4: \"Absence of Knowledge Discovery Capabilities: The framework's definition of knowledge is confined to explicit statements within the source text, missing a key value proposition of traditional knowledge graphs: data mining and insight discovery.\"**\n- We thank the reviewer for this valuable point. We clarify that HyperGraphRAG is designed for **Graph-enhanced Retrieval-Augmented Generation (GraphRAG)**—a task fundamentally different from traditional **knowledge discovery** such as link prediction or rule mining.\n- HyperGraphRAG focuses on organizing **explicit textual knowledge** into structured, n-ary hypergraphs to enhance retrieval and generation accuracy. This is especially important in domains like **medicine and law**, where reliability and traceability outweigh speculative insight.\n- For example:\n  - A **knowledge discovery task** might infer:  \n    *\"Drug A may treat Disease B based on similar patterns.\"*\n  - HyperGraphRAG retrieves a **verifiable source**:  \n    *\"Clinical trial X shows Drug A reduces blood pressure in resistant hypertension.\"*\n- While we agree that knowledge discovery is valuable, it often introduces **uncertainty**—a risk we deliberately avoid in high-stakes settings. Instead, our goal is to improve grounding and reduce hallucination by **faithfully structuring existing knowledge**, such as **pre-existing official clinical guidelines by medical experts** or **private user-collected knowledge**. Then, LLM can be used as a reliable QA system based on structured knowledge.\n- Thus, while our task does not target implicit discovery, it **maximizes retrieval quality over explicit knowledge**—a distinct yet equally important goal.\n---\nAt last, we sincerely appreciate your valuable feedback, and we will carefully consider all your suggestions to further improve our paper. We would be deeply grateful if you could kindly reconsider raising the score to 4 or above. Thank you very much!"}, {"review_id": "Br8wuJNVQ9", "reviewer": "Reviewer_LzEy", "summary": "This paper introduces HyperGraphRAG, a retrieval-augmented generation (RAG) framework that represents domain knowledge using hypergraphs to capture complex, n-ary relationships between entities. \nHyperGraphRAG consists of a three-stage pipeline: knowledge hypergraph construction, retrieval, and generation. First, it uses a large language model (LLM) to perform n-ary relation extraction from source documents, creating hyperedges that connect multiple entities. This hypergraph is then stored as a bipartite graph for efficient querying and vector embeddings are created for semantic retrieval. The retrieval strategy involves extracting entities from a user's question, searching for relevant entities and hyperedges, and then expanding the retrieved set to include related facts from the hypergraph. Finally, a hypergraph-guided generation mechanism fuses these structured n-ary facts with traditional chunk-based passages to produce the final answer. \nThe authors evaluate HyperGraphRAG on datasets from several domains and compare it against naive generation, standard RAG, and several graph-based RAG baselines. The results show that HyperGraphRAG consistently outperforms these methods in terms of answer accuracy (F1 score), retrieval similarity (R-S), and generation evaluation (G-E).", "questions": "Q1: Following W1, do you ever try to evaluate the method on existing QA datasets such as those used by HippoRAG2? How does HyperGraphRAG compare against other graph-based RAG methods on their datasets?\n\nQ2:  The results in Table 2 show that the graph-based baselines consistently underperform the simpler StandardRAG method. This is a counter-intuitive finding. Could you provide more detail on the implementation and hyperparameter tuning for these baselines to ensure fair comparison and to help the reader understand why these methods failed to show an advantage in this setting?", "limitations": "No, the authors have not adequately addressed the limitations of their work.\n- Potential for Evaluation Bias: The authors should acknowledge that generating evaluation questions from the knowledge graph's own facts may create a benchmark that favors graph-centric methods. Discussing this potential bias and its effect on the reported performance gains would provide important context.", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "S1: The paper introduces a novel and intuitive approach by using hypergraphs to represent n-ary relations in knowledge sources, addressing a key limitation of previous GraphRAG methods that are restricted to binary relations. This allows for a more complete and expressive representation of complex, real-world knowledge.