Structure Over Scale: Schema-Constrained Causal Graphs for RAG

# Structure Over Scale: Schema-Constrained Causal Graphs for RAG
Source: [https://arxiv.org/html/2607.22592](https://arxiv.org/html/2607.22592)
Marc Saouda Rajprakash Bale Eren Aldis Cloves Almeida Boston Consulting Group saouda\.marc@bcg\.com bale\.rajprakash@bcg\.com aldis\.eren@bcg\.com almeida\.cloves@bcg\.com

###### Abstract

Graph\-based retrieval\-augmented generation \(GraphRAG\) grounds answers in structured knowledge, but current systems extract entities and relationships exhaustively, producing graphs whose size and construction cost scale with corpus length rather than with the reasoning a query requires\. We introduceHCG\-RAG\(Hierarchical Causal Graph RAG\), which replaces open\-ended extraction with*schema\-constrained causal graphs*: an automated pipeline distills a corpus into a fixed, typed vocabulary of causal variables and materializes a compact two\-tier graph over it\. Our schema\-constrained graphs match entity\-relation baselines on answer quality at a fraction of the cost: 3–20×\\timesfewer nodes, 8×\\times–135×\\timesfewer build\-time LLM calls than the most LLM\-intensive baseline \(MS\-GraphRAG\), and graphs compact enough for a domain expert to audit, correct, and extend\. On medical and clinical benchmarks, including a neurologist\-validated epilepsy dataset,HCG\-RAGmatches or exceeds the best entity\-relation systems\. An ablation isolates the causal graph as a*structured retrieval filter*, contributing\+\+6 percentage points \(pp\) over embedding\-only retrieval\. Across all domains with discoverable hierarchical causal structure, only methods imposing higher\-level organization outperform flat entity\-relation retrieval, indicating that*what*is placed in the graph matters more than how many nodes it contains\.

## 1Introduction

Retrieval\-augmented generation \(RAG\) grounds LLM responses in external knowledge, improving factuality and adaptability by separating knowledge access from parametric memory\(Lewiset al\.,[2020](https://arxiv.org/html/2607.22592#bib.bib5); Guuet al\.,[2020](https://arxiv.org/html/2607.22592#bib.bib8); Karpukhinet al\.,[2020](https://arxiv.org/html/2607.22592#bib.bib7); Gaoet al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib6)\)\. Modern systems retrieve passages, fuse evidence across documents, decide when to retrieve, or interleave retrieval with reasoning steps\(Izacard and Grave,[2021](https://arxiv.org/html/2607.22592#bib.bib9); Jianget al\.,[2023](https://arxiv.org/html/2607.22592#bib.bib10); Trivediet al\.,[2023](https://arxiv.org/html/2607.22592#bib.bib11); Asaiet al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib12)\)\. This is powerful but largely unstructured: a top\-kkretriever can surface relevant passages without representing how concepts, mechanisms, and outcomes depend on one another\. The Graph RAG paradigm\(Edgeet al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib2); Guoet al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib3)\)addresses this gap by extracting entity\-relation graphs from the corpus for structured, multi\-hop retrieval\. In practice, however, these systems extract entities exhaustively, producing graphs whose size scales with corpus length rather than with task\-relevant structure:MS\-GraphRAG\(Edgeet al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib2)\),LightRAG\(Guoet al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib3)\), andFast\-GraphRAG\(Circlemind AI,[2024](https://arxiv.org/html/2607.22592#bib.bib4)\)each build graphs of 4,800–5,800 nodes on GraphRAG\-Bench medical \(Table[1](https://arxiv.org/html/2607.22592#S5.T1)\)\.

The scale problem is especially visible in specialized scientific and clinical domains, where useful answers often require following mechanistic links rather than merely retrieving co\-mentioned entities\. Medical QA benchmarks and