Graph-Based Retrieval Augmented Generation

Large Language Models (LLMs) have advanced rapidly, but their limitations in structured and multi-hop reasoning underscore the need for graph-native, synergistic artificial intelligence (AI) systems. Graph-structured data underpins critical applications across social, biological, financial, transportation, web, and knowledge domains, making it essential to understand how LLMs can leverage graph computation for grounded, context-rich inference. Three complementary synergies are emerging: LLMs augmented with graph computation for retrieval and reasoning; bidirectional integration between LLMs and knowledge graphs (KGs), where LLMs support KG construction and curation while KGs enforce semantic constraints and factual consistency; and AI agents strengthened by graph algorithms for planning, decision making, and multi-step reasoning. In parallel, LLMs introduce new capabilities for graph data management and graph machine learning (ML) through natural language interfaces and hybrid LLM-graph neural network (GNN) pipelines. This tutorial synthesizes the algorithms, systems, and design principles driving these converging directions, offering data science and data mining researchers a unified perspective on integrating LLMs, graph data management, graph mining, graph ML, and agentic computation into next-generation graph-native AI systems.

Generating novel, feasible, and high-quality research ideas is an important yet challenging task in scientific discovery. Recent Large Language Model (LLM)-based methods often ground idea generation with retrieved literature, but the retrieved evidence is usually provided as flat text, such as titles, abstracts, or summaries. Such flat contexts may contain redundant or weakly relevant information, while making cross-paper relations among problems, methods, mechanisms, and findings difficult to identify and trace. To address this challenge, we propose Graph2Idea, a knowledge graph-guided framework for retrieval-augmented scientific idea generation.Graph2Idea first retrieves papers according to the input topic, transforms them into structured knowledge triples, and dynamically constructs a target-centered knowledge graph to make literature relations explicit. It then extracts compact graph-derived contexts that retain target-relevant relational evidence while reducing noisy textual input. Based on these contexts, a two-stage generation process first identifies promising research directions and then guides the LLM to synthesize candidate ideas from graph-grounded evidence. Experiments on a scientific idea generation benchmark show that Graph2Idea outperforms representative baselines under the automatic evaluation protocol. Compared with the strongest baseline scores, it improves Novelty from 0.45 to 0.52, Quality from 0.24 to 0.29, and Feasibility from 0.22 to 0.28. These results suggest that graph-structured evidence helps LLMs generate research ideas through more explicit, compact, and traceable recombination of prior scientific knowledge.

Collaborative filtering and graph-based recommendation models are highly effective because they leverage observed user interactions, but this dependence creates a fundamental cold-start challenge when newly added content has no interaction history. In Tubi's production retrieval system, this challenge is further constrained by the serving interface: new content must be assigned a standalone embedding immediately, and the model must also produce device embeddings suitable for approximate nearest-neighbor retrieval. We address this setting by formulating cold-start recommendation as an inductive graph-completion problem on a temporal bipartite device-content graph. We propose Shallow-RHS, an asymmetric link-prediction architecture in which the left-hand side (LHS) device tower leverages temporally valid watch-history message passing to capture collaborative signals, while the right-hand side (RHS) content tower is intentionally shallow with respect to the graph and encodes content solely from intrinsic features. The RHS tower does not use ID-based embeddings, content-side subgraphs, neighbor aggregation, or interaction-derived representations, forcing the content encoder to map intrinsic features into a collaborative-filtering-aware embedding space. After training, the learned content encoder generates embeddings for both warm and newly ingested content, enabling implicit graph completion through retrieval of warm surrogate neighbors. We further extend the same representation-completion principle to device cold-start by constructing cohort-based embeddings from demographic features. Large-scale online experiments demonstrate consistent relative improvements in content cold-start engagement, promotion speed, impression acquisition, and device cold-start engagement.

Retrieval-Augmented Generation (RAG) fails systematically on queries requiring structural reasoning over interconnected entities. We compare eight retrieval architectures for aerospace supply chain intelligence, progressing from text retrieval through graph traversal to graph computation. Using a 46-node knowledge graph with 64 typed edges, we evaluate 23 queries across 10 intent categories and demonstrate that five query classes are structurally unreachable for vector retrieval. Our central finding is the operator vocabulary thesis: the barrier to LLM-based graph reasoning is not model intelligence but the computational operators available as tools. An LLM Query Planner with 9 typed traversal primitives outperforms bespoke handlers (F1 = 0.632 vs. 0.472) while generalizing to unseen queries. Adding 6 graph computation tools, the LLM selectively adopts them for exactly the query categories where traversal fails. We also identify a measurement gap: entity-level F1 systematically underscores structural queries where comprehensive answers are correct.

Graph foundation models (GFMs) emerged as a dominant paradigm in graph representation learning by leveraging large-scale pre-training for cross-domain inference. However, the parameterized knowledge encoded within these models is insufficient to cope with distribution shifts, limiting their generalization ability. To mitigate this issue, retrieval-augmented generation (RAG) has been introduced to incorporate external knowledge at inference time. Nevertheless, existing RAG frameworks operating in Euclidean space suffer from a fundamental geometric limitation: the polynomial volume growth of Euclidean space is inherently mismatched with the tree-structured external knowledge bases. This mismatch leads to the loss of semantic granularity in retrieval and gives rise to the hubness phenomenon.To address this limitation, we propose a Hyperbolic Retrieval-Augmented Generation (HyRAG) framework designed to enhance the generalization capabilities of GFMs. Specifically, the introduced Hyperbolic Knowledge Indexing module retains the tree-like hierarchies of the external knowledge base by modeling them within hyperbolic space. The Multi-granularity Retrieval module then provides GFMs with the global semantic anchors and local semantic nuances through coarse-grained and fine-grained knowledge retrieval, respectively. Finally, the Dual-path Fusion module achieves effective knowledge integration for graph tasks at both the feature and structural levels. Experiments on multiple graph benchmarks demonstrate significant improvements in the zero-shot setting, highlighting the generalization of our method for robust GFMs inference.

Document-grounded dialogue systems (DGDS) utilize knowledge from external documents to answer domain-specific user questions. Existing solutions typically divide documents into independent passages for retrieval and response generation. This approach, however, neither makes good use of structural information within documents nor provides enough (document) context for knowledge selection and responses. This paper proposes SF-Re2G to address such issues systematically. Firstly, we seek to improve a passage representation by contrasting it with others of the same section, thus improving the retrieval performance. Secondly, a structure-enhanced reranker is built, leveraging the fact that multiple grounding passages of one dialog turn tend to be in the same neighborhood. Specifically, candidates from the retrieval are grouped into subgraphs according to the document structure. The reranker will rescore the candidate integrating its group information. Finally, the chosen passages are used for responses, taking into account the subgraph context for better generation. Experimental results on two DGDS datasets validate our method for both Chinese and English.