\n\nS2: The authors performed extensive and rigorous evaluation to show the advantage of the proposed method, evaluating on datasets from multi-domains and comparing against baselines of different methodologies. They also validates the architectural choices through a systematic ablation study, which helps understand the contribution of each component.\n\nS3: The paper is well presented and the source codes are open sourced, which helps reproduction of the proposed method and experiment results.\n\nW1: The evaluation benchmark is constructed by first sampling knowledge facts from the documents and then using an LLM to generate corresponding question-answer pairs. This synthetic generation process may create questions that are too neatly aligned with the structure of the knowledge graph, potentially favoring methods that are designed to traverse these explicit structures. \n\nW2:  The competing graph-based RAG methods consistently underperform the StandardRAG baseline, which might suggest that the implementations or hyperparameters used for these baselines were not fully optimized, or the datasets are construct in the favor of the proposed method.", "was_revised": true, "final_justification": "The authors have provided detailed and thoughtful responses for my concerns regarding the biased dataset and potential unfairness in comparison with the baselines. As such, I have updated my final rating to accept.", "rebuttal": "Thank you very much for your time and effort in reviewing our paper. We sincerely appreciate your feedback. Below, we respectfully provide our detailed responses to address your concerns.\n\n---\n**W1: \"The evaluation benchmark may create questions that are too neatly aligned with the structure of the knowledge graph.\"**\n- We appreciate the reviewer’s thoughtful observation. Indeed, **a key limitation in prior works** such as *LightRAG* and *PathRAG* lies in the evaluation protocol itself: they typically rely on prompting LLMs to compare outputs in a pairwise format. We also tried this **AB-testing setup but observed that it can produce biased results**, especially when generations are of similar quality. For instance, GPT tends to prefer the first response in the prompt, regardless of actual content quality, making the evaluation unstable and sensitive to formatting order.\n- To address these concerns, we use the same knowledge construction settings but a different evaluation for accuracy and generation quality. **Our benchmark is not constructed based on any pre-existing knowledge graph**, nor does it assume or enforce alignment with the hypergraph structure used by HyperGraphRAG. Instead, we adopt a fully automatic, model-agnostic construction process inspired by *FlashRAG* to ensure objectivity and neutrality in evaluation.\n- Concretely, take a two-hop QA as an example, the process involves:  \n  1. Randomly sampling a knowledge sentence from the domain-specific corpus.  \n  2. Using NER to extract entities from this sentence.  \n  3. Selecting one entity and finding another sentence that contains it.  \n  4. Feeding both sentences into an LLM to generate a multi-hop question and a corresponding golden answer.\n- This ensures that **questions are grounded in real domain knowledge**, but not artificially aligned to favor any retrieval strategy. **HyperGraphRAG outperforms other baselines because its hyperedges not only model knowledge involving multiple related entities, but also significantly reduce semantic loss.** At the same time, **its hypergraph structure captures complex relationships between entities, which boosts retrieval efficiency**. We provide detailed theoretical proofs in **Appendix B.3**.\n- Finally, our evaluation protocol includes **three complementary metrics**:  \n  - **Answer F1** to measure factual correctness.  \n  - **Retrieval similarity** to assess grounding.  \n  - **LLM-as-a-judge scoring** over coherence, relevance, and faithfulness.\n- Together, these components ensure a **comprehensive and unbiased evaluation**, and we believe they better reflect the performance of retrieval-augmented generation systems in practical settings. We thank the reviewer again for encouraging us to clarify this important point.\n---\n**W2: \"The competing graph-based RAG methods consistently underperform the StandardRAG baseline, which might suggest that the implementations or hyperparameters used for these baselines were not fully optimized.\"**\n- We thank the reviewer for raising this important point. To ensure **fair comparison**, we implemented all competing methods based on the **official LightRAG codebase**, which provides an excellent GraphRAG framework. Our implementations **retain nearly all original hyperparameters and configurations** from LightRAG for HyperGraphRAG and baselines, so as to ensure consistency across methods. We also **release the full implementation details and baseline configurations in Appendix G, Table 4**, to support fairness.