Evaluating large language models (LLMs) across comprehensive benchmarks is expensive and time-consuming. We propose a graph-based prompt selection framework that models each benchmark as a similarity graph -- nodes are prompts connected if their embedding-space distance falls above a configurable threshold -- and applies Maximum Independent Set (MIS) algorithms to select a maximally diverse, non-redundant subset. We evaluate four MIS solvers (CPLEX, GREEDY, Online-MIS, ReduMIS) across six embedding models, three distance measures, six percentile thresholds, and four benchmarks (GPQA, IFEval, MMLU-Pro, Omni-MATH) covering 66 LLMs. Our central hypothesis -- that repeated selection under different random seeds yields consistent LLM rankings that may also differ from the full-benchmark baseline -- is strongly confirmed: Kendall's $W \geq 0.90$ in 99.2% of stochastic configurations (mean $W = 0.997 \pm 0.008$), while at higher percentile thresholds selected subsets achieve 25--48% prompt reduction on average. Ranking divergence from the full benchmark ($ρ< 0.95$) occurs in only 15.95% of configurations, concentrated at low thresholds ($p_{10}$--$p_{20}$) and benchmarks (GPQA, IFEval), identifying overly dense graphs as the primary failure mode.

Systematic characterization of drug-disease relationships is essential for drug discovery and repurposing, yet is hindered by the heterogeneity and rapid growth of biomedical literature. Existing datasets rely on labor-intensive curation and are often incomplete, while LLM-only approaches suffer from hallucination and weak evidence grounding. We introduce UniD$^3$, a unified framework that integrates Large Language Models with Knowledge Graph-enhanced Retrieval-Augmented Generation (KG-RAG) to extract, organize, and validate drug-disease knowledge across Drug-Disease Matching (DDM), Drug Effectiveness Assessment (DEA), and Drug-Target Analysis (DTA). UniD$^3$ processes 157,849 PubMed articles with Llama 3.3-70B and constructs knowledge graphs via a dual-stage strategy combining paper-level extraction with KG-level consolidation centered on drug and disease entities. These graphs support KG-RAG-based generation of structured datasets, evaluated through external benchmarks, fuzzy matching with curated resources, and clinician review. UniD$^3$ produces six knowledge graphs and large-scale datasets, including 28,915 DDM, 15,042 DEA, and over 4,000 DTA QA pairs. External validation shows strong performance (F1: 0.85-0.87 for DDM/DEA; 0.82 for DTA), with clinician review confirming high reliability (AUROC = 0.90). KG-RAG-augmented models outperform standalone LLMs, and the UniD$^3$ chatbot enables interpretable, citation-supported exploration of drug-disease relationships. UniD$^3$ provides a scalable, extensible framework for transforming unstructured biomedical literature into high-quality, structured drug-disease knowledge, supporting AI-driven discovery, repurposing, and precision medicine.

Retrieval-Augmented Generation (RAG) has become an essential method for mitigating hallucinations in Large Language Models (LLMs) by leveraging external knowledge. Although effective for simple queries, traditional RAG struggles with large-scale, unstructured corpora where information is highly fragmented. Graph-based RAG (GraphRAG) incorporates knowledge graphs to capture structural relationships, enabling more comprehensive retrieval for complex reasoning. However, existing GraphRAG methods rely on isolated, fragment-level extraction for graph construction, lacking a global perspective on the whole corpus. As a result, these methods frequently lead to thematically inconsistent, logically conflicting, and structurally fragmented graphs that degrade retrieval performance. In this paper, we propose MemGraphRAG, a novel framework that introduces a memory-based multi-agent system to ensure high-quality graph construction. Specifically, MemGraphRAG employs a collaborative society of agents supported by shared memory, which provides a unified global context throughout the extraction process. This mechanism allows agents to dynamically resolve logical conflicts and maintain structural connectivity throughout the corpus. Furthermore, we propose a memory-aware hierarchical retrieval algorithm tailored for the constructed graph. Extensive experiments on multiple benchmarks demonstrate that MemGraphRAG outperforms the state-of-the-art baseline models with comparable efficiency. Our code is available at https://github.com/XMUDeepLIT/MemGraphRAG.

Retrieval-augmented generation is intensively studied to ground large language models on external evidence. However, retrieving from a unified knowledge base could inevitably introduce irrelevant information that may mislead generation for complex reasoning. Inspired by the conditional computation of mixture of experts (MoE), where a router sparsely selects specialized experts alongside shared ones for each input, we propose \textbf{M}ixture \textbf{o}f experts for \textbf{G}raph-based Retrieval-Augmented Generation, i.e., \textbf{MoG}. It organizes knowledge into two core components: (i) diverse, always-accessible hub graphs that encode semantically and structurally central knowledge and provide contextual clues for expert activation, and (ii) sparsely activated expert graphs that contain domain-specific evidence. MoG first accesses hub graphs to identify general evidence and derive contextual clues. Then, a topology-aware router dynamically activates a limited set of expert graphs conditioned on the query, thereby confining retrieval to a focused evidence subspace. Extensive experiments on challenging benchmarks show that MoG consistently outperforms strong baselines, with over 20% relative improvement on MuSiQue. Our code is available in https://github.com/DEEP-PolyU/MoG.

Drug synergy prediction (DSP) aims to identify efficacious drug combinations under various cellular contexts with different targets. However, the continual emergence of novel compounds results in variations in molecular scaffolds and sizes, causing drug synergy data to exhibit out-of-distribution (O.O.D.) shifts with respect to topological structure. Existing works rely on in-distribution (I.D.) assumption, failing to handle the O.O.D. shifts. To solve this problem, we study out-of-distribution generalized drug synergy prediction through a graph large language model for the first time. Nevertheless, O.O.D. generalized DSP is highly non-trivial, posing several challenges: i) how to discover structurally relevant and irrelevant molecular representations with respect to cell targets; ii) how to find the optimal graph neural architectures that accurately calculate molecular representations; and iii) how to jointly leverage molecular structural and semantic information in LLMs. To address these challenges, we propose OOD-GraphLLM, a novel graphLLM framework which is able to accurately predict drug synergy under O.O.D. settings via jointly optimizing molecular graph representation and biomedical semantic language representations in a unified manner. Furthermore, we finetune DrugSyn-LLM, a biomedical LLM, and employ a retrieval-augmented biomedical instruction tuning strategy to align molecular topological information and molecular semantic information with language-based reasoning for O.O.D. generalized DSP. Both the source code (https://github.com/EkkoXiao/Bio-GraphLLM) and released model (https://mn.cs.tsinghua.edu.cn/bio-graphllm/) are publicly available, where users are allowed to download model resources and interactively use the system through a web interface.

Semi-structured knowledge bases (SKBs) embed textual documents in a typed graph of entities and relations, and underpin applications such as product search, academic paper search, and precision-medicine inquiries. Existing hybrid retrieval systems on SKBs either use the graph only for query expansion, mix textual and structural branches under a global weighting, or rely on fine-tuned graph-traversal generators. We present GRASP, a three-stage SKB retrieval framework unifying plan-based graph retrieval, plan-conditioned fusion with a dense retriever, and a fine-tuned reranker over the fused candidates. GRASP substantially advances the state of the art on every metric across the three STaRK benchmarks, lifting average Hit@1 from 62.0 to 73.9. Ablation and sensitivity studies further confirm the effectiveness and robustness of GRASP.

Retrieval-Augmented Generation (RAG) enhances LLMs by grounding generation in query-relevant external evidence. Beyond unstructured text corpora, Graph RAG integrates knowledge graphs into the retrieval pipeline, enabling LLMs to access entities, relations, and multi-hop dependencies encoded in structured knowledge. However, the same structured knowledge that empowers Graph RAG also creates a new privacy attack surface. We demonstrate that Graph RAG systems can be turned into structural oracles: through adaptive black-box interactions, an adversary can elicit sufficient relational evidence to reconstruct substantial portions of the hidden knowledge graph. We propose a structure-oriented reconstruction framework that recovers targeted graphs from both local and global perspectives. Specifically, Depth-Wise Heuristic Search extracts fine-grained node attributes by recursively expanding entity-centered evidence, while Breadth-Wise Diffusion Search infers graph topology by propagating across relation-induced neighborhoods. Experiments on generic and healthcare scenarios demonstrate that our method can recover over 90% of the original knowledge graph from representative Graph RAG systems, revealing sensitive entities, relations, and structural dependencies with high fidelity. Existing guradrails provide limited defense against our attack, highlighting the inherent difficulty of safeguarding structural privacy in Graph RAG pipelines.

Methods to represent literary texts as graphs or sequences of graphs mainly focus on representing character interactions, and often overlook another crucial aspect: the textual context in which characters interact. We introduce Dynamic Heterogeneous Character Networks (DHCNs), which organize long novels into temporally localized heterogeneous graphs that align characters with their textual contexts. We extract around 20,000 DHCNs from Project Gutenberg, and propose GraphLit, a self-supervised learning framework that learns rich literary representations through a masked graph autoencoder objective. Across a wide range of 12 character-related tasks, GraphLit improves over text-only, graph-only and prior hybrid baselines. Ablations over different kinds of dynamic graph structures and architectural elements show that grounding characters in their context is the main performance driver, while explicitly encoding narrative order and character relationships provide task-dependent improvements. Finally, we demonstrate the applicability of DHCNs and GraphLit for literary analysis by studying the link between narrative non-linearity and dynamic social features.

Graph-based Retrieval-Augmented Generation (GraphRAG) advances flat document retrieval by structuring knowledge as relational graphs, enabling more coherent and effective reasoning. However, applying it to specific domains like legal reasoning faces critical challenges. (i) Legal corpora are heterogeneous, containing multi-granular knowledge from cases, articles and interpretations. A flat knowledge graph cannot adequately differentiate between factual details, applied rules, and abstract principles, limiting accurate retrieval. (ii) Reliable legal judgment demands transparent, evidence-based reasoning. Traditional RAG passes retrieved context directly to an LLM without verification, resulting in opaque, error-prone reasoning. To this end, we propose LegalGraphRAG, a framework designed for reliable legal reasoning. Our approach introduces two core components: a hierarchical legal graph that hierarchically organizes legal sources to enable retrieval at appropriate abstraction levels, and a multi-agent system for reliable legal reasoning, where a Researcher retrieves candidate evidence, an Auditor rigorously verifies its validity against source documents, and an Adjudicator synthesizes the set of verified evidence to render a final judgment. Extensive experiments show that LegalGraphRAG achieves the state-of-the-art performance, outperforming existing GraphRAG baselines in accurate and trustworthy legal analysis. Our code, datasets and implementation details are available at https://github.com/XMUDeepLIT/LegalGraphRAG.

GraphRAG extends retrieval-augmented generation by organizing corpora as explicit knowledge graphs, enabling graph-based retrieval for complex question answering. However, existing frameworks extract entities and relations within individual chunks, leaving cross-chunk relations -- those whose evidence spans multiple passages -- systematically absent from the index. Exhaustive LLM-based recovery of such relations is impractical due to the combinatorial explosion of chunk combinations. We present CrossAug, a GNN-guided CROSS-Chunk Graph AUGmentation method that enriches GraphRAG indices with cross-chunk relational structure as an offline step before query-time retrieval. CrossAug derives training supervision through self-supervised graph corruption, uses a topology-aware GNN to score subgraphs for missingness, and applies evidence-grounded LLM completion only to selected high-scoring regions. Experiments on three LLM-based GraphRAG frameworks across four multi-hop and long-document QA benchmarks demonstrate that CrossAug consistently improves performance, confirming the benefit of cross-chunk graph augmentation for retrieval-based question answering. Our code is available at https://github.com/DonFinliani/CrossAug.

Scientific diagrams are essential for communicating complex methodologies in academic papers. A natural way for researchers to specify such diagrams is through rough sketches, where text labels, connectors, and spatial arrangements express early semantic and topological intentions. However, sketches are usually incomplete, making them insufficient for directly producing publication-quality diagrams. Existing sketch-based generation methods mainly reconstruct the sketch itself, while recent text-driven diagram generation frameworks rely on textual semantics and do not fully exploit the topological structure contained in sketches. In this paper, we introduce DiagramRAG, a lightweight retrieval-augmented framework for sketch-based scientific diagram completion. Given a user sketch, DiagramRAG retrieves reference diagrams that are both semantically relevant to the sketch content and topologically compatible with its structure, and uses them to guide downstream diagram generation. To enable efficient structure-aware retrieval, we represent diagrams as knowledge graphs, synthesize sketch variants at different simplification levels, and train an embedding model to align sketches with compatible diagrams in a shared space. The retrieved references further provide content, topology, and visual priors for completing and rendering the final diagram. Experiments show that DiagramRAG achieves F1-scores of 0.848 and 0.802 on DiagramBank and FigureBench, respectively, and improves generation quality with the best VLM-as-a-Judge score of 7.170, while reducing inference latency to 35.48 seconds per sample. Our code and data are available at https://anonymous.4open.science/r/DiagramRAG-A262 and https://huggingface.co/datasets/anonymous-review-a262/DiagramSketch.