\n- Regarding the observation that graph-based RAG methods underperform StandardRAG, this is a **newly well-discussed insight** also discussed in several recent works. As several studies have noted, binary-relation-based GraphRAG methods may not always outperform chunk-based RAG under fair evaluations, especially on tasks that require rich semantic grounding. Because they often suffer from semantic loss, where **the decomposition of multi-entity facts into pairwise triples leads to substantial information loss**.\n- This is precisely where **HyperGraphRAG provides an advantage**: by modeling n-ary relations as natural language hyperedges, it preserves semantic completeness while still supporting structured graph-based retrieval. This **overcomes the expressive limitations of traditional GraphRAG** and demonstrates greater potential in domains that demand both relational accuracy and retrieval efficiency.\n---\n**Q1: \"Following W1, do you ever try to evaluate the method on existing QA datasets such as those used by HippoRAG2?\"**\n- We thank the reviewer for this insightful question. While our main paper focuses on domain-specific knowledge-intensive scenarios, we have conducted a **follow-up experiment** on six general-domain QA datasets adopted in **HippoRAG2**, including 2Wiki, HotpotQA, Musique, NQ, PopQA, and TriviaQA.\n\n| Method            | 2Wiki. F1 | 2Wiki. G-E | HotpotQA F1 | HotpotQA G-E | Musique F1 | Musique G-E | NQ F1  | NQ G-E | PopQA F1 | PopQA G-E | TriviaQA F1 | TriviaQA G-E | Avg. F1 | Avg. R-S | Avg. G-E |\n|------------------|-----------|------------|-------------|--------------|------------|--------------|--------|--------|----------|-----------|--------------|----------------|---------|----------|-----------|\n| GraphRAG         | 16.02     | 72.81      | 31.67       | 77.37        | 15.14      | 74.43        | 20.31  | 82.36  | 20.58    | 65.74     | 45.13        | 82.76          | 24.87   | 32.48    | 75.94     |\n| LightRAG         | 16.59     | 71.94      | 30.70       | 73.42        | 14.39      | 73.75        | 19.09  | 80.20  | 20.77    | 63.67     | 40.18        | 81.60          | 23.57   | 47.42    | 74.78     |\n| PathRAG          | 12.42     | 67.19      | 23.12       | 71.81        | 11.49      | 69.94        | 20.10  | 81.99  | 15.65    | 60.57     | 37.44        | 80.94          | 20.02   | 46.71    | 72.08     |\n| HippoRAG2        | 16.27     | 68.78      | 31.78       | 76.43        | 12.37      | 73.05        | **24.56** | **84.65** | 21.10    | 70.05     | **46.86**    | 83.55          | 25.49   | 36.41    | 74.96     |\n| **HyperGraphRAG**| **21.14** | **76.76**  | **37.46**   | **80.50**    | **20.40**  | **79.29**    | 22.95  | 81.22  | **29.48**| **70.85** | 44.95        | **85.20**       | **29.40** | **61.82** | **78.92** |\n- As shown in the table below, **HyperGraphRAG usually outperforms other graph-based RAG baselines** across most datasets and metrics. This validates its general retrieval and generation capabilities.\n- However, we note that these datasets may **lack high-order relations or structured n-ary knowledge**, which are key to the hypergraph paradigm. For this reason, they were not included in the main paper, as they do not fully reflect the design motivation of HyperGraphRAG. Nonetheless, we believe this additional evidence demonstrates the broader potential of our approach.\n---\n**Q2: \"Could you provide more detail on the implementation and hyperparameter tuning for these baselines to ensure fair comparison?\"**\n- We thank the reviewer for pointing this out. To ensure rigorous and fair comparison, we strictly followed the LightRAG open-source implementation and preserved the original hyperparameters and retrieval modules for all baselines. Our evaluation adopts a unified configuration across all methods as summarized below:\n\n| Method             | Retrieval Type            | Top-k Units | Parallel Cores | Generation Model |\n|--------------------|---------------------------|-------------|----------------|------------------|\n| NaiveGeneration    | None                      | –           | 16             | GPT-4o-mini      |\n| StandardRAG        | Chunk                     | 6 chunks    | 16             | GPT-4o-mini      |\n| GraphRAG           | Entity → Community        | 60          | 16             | GPT-4o-mini      |\n| LightRAG           | Entity + Relation         | 60          | 16             | GPT-4o-mini      |\n| PathRAG            | Graph Path                | 60          | 16             | GPT-4o-mini      |\n| HippoRAG2          | PageRank over Graph       | 60          | 16             | GPT-4o-mini      |\n| **HyperGraphRAG**  | **Entity + Hyperedge**    | **60**      | **16**         | **GPT-4o-mini**  |\n\n- To ensure fair comparison during answer generation, we observed that GraphRAG and similar graph methods are highly sensitive to prompt formatting. To eliminate such confounding factors, we use the same generation prompt for all methods, as shown below:\n\n```str\n---Role---\nYou are a helpful assistant responding to questions based on given knowledge.\n\n---Knowledge---\n{d['knowledge']}\n\n---Goal---\nAnswer the given question.\nYou must first conduct reasoning inside <think>...</think>.\nWhen you have the final answer, you can output the answer inside <answer>...</answer>.\n\nOutput format for answer:\n<think>\n...\n</think>\n<answer>\n...\n</answer>\n\n---Question---\n{d['question']}\n```\n- This unified prompt encourages consistent zero-shot CoT reasoning and avoids format-induced performance differences.\n\n- Why Some GraphRAG Baselines Underperform?\n    - Despite fair implementation and tuning, binary-relation-based GraphRAG baselines often suffer from semantic loss during knowledge encoding. Each edge in a binary graph only captures limited pairwise relations, which can fragment original facts and introduce ambiguity or redundancy during retrieval.\n    - In contrast, HyperGraphRAG encodes n-ary relations as natural-language hyperedges, preserving full semantic granularity. This leads to better alignment between retrieval and generation, resulting in more faithful and context-complete answers. We also provide theoretical proof in **Appendix B.3**.\n---\nAt last, we sincerely appreciate your valuable feedback, and we will carefully consider all your suggestions to further improve our paper. We would be deeply grateful if you could kindly reconsider raising the score further. Thank you very much!"}, {"review_id": "8k43EwkEG2", "reviewer": "Reviewer_tp2y", "summary": "This paper explores the problem of retrieval augmented generation with hypergraphs. Different from vanilla RAG methods, which mainly focus on chunk-based retrieval, in this work, the author proposes to construct hypergraphs based on the knowledge sources and conduct retrieval on such structured knowledge. The retrieved sub-hypergraphs are adopted to augment the generation for question answering. To be specific, the author proposes a pipeline for knowledge hypergraph construction, hypergraph retrieval, and hypergraph-guided generation. Experiments are conducted on several domains, where hypergraphRAG demonstrates its effectiveness and efficiency.", "questions": "See the weakness section above.", "limitations": "NA", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strength\n- The paper is very well written and easy to follow.\n- The idea of constructing a hypergraph and augmenting the LLM with such structured knowledge makes sense.\n- Experiments are conducted to demonstrate the effectiveness and efficiency of the proposed method.\n\nWeakness\n- The main concerns lie in the evaluation setup. It seems to me that the knowledge sources from each domain are just several documents, and this is quite different to real-world scenarios.\n- It is questionable whether the method can be generalized to scenarios where we have a much bigger knowledge source (e.g., wikipedia), and there may also be efficiency problems if we would like to construct a hypergraph from a big corpus.\n- Since the question samples are constructed by the author themselves and there is no clear explanation for this process, I would challenge if the question construction itself benefits the hypergraphRAG and thus leading to better performance comparing with baseline methods.\n- Some technique details are not well explained: (1) It is unclear how v^{score} in line 145 and e^{score}_H in line 153 are calculated. (2) It is questionable how the similarity calculation between two vectors of different dimensions (h_{V_q} and h_v) is performed in line 143.", "was_revised": true, "final_justification": "My concern about the evaluation dataset still exists. Thus, I will keep my score.", "rebuttal": "Thank you very much for your time and effort in reviewing our paper. We sincerely appreciate your feedback. Below, we respectfully provide our detailed responses to address your concerns.\n\n---\n**Q1: \"The main concerns lie in the evaluation setup. It seems to me that the knowledge sources from each domain are just several documents, and this is quite different to real-world scenarios.\"**\n- We sincerely thank the reviewer for highlighting this important concern regarding the evaluation setup. We would like to clarify and justify our choice of knowledge sources and their scale as follows.\n- First, to ensure fair comparison with existing GraphRAG baselines, we adopt **the same knowledge construction settings used in LightRAG and PathRAG**, both of which are based on domain-specific corpora derived from the UltraDomain benchmark. These corpora each contain over 1 million tokens, covering technical content across diverse verticals, and are widely regarded as a reasonable approximation of structured domain knowledge for research purposes.