Large Language Models (LLMs) have been widely adopted in conversational applications. However, their reliance on parametric knowledge limits reliability in real-world scenarios that require dynamic or domain-specific information. Retrieval-Augmented Generation (RAG) addresses this limitation by incorporating external knowledge during generation, but existing text-based and graph-based RAG methods often struggle with noisy or irrelevant contexts. In this work, we propose Structure-aware Retrieval Augmented Generation (SA-RAG), which uses tables as an intermediate structured representation to provide a compact and controllable interface that reduces noise while preserving essential information. We introduce a quality-aware table metadata generation framework that models metadata normalization and effectiveness, improving metadata quality and downstream performance. Furthermore, we explore both training-free and training-based table generation methods. Generation validation and direct preference optimization further improve table quality while maintaining semantic and structural consistency. Experiments on two noisy real-world datasets show that SA-RAG significantly outperforms existing RAG baselines. Our code is publicly available at a public repository.

Knowledge graphs (KGs) offer a rich representation for relational knowledge, but their irregular structure makes retrieval challenging: ego-graph expansion grows rapidly, and dense embedding methods struggle with multi-hop compositional queries. Existing agent-based graph exploration approaches, while expressive, are often too expensive for large-scale retrieval. We introduce SeedER (Seed-and-Expand Retrieval), a retrieval framework that explicitly leverages KG structure through iterative, low-cost expansion. SeedER first seeds a compact set of core nodes using lightweight dense and entity-based retrieval, then selectively expands this set via a learned graph-aware policy trained with reinforcement learning. This design decomposes global reasoning into reusable local decisions, enabling efficient discovery of query-relevant nodes while tightly controlling expansion cost. We show theoretical limitations of dense retrieval on compositional graph queries, and establish advantages of SeedER from both compositional generalization and graph-constrained submodular optimization perspectives. Empirically, SeedER substantially improves recall with compact candidate sets over strong dense and graph-augmented baselines, making it an effective first-stage retriever for knowledge-intensive reasoning systems.

GraphRAG conditions language models on subgraphs retrieved from knowledge graphs, encoded via message-passing GNNs. Because these encoders entangle node contributions through iterated neighborhood aggregation, there is no closed-form way to determine how much each retrieved entity influenced the encoder's output, and therefore no way to faithfully audit what structural evidence actually reached the model. We introduce Ex-GraphRAG, which replaces the GNN encoder with a Multivariate Graph Neural Additive Network (M-GNAN), an extension of additive graph models to high-dimensional embedding spaces that yields an exact decomposition of the encoder's output across individual nodes and feature groups, without post-hoc approximation. On STaRK-Prime, this auditable encoder matches black-box performance. Using it to audit evidence routing, we uncover a semantic-structural mismatch: the nodes that dominate the encoder's output are structurally disconnected in the retrieved subgraph, held together by low-attribution intermediaries whose removal degrades multi-hop QA by up to 28%. This mismatch, invisible to any opaque encoder, reveals that semantic importance and structural connectivity are governed by disjoint sets of nodes, with direct implications for retrieval pruning, context construction, and failure diagnosis in graph-augmented LLMs.

Graph-based Retrieval Augmented Generation (GraphRAG) extends retrieval-augmented generation to support structured reasoning over complex corpora, but its reliability under resource-constrained, privacy-sensitive deployments remains unclear. In healthcare, where Electronic Health Record (EHR) data is complex and strictly regulated, reliance on cloud-based large language models (LLMs) introduces challenges in cost, latency, and compliance. In this work, we present a systematic evaluation of GraphRAG for EHR schema retrieval using locally deployed open-source LLMs. We implement the Microsoft GraphRAG pipeline on real-world EHR schema documentation and benchmark four models, including Llama 3.1 (8B), Mistral (7B), Qwen 2.5 (7B), and Phi-4-mini (3.8B), each deployed via Ollama on a single consumer GPU (8 GB VRAM). We evaluate indexing efficiency, knowledge graph construction, query latency, answer quality, and hallucination under both global and local retrieval modes. Our results reveal substantial differences: Llama 3.1 produces the richest knowledge graph (1,172 entities), Qwen 2.5 achieves the best answer quality (3.3/5), Phi-4-mini fails to complete the pipeline due to structured-output errors, and Mistral exhibits degenerate repetition behavior. We further show that GraphRAG exhibits a practical capacity threshold, where models below approximately 7B parameters fail to reliably produce valid structured outputs and cannot complete the pipeline. In addition, indexing and answer quality are decoupled across models, and local retrieval consistently outperforms global summarization in both latency and factual grounding, with reduced hallucination. These findings demonstrate that GraphRAG is feasible on consumer hardware while highlighting the importance of model selection and retrieval design for robust deployment in regulated settings.

Retrieval-Augmented Generation (RAG) has become foundational for grounding large language models in domain-specific corpora, yet conventional vector-based RAG systems are fundamentally limited in their ability to capture the structured, multi-entity relationships that underpin financial market analysis. This paper presents a comprehensive comparative study of a novel two-hop Graph-RAG architecture versus a standard vector-only baseline for cross-entity financial sentiment analysis. Our system constructs a sentiment-weighted knowledge graph of 59 equity entities from 255 news articles covering 10 major technology stocks, then augments dense retrieval with intensity-filtered graph traversal over INFLUENCES edges to surface relational evidence inaccessible to vector search alone. We evaluate both architectures on 100 grounded queries (30 Direct, 70 Relational) using semantic similarity, entity recall, RAGAS metrics, latency benchmarks, and ablation studies. Graph-RAG achieves a statistically significant improvement in entity recall (+6.4%, p < 0.001, Wilcoxon signed-rank) and delivers substantially more relevant answers for complex multi-entity queries (+11.7% Answer Relevancy), with gains concentrating in relational question types (+16.1%). Critically, these improvements come at no measurable cost to answer quality (delta = +0.001 semantic similarity, Cohen's d = 0.078), with a modest 22.6% increase in mean latency offset by an 80% reduction in latency variance. An ablation study on the graph traversal intensity threshold reveals an inverted-U relationship with answer quality, identifying tau = 0.5 as optimal over the production default of tau = 0.7. These findings characterize a precision-for-coverage trade-off inherent to graph-augmented retrieval and provide actionable architectural guidance for practitioners building RAG systems for multi-entity financial analysis.

Graph-structured retrieval-augmented generation (RAG) systems can improve answer quality on multi-hop questions, but many current systems rely on large language models (LLMs) to extract entities, relations, and summaries during indexing. These calls add token and wall-clock costs that grow with corpus size. We present ContextRAG, a graph RAG system whose graph topology is constructed without LLM-based entity or relation extraction. ContextRAG derives a fuzzy concept graph over chunk embeddings using residual-quantization k-means and Formal Concept Analysis with Lukasiewicz residuated logic. Bridge-like and meet-derived context nodes are induced by soft fuzzy join and meet operations, rather than by LLM-written graph edges. On a 130-task UltraDomain subset, ContextRAG builds its index with 30 LLM calls and 22,073 tokens. In contrast, a local HiRAG reproduction stress test required 870 indexing calls and 3.54M tokens on a 20-task subset before failing during graph construction; linear extrapolation to 130 tasks implies over 23M indexing tokens. ContextRAG obtains 33.6% F1 overall and 36.8% F1 on multi-hop tasks. An activation analysis shows that queries retrieving at least one lattice-derived node in the top five achieve +3.9 percentage points F1 over queries that do not; this association is diagnostic rather than causal.

Retrieval-Augmented Generation can improve factuality by grounding answers in external evidence, but Agentic GraphRAG complicates what it means for citations to be faithful. In these systems, an agent explores a knowledge graph before producing an answer and a small set of citations. We frame citation faithfulness as a trajectory-level problem: final citations should not only support the answer, but also account for the graph traversal, structure, and visited-but-uncited entities that may influence it. Through controlled ablation experiments, we compare the effects of isolating, removing, and masking cited and uncited graph entities. Our results show that cited evidence is often necessary, as removing it substantially changes answers and reduces accuracy. However, citations are not sufficient, because accurate answers can also depend on uncited traversal context and surrounding graph structure. These findings suggest that citation evaluation in Agentic GraphRAG should move beyond source support toward provenance over the broader retrieval trajectory.

Wide applications of LLM-based agents require strong alignment with human social values. However, current works still exhibit deficiencies in self-cognition and dilemma decision, as well as self-emotions. To remedy this, we propose a novel value-based framework that employs GraphRAG to convert principles into value-based instructions and steer the agent to behave as expected by retrieving the suitable instruction upon a specific conversation context. To evaluate the ratio of expected behaviors, we define the expected behaviors from two famous theories, Maslow's Hierarchy of Needs and Plutchik's Wheel of Emotion. By experimenting with our method on the benchmark of DAILYDILEMMAS, our method exhibits significant performance gains compared to prompt-based baselines, including ECoT, Plan-and-Solve, and Metacognitive prompting. Our method provides a basis for the emergence of self-emotion in AI systems.

We introduce PersonalAI 2.0 (PAI-2), a novel framework designed to enhance LLM-based systems through integration of external knowledge graphs (KGs). The proposed approach addresses key limitations of existing Graph Retrieval-Augmented Generation (GraphRAG) methods by incorporating a dynamic, multistage query-processing pipeline. The central point of the PAI-2 design is its ability to perform adaptive, iterative information search, guided by extracted entities, matched graph vertices, and generated clue-queries. An evaluation conducted on five benchmarks (Natural Questions, TriviaQA, HotpotQA, 2WikiMultihopQA, and MuSiQue) demonstrates an improvement in the factual correctness of generated answers compared to analogue methods (LightRAG, RAPTOR, HippoRAG 2, and PAI-1). PAI-2 achieves a 9% average gain by LLM-as-a-Judge on the 2WikiMultihopQA and MuSiQue benchmarks, and attains accuracy comparable to HippoRAG 2 on the TriviaQA and HotpotQA benchmarks, reflecting its effectiveness in reducing hallucination rates and increasing precision. We show that enabled search plan enhancement mechanism gain 18% boost compared to disabled one by LLM-as-a-Judge across five benchmarks. In addition, an ablation study reveals that PAI-2 achieves SOTA result on the MINE-1 benchmark, obtaining an 89% information-retention score with LLMs in the 7--15B tiers. Collectively, these findings underscore the potential of PAI-2 to serve as a reusable component for personalized AI applications, which require scalable, context-aware knowledge-representation and reasoning capabilities. The source code of PAI-2 is available at the following link: https://github.com/Dzigen/PersonalAI.

Long-term memory is becoming a central bottleneck for language agents. Exsting RAG and GraphRAG systems largely treat memory graphs as static retrieval middleware, which limits their ability to recover complete evidence chains from partial cues, exploit reusable graph-structrual roles, and improve the memory itself through downstream feedback. We introduce SAGE, a Self-evolving Agentic Graph-memory Engine that models graph memory as a dynamic long-term memory substrate. SAGE couples two roles: a memory writer that incrementally constucts structured graph memory from interaction histories, and a Graph Foundation Model-based memory reader to perform retrieval and provide feedback to the memory writer. We provide rigorooous theoretical annalyses supporting the framework. Across multi-hop QA, open-domain retireval, domain-specific review QA, and long-term agent-memory benchmarks, SAGE improves evidence recovery, answer grounding, and retrieval efficiency: after two self-evolution rounds, it achieves the best average rank on multi-hop QA; in zero-shot open-domain transfer, it reaches 82.5/91.6 Recall@2/5 on NQ. Further results on LongMemEval and HaluMem show that traning and reader-writer feedback improve multiple long-term memory and hallucination-diagnostic metrics, suggesting that self-evolving, structure-aware graph memory is a promising foundation for robust long-horizon language agents.

Using Large Language Models (LLMs) to process graph-structured data is an active research area, yet current state-of-the-art approaches typically rely on multi-step pipelines with Graph Neural Network (GNN) encoders that compress rich textual attributes into solitary tokens, creating a significant semantic bottleneck. In this paper, we introduce the Graph Transformer Language Model (GTLM), a novel architecture that enables pretrained LLMs to natively process graph topologies while entirely eliminating this compressive bottleneck. GTLM is exceptionally parameter-efficient: by injecting graph-aware attention biases directly into the LLM's attention modules, it introduces only 0.015% additional parameters relative to the base model. We theoretically prove that our bidirectional attention prefix preserves node permutation equivariance while maintaining exact backward compatibility with the pretrained base model. Extensive evaluations demonstrate that a 1B-parameter GTLM matches or exceeds the performance of 7B-parameter state-of-the-art models on standard Text-Attributed Graph benchmarks, while significantly surpassing baselines on GraphQA. Finally, we demonstrate that GTLM attention heads implicitly learn to simulate message passing, explaining its superior performance on algorithmic tasks. This paradigm shift enables true algorithmic reasoning within LLMs and provides a scalable foundation for next-generation GraphRAG and relational deep learning.