\n- Second, **to better reflect real-world deployment scenarios**, we additionally introduce an application-level medical dataset. **In collaboration with medical experts specializing in hypertension, we constructed a new Medicine benchmark using official clinical guidelines as the sole knowledge source.** This ensures that the retrieval and generation processes closely simulate real-world use in high-stakes settings, and the resulting setup has been positively validated **by our professional clinical partners**.\n- Furthermore, our system is designed to be highly accessible in practical usage. Users can easily input their own knowledge in plain text, and HyperGraphRAG automatically constructs a hypergraph representation for enhanced retrieval and generation. This makes it a practical solution for building personal knowledge bases or LLM-powered QA systems that leverage structured knowledge without manual annotation or ontology design.\n- Together, these choices strike a balance between experimental comparability and realistic applicability, and we hope this clarification addresses the reviewer’s concern.\n---\n**Q2: \"It is questionable whether the method can be generalized to scenarios where we have a much bigger knowledge source (e.g., wikipedia), and there may also be efficiency problems if we would like to construct a hypergraph from a big corpus.\"**\n- We appreciate the reviewer’s concern regarding the scalability of HyperGraphRAG to large-scale knowledge sources. To address this, we provide quantitative evidence and clarify the design philosophy of our system.\n\n| Method           | Time (s)   | Cost (USD) |\n|------------------|------------|------------|\n| GraphRAG         | 9.272      | $0.0096    |\n| LightRAG         | 5.168      | $0.0081    |\n| HippoRAG2        | 2.758      | $0.0056    |\n| **HyperGraphRAG**| **3.084**  | **$0.0063**|\n- As shown in **Table 3**, constructing a hypergraph from 1,000 tokens takes 3.084 seconds and costs $0.0063 for HyperGraphRAG. This is significantly faster than GraphRAG (9.272 s) and LightRAG (5.168 s), and comparable to HippoRAG2 (2.758 s). These results indicate that the construction efficiency of HyperGraphRAG is already **on par with or even more efficient than existing structured GraphRAG baselines under the same settings**.\n- It is also important to note that our construction process is fully preprocess and supports incremental updates and cache reuse. This ensures that once constructed, the knowledge base can be efficiently maintained and scaled without repeated cost, and further **allows knowledge to continuously accumulate and be refined over time**, offering long-term value in real-world deployment.\n- Moreover, to further address large-scale use cases, we acknowledge that lighter and faster alternatives can be used. For example, **combining NER and semantic chunking with small models can enable efficient**, zero-cost hypergraph construction without relying on LLM inference. This lightweight method is enabled by **the inherent advantages of the hypergraph representation** and represents a promising direction for future work.\n- In summary, HyperGraphRAG achieves a practical balance between expressiveness and construction efficiency. It matches or exceeds the scalability of existing binary relational GraphRAG methods and offers extensibility to both high-fidelity and lightweight settings.\n---\n**Q3: \"Since the question samples are constructed by the author themselves and there is no clear explanation for this process, I would challenge if the question construction itself benefits the hypergraphRAG and thus leading to better performance comparing with baseline methods.\"**\n- We thank the reviewer for the insightful concern regarding the fairness of question construction. To ensure a rigorous and balanced evaluation, we tried to follow the common setups established in **LightRAG** and **PathRAG**, which evaluate generation quality by prompting GPT-based models to rank different outputs in a pairwise comparison.\n- However, we observed a key limitation in such AB-test-based evaluation: when two generations are close in quality, the choice of LLM becomes unstable, and the result heavily depends on the order in which the outputs are presented in the prompt for comparison. In practice, we found that GPT often favors the first response, even when the second one is equally or more accurate. This issue undermines evaluation fairness, especially when comparing strong baselines.