Repository-level coding agents must first localize the files and symbols relevant to a task; failures at this stage can cascade across downstream objectives ranging from patch generation to test writing and codebase question answering. Existing agents navigate repositories primarily through lexical search, often missing structural relations such as imports, call chains, type hierarchies, and code-test links. Graph-based retrieval can recover such dependencies, but existing approaches often require separate graph tools or traversal stages that fragment the agent's interaction loop. We formalize repository context localization as Lexically Anchored Structural Localization, where success depends on turning lexical matches into high-precision structural entry points and exposing the most useful confidence-filtered local neighborhoods within the agent's existing search loop. We introduce LARGER (Lexically Anchored Repository Graph Exploration and Retrieval), a lexically anchored active-set retrieval framework that starts from lexical matches, aligns them to graph anchors, and performs confidence-filtered local expansion within the agent's existing search loop. LARGER integrates directly into existing CLI coding agents without requiring external graph databases or specialized graph interfaces. Across four benchmarks spanning localization, test generation, and codebase understanding, LARGER improves file-level Acc@5 on LocBench by +13.9 points with tuned hyperparameters and still gains +11.8 points with fixed hyperparameters over the strongest baseline, while delivering consistent gains on MuLocBench, SWE-Atlas Test Writing, and SWE-Atlas Codebase QA.

Zero-shot single-cell cell-type annotation aims to determine a cell's type from a given set of expressed genes without any training. Existing knowledge-graph-based RAG approaches retrieve evidence by expanding from source entities and relying on iterative LLM reasoning. However, in this setting each query contains tens to hundreds of genes, where no single gene is decisive and the label emerges only from their collective co-occurrence. Such hyper-entity queries fundamentally challenge local, entity-wise exploration strategies, which reason from individual genes, leading to poor scalability and substantial LLM cost. We propose GATHER (Graph-Aware Traversal with Hyper-Entity Retrieval), a convergence-centric retriever tailored to hyper-entity queries. It performs global multi-source graph traversal and identifies topological convergence points -- nodes jointly reachable from many input genes. These convergence nodes act as high-information hyper-entities that capture entity synergy. By incorporating node- and path-importance scoring, GATHER selects informative evidence entirely without LLM involvement during retrieval. Instantiated on a self-constructed cell-centric biological knowledge graph (VCKG), GATHER outperforms strong KG-RAG baselines (ToG, ToG-2, RoG, PoG) on two datasets (Immune and Lung), achieving the highest exact-match accuracy (27.45% and 59.64%) with only a single LLM call per sample, compared to 2--61 calls for KG-RAG baselines. Our results demonstrate that convergence nodes compress multi-entity signals into compact, high-information evidence that conveys more per item than multi-hop paths, providing an efficient global alternative to local entity-wise reasoning.

Retrieval-Augmented Generation (RAG) has become a core paradigm for enhancing factual grounding and multi-hop reasoning in Large Language Models (LLMs). Traditional text-based RAG often retrieves logically irrelevant pseudo-evidence, while graph-based RAG is frequently hindered by search-time pruning, which may discard potentially valid reasoning paths. Existing hybrid approaches primarily adopt simple evidence concatenation or unidirectional enhancement, which fails to address the fundamental "Information Island" problem caused by asymmetric reasoning flows between unstructured text and structured graphs. We propose \textbf{TGS-RAG}, a unified framework for \textbf{T}ext-\textbf{G}raph \textbf{S}ynergistic enhancement. TGS-RAG introduces a bidirectional mechanism: (i) a \textbf{Graph-to-Text} channel that employs a Global Voting strategy from visited graph nodes to re-rank and refine textual evidence, filtering out semantic noise; and (ii) a \textbf{Text-to-Graph} channel that utilizes the \textbf{Memory-based Orphan Entity Bridging} algorithm. This algorithm utilizes textual cues to proactively resurrect valid but previously pruned reasoning paths from the search history without additional database overhead. Experimental results on multiple multi-hop reasoning benchmarks demonstrate that TGS-RAG significantly outperforms state-of-the-art baselines, achieving a superior balance between retrieval precision and computational efficiency.

Graph-based Retrieval-Augmented Generation (GraphRAG) extends traditional RAG by using knowledge graphs (KGs) to give large language models (LLMs) a structured, semantically coherent context, yielding more grounded answers. However, GraphRAG reasoning process remains a black-box, limiting our ability to understand how specific pieces of structured knowledge influence the final output. Existing explainability (XAI) methods for RAG systems, designed for text-based retrieval, are limited to interpreting an LLM response through the relational structures among knowledge components, creating a critical gap in transparency and trustworthiness. To address this, we introduce XGRAG, a novel framework that generates causally grounded explanations for GraphRAG systems by employing graph-based perturbation strategies, to quantify the contribution of individual graph components on the model answer. We conduct extensive experiments comparing XGRAG against RAG-Ex, an XAI baseline for standard RAG, and evaluate its robustness across various question types, narrative structures and LLMs. Our results demonstrate a 14.81% improvement in explanation quality over the baseline RAG-Ex across NarrativeQA, FairyTaleQA, and TriviaQA, evaluated by F1-score measuring alignment between generated explanations and original answers. Furthermore, XGRAG explanations exhibit a strong correlation with graph centrality measures, validating its ability to capture graph structure. XGRAG provides a scalable and generalizable approach towards trustworthy AI through transparent, graph-based explanations that enhance the interpretability of RAG systems.

Knowledge Graph-based Question Answering (KGQA) plays a pivotal role in complex reasoning tasks but remains constrained by two persistent challenges: the structural heterogeneity of Knowledge Graphs(KGs) often leads to semantic mismatch during retrieval, while existing reasoning path retrieval methods lack a global structural perspective. To address these issues, we propose Structure-Tracing Evidence Mining (STEM), a novel framework that reframes multi-hop reasoning as a schema-guided graph search task. First, we design a Semantic-to-Structural Projection pipeline that leverages KG structural priors to decompose queries into atomic relational assertions and construct an adaptive query schema graph. Subsequently, we execute globally-aware node anchoring and subgraph retrieval to obtain the final evidence reasoning graph from KG. To more effectively integrate global structural information during the graph construction process, we design a Triple-Dependent GNN (Triple-GNN) to generate a Global Guidance Subgraph (Guidance Graph) that guides the construction. STEM significantly improves both the accuracy and evidence completeness of multi-hop reasoning graph retrieval, and achieves State-of-the-Art performance on multiple multi-hop benchmarks.

Large language model assistants are increasingly expected to retain and reason over information accumulated across many sessions. We introduce EngramaBench, a benchmark for long-term conversational memory built around five personas, one hundred multi-session conversations, and one hundred fifty queries spanning factual recall, cross-space integration, temporal reasoning, adversarial abstention, and emergent synthesis. We evaluate Engrama, a graph-structured memory system, against GPT-4o full-context prompting and Mem0, an open-source vector-retrieval memory system. All three use the same answering model (GPT-4o), isolating the effect of memory architecture. GPT-4o full-context achieves the highest composite score (0.6186), while Engrama scores 0.5367 globally but is the only system to score higher than full-context prompting on cross-space reasoning (0.6532 vs. 0.6291, n=30). Mem0 is cheapest but substantially weaker (0.4809). Ablations reveal that the components driving Engrama's cross-space advantage trade off against global composite score, exposing a systems-level tension between structured memory specialization and aggregate optimization.

Graph-based Retrieval-Augmented Generation (RAG) systems leverage interconnected knowledge structures to capture complex relationships that flat retrieval struggles with, enabling multi-hop reasoning. Yet most existing graph-based methods suffer from (i) heuristic designs lacking theoretical guarantees for subgraph quality or relevance and/or (ii) the use of static exploration strategies that ignore the query's holistic meaning, retrieving neighborhoods or communities regardless of intent. We propose Query-Aware Flow Diffusion RAG (QAFD-RAG), a training-free framework that dynamically adapts graph traversal to each query's holistic semantics. The central innovation is query-aware traversal: during graph exploration, edges are dynamically weighted by how well their endpoints align with the query's embedding, guiding flow along semantically relevant paths while avoiding structurally connected but irrelevant regions. These query-specific reasoning subgraphs enable the first statistical guarantees for query-aware graph retrieval, showing that QAFD-RAG recovers relevant subgraphs with high probability under mild signal-to-noise conditions. The algorithm converges exponentially fast, with complexity scaling with the retrieved subgraph size rather than the full graph. Experiments on question answering and text-to-SQL tasks demonstrate consistent improvements over state-of-the-art graph-based RAG methods.

As the world of agentic artificial intelligence applied to robotics evolves, the need for agents capable of building and retrieving memories and observations efficiently is increasing. Robots operating in complex environments must build memory structures to enable useful human-robot interactions by leveraging the mnemonic representation of the current operating context. People interacting with robots may expect the embodied agent to provide information about locations, events, or objects, which requires the agent to provide precise answers within human-like inference times to be perceived as responsive. We propose the Embodied Light Graph Retrieval Agent (EmbodiedLGR-Agent), a visual-language model (VLM)-driven agent architecture that constructs dense and efficient representations of robot operating environments. EmbodiedLGR-Agent directly addresses the need for an efficient memory representation of the environment by providing a hybrid building-retrieval approach built on parameter-efficient VLMs that store low-level information about objects and their positions in a semantic graph, while retaining high-level descriptions of the observed scenes with a traditional retrieval-augmented architecture. EmbodiedLGR-Agent is evaluated on the popular NaVQA dataset, achieving state-of-the-art performance in inference and querying times for embodied agents, while retaining competitive accuracy on the global task relative to the current state-of-the-art approaches. Moreover, EmbodiedLGR-Agent was successfully deployed on a physical robot, showing practical utility in real-world contexts through human-robot interaction, while running the visual-language model and the building-retrieval pipeline locally.

Graph-based Retrieval-Augmented Generation (GraphRAG) enhances LLMs by structuring corpus into graphs to facilitate multi-hop reasoning. While recent lightweight approaches reduce indexing costs by leveraging Named Entity Recognition (NER), they rely strictly on structural co-occurrence, failing to capture latent semantic connections between disjoint entities. To address this, we propose EHRAG, a lightweight RAG framework that constructs a hypergraph capturing both structure and semantic level relationships, employing a hybrid structural-semantic retrieval mechanism. Specifically, EHRAG constructs structural hyperedges based on sentence-level co-occurrence with lightweight entity extraction and semantic hyperedges by clustering entity text embeddings, ensuring the hypergraph encompasses both structural and semantic information. For retrieval, EHRAG performs a structure-semantic hybrid diffusion with topic-aware scoring and personalized pagerank (PPR) refinement to identify the top-k relevant documents. Experiments on four datasets show that EHRAG outperforms state-of-the-art baselines while maintaining linear indexing complexity and zero token consumption for construction. Code is available at https://github.com/yfsong00/EHRAG.

When does an LLM controller outperform rule-based traversal for knowledge graph exploration? We study this question through RLM-on-KG, a retrieval system that treats an LLM as an autonomous navigator over an RDF-encoded mention graph for grounded question answering. Unlike GraphRAG pipelines that rely on offline LLM indexing, RLM-on-KG performs entity-first, multi-hop exploration at query time using deterministic graph construction and a fixed tool set. Our central finding is a conditional advantage: the value of LLM control depends on evidence scatter and tool-calling sophistication. The paper's core claim is LLM control versus heuristic traversal, not a generic win over GraphRAG. On GraphRAG-Bench Novel (519 questions), Gemini 2.0 Flash achieves +2.47 pp F1 over a rule-based heuristic baseline (p < 0.0001), but only +0.16 pp over a GraphRAG-local variant (not significant). With a stronger controller, Claude Haiku 4.5, the gain over heuristic grows to +4.37 pp (p < 0.001) and extends to a +2.42 pp significant improvement over GraphRAG-local (p < 0.001). The gain is largest when gold evidence is scattered across 6-10 chunks (+3.21 pp) and smallest for concentrated evidence (+1.85 pp). Cross-scale validation on MuSiQue confirms that the LLM-over-heuristic advantage transfers, with expected attenuation on smaller per-question graphs. The core architectural insight is the separation of candidate discovery from ranking: the LLM adds value through exploration breadth, while final evidence selection is best handled by pure vector re-ranking. Beyond retrieval, exploration traces provide a proposed stress-test harness for structured data quality, yielding diagnostics for coverage, connectivity, provenance, and queryability.

Generative AI, particularly Large Language Models, increasingly integrates graph-based representations to enhance reasoning, retrieval, and structured decision-making. Despite rapid advances, there remains limited clarity regarding when, why, where, and what types of graph-LLM integrations are most appropriate across applications. This survey provides a concise, structured overview of the design choices underlying the integration of graphs with LLMs. We categorize existing methods based on their purpose (reasoning, retrieval, generation, recommendation), graph modality (knowledge graphs, scene graphs, interaction graphs, causal graphs, dependency graphs), and integration strategies (prompting, augmentation, training, or agent-based use). By mapping representative works across domains such as cybersecurity, healthcare, materials science, finance, robotics, and multimodal environments, we highlight the strengths, limitations, and best-fit scenarios for each technique. This survey aims to offer researchers a practical guide for selecting the most suitable graph-LLM approach depending on task requirements, data characteristics, and reasoning complexity.