\n- To address this, we adopted a more principled evaluation setup inspired by **FlashRAG**, which ensures both automatic generation and objective supervision. Specifically, take a two-hop question, we:\n1. First randomly sample a knowledge sentence from the knowledge context.\n2. Then apply NER to extract all entities from this sentence.\n3. One entity is randomly selected, and then another sentence in the knowledge context containing this entity is retrieved.\n4. These two sentences jointly form the knowledge context of this sample, from which an LLM generates both a question and a golden answer.\n- This process is model-agnostic and automatic, ensuring **no bias toward HyperGraphRAG**, and faithfully reflects the structure of multi-hop questions grounded in real-world domain knowledge. Why does HyperGraphRAG outperform other baselines? We attribute this to several key factors: **HyperGraphRAG’s hyperedges not only model knowledge involving multiple related entities, but also significantly reduce semantic loss.** At the same time, **its hypergraph structure captures complex relationships between entities, which boosts retrieval efficiency**. We provide detailed theoretical proofs in **Appendix B.3**.\n- In addition, to ensure a comprehensive and fair comparison, we evaluate each method across **three complementary dimensions**:\n1. **Answer F1 score** with respect to golden answers.\n2. **Retrieval quality** based on semantic similarity with relevant ground-truth sentences.\n3. **Score-based generation assessment by LLM-as-a-Judge** over multiple axes such as faithfulness, coherence, and relevance.\n- The example shown in **Figure 8** is a case generated by this standardized protocol with question, knowledge context, and golden answer:\n```json\n{\n  \"question\": \"What type of renal denervation has been shown to demonstrate BP-lowering efficacy over 24 hours in several randomized, sham-controlled trials, particularly for resistant hypertension?\",\n  \"golden_answers\": [\n    \"ULTRASOUND RENAL DENERVATION\"\n  ],\n  \"context\": [\n    \"Several randomized, sham-controlled trials have been published, demonstrating a BP-lowering efficacy over 24h.\",\n    \"As discussed in Section 8.6.1, several randomized, sham-controlled trials have been published, demonstrating a BP-lowering efficacy over 24h for radiofrequency and ultrasound renal denervation in a broad spectrum of hypertension, including resistant hypertension.\"\n  ],\n  \"nary\": 3,\n  \"nhop\": 2\n}\n```\n---\n**Q4: \"Some technique details are not well explained: (1) It is unclear how v^{score} in line 145 and e^{score}H in line 153 are calculated. (2) It is questionable how the similarity calculation between two vectors of different dimensions (h{V_q} and h_v) is performed in line 143.\"**\n- We thank the reviewer for the detailed and constructive feedback. We address both concerns below:\n1. **Clarification of \\( v^{\\text{score}} \\) and \\( e_H^{\\text{score}} \\)**:  \n   As described in **Section 4.1**, both scores are generated by the LLM during the entity and relation extraction stage. Specifically, the LLM outputs a confidence score for each extracted entity \\( v \\) and hyperedge \\( e_H \\), which we denote as \\( v^{\\text{score}} \\) and \\( e_H^{\\text{score}} \\). These scores represent the model’s confidence in the extracted components. An example of this LLM output, including such scores, is shown in **Figure 3**.\n2. **Similarity between \\( h_{V_q} \\) and \\( h_v \\)**:  \n   The query vector \\( h_{V_q} \\) is obtained by concatenating all extracted entity mentions into a single string, then encoding it with a retriever encoder. Each entity \\( v \\) in the entity vector base is similarly stored as a single string and encoded using the same encoder. As a result, both \\( h_{V_q} \\) and \\( h_v \\) reside in the same vector space and have identical dimensions, making the similarity calculation valid.\n- We will update the manuscript to clarify these implementation details and prevent further ambiguity. Thank you again for pointing out these important aspects.\n---\nAt last, we sincerely appreciate your valuable feedback, and we will carefully consider all your suggestions to further improve our paper. We would be deeply grateful if you could kindly reconsider raising the score to 4 or above. Thank you very much!"}]

Author rebuttal:

Meta-review: HyperGraphRAG introduces a novel hypergraph-based RAG framework that effectively models n-ary relations, addressing the semantic limitations of prior GraphRAG methods. The paper is technically solid, well-written, and thoroughly evaluated across multiple domains and metrics, with reproducible code and additional experiments on general-domain QA datasets supporting its generality. While one reviewer raised minor concerns about evaluation realism, the author provided clarifications and unbiased, multi-metric evaluation.
Decision: Accept (poster)