Learned top-K search improves the accuracy-latency trade-off of graph-based vector search, but existing methods are designed for a fixed K: serving production workloads with varying K values requires preprocessing cost proportional to the number of distinct Ks served - prohibitive in practice. This paper shows that learned search can support arbitrary K with the preprocessing cost of a single top-1 model. The key idea is to reduce top-K learned search to repeated masked top-1 refinement, which works because the distance-reduction trajectory for discovering the next top-1 vector is largely invariant to the number of results already found. We therefore train the model on trajectory features that remain effective under masking. To make repeated refinement robust and efficient, OMEGA counters error accumulation across iterations with rank-wise confidence allocation, and skips unnecessary model invocations with a statistical forecast of recall from partial results. Across nine dataset-scale configurations, OMEGA meets the 0.95 recall target with one K-independent model. Under the lowest-preprocessing configuration of each learned baseline,it reduces mean latency by 7-36% versus DARTH, 3-25% versus MultiK-DARTH, and 8-21% versus LAET on BIGANN, BIGANN-1B, DEEP, and three production workloads. On GIST, Text2Image, and MS MARCO, its latency remains within 9% of DARTH and MultiK-DARTH. On production traces, OMEGA further reduces total serving and preprocessing computation by up to 28%.

Retrieval augmented generation (RAG) has enhanced large language models by enabling access to external knowledge, with graph-based RAG emerging as a powerful paradigm for structured retrieval and reasoning. However, existing graph-based methods often over-rely on entity-centric node matching and lack explicit causal modeling, leading to unfaithful or spurious answers. Prior attempts to incorporate causality are typically limited to local or single-document contexts and also suffer from information isolation that arises from modular graph structures, which hinders scalability and cross-module causal reasoning. To address these challenges, we propose CausalRAG2, a framework that rethinks knowledge organization for graph-based RAG through causal gating across hierarchical modules. CausalRAG2 explicitly models causal relationships to suppress spurious correlations while enabling scalable reasoning over large-scale knowledge graphs. We also introduce HolisQA, a benchmark for holistic comprehension beyond entity-centric matching. Extensive experiments demonstrate that CausalRAG2 consistently outperforms competitive graph-based RAG baselines across multiple datasets and evaluation metrics. Our work establishes a principled foundation for structured, scalable, and causally grounded RAG systems. Our code and HolisQA benchmark are available at https://github.com/Pwnb/CausalRAG2.

Retrieving code functions, classes or files relevant to a user query, bug report or feature request from large codebases is a fundamental challenge for Large Language Model (LLM)-based coding agents. Agentic approaches typically employ sparse methods like BM25 or dense embedding strategies to identify semantically relevant units. While dense embedding approaches can outperform BM25 by large margins, both ignore the graph-structured characteristics of the codebase. To address this, we propose SpIDER (Spatially Informed Dense Embedding Retrieval), a dense retrieval approach that integrates LLM-based reasoning with graph-based exploration of the codebase. We further introduce SpIDER-Bench, a graph-structured benchmark curated from SWEPolyBench, SWEBench-Verified and Multi-SWE-bench, spanning Python, Java, JavaScript and TypeScript repositories. SpIDER's graph-based candidate expansion attaches a structural reason for inclusion to each surfaced function (its seed and the edge type linking them), making the candidate set auditable while keeping the retrieval budget fixed. The graph is built from per-repository syntax trees, so it can be constructed on-demand at the start of a developer session rather than precomputed offline. Empirical results show that SpIDER consistently improves dense retrieval Recall@20 across every language and benchmark in SpIDER-Bench: by at least 13% relative (+0.05 to +0.12 absolute) along containment edges, rising to at least 27% relative (+0.11 to +0.19 absolute) once call edges are explored.

Retrieval-Augmented Generation (RAG) systems empower large language models (LLMs) with external knowledge, yet struggle with efficiency-accuracy trade-offs when scaling to large knowledge graphs. Existing approaches often rely on monolithic graph retrieval, incurring unnecessary latency for simple queries and fragmented reasoning for complex multi-hop questions. To address these challenges, this paper propose SPLIT-RAG, a multi-agent RAG framework that addresses these limitations with question-driven semantic graph partitioning and collaborative subgraph retrieval. The innovative framework first create Semantic Partitioning of Linked Information, then use the Type-Specialized knowledge base to achieve Multi-Agent RAG. The attribute-aware graph segmentation manages to divide knowledge graphs into semantically coherent subgraphs, ensuring subgraphs align with different query types, while lightweight LLM agents are assigned to partitioned subgraphs, and only relevant partitions are activated during retrieval, thus reduce search space while enhancing efficiency. Finally, a hierarchical merging module resolves inconsistencies across subgraph-derived answers through logical verifications. Extensive experimental validation demonstrates considerable improvements compared to existing approaches.

Novice math teachers often encounter students' mistakes that are difficult to diagnose and remediate. Misconceptions are especially challenging because teachers must explain what went wrong and how to solve them. Although many existing large language model (LLM) platforms can assist in generating instructional feedback, these LLMs loosely connect pedagogical knowledge and student mistakes, which might make the guidance less actionable for teachers. To address this gap, we propose MisEdu-RAG, a dual-hypergraph-based retrieval-augmented generation (RAG) framework that organizes pedagogical knowledge as a concept hypergraph and real student mistake cases as an instance hypergraph. Given a query, MisEdu-RAG performs a two-stage retrieval to gather connected evidence from both layers and generates a response grounded in the retrieved cases and pedagogical principles. We evaluate on \textit{MisstepMath}, a dataset of math mistakes paired with teacher solutions, as a benchmark for misconception-aware retrieval and response generation across topics and error types. Evaluation results on \textit{MisstepMath} show that, compared with baseline models, MisEdu-RAG improves token-F1 by 10.95% and yields up to 15.3% higher five-dimension response quality, with the largest gains on \textit{Diversity} and \textit{Empowerment}. To verify its applicability in practical use, we further conduct a pilot study through a questionnaire survey of 221 teachers and interviews with 6 novices. The findings suggest that MisEdu-RAG provides diagnosis results and concrete teaching moves for high-demand misconception scenarios. Overall, MisEdu-RAG demonstrates strong potential for scalable teacher training and AI-assisted instruction for misconception handling. Our code is available on GitHub: https://github.com/GEMLab-HKU/MisEdu-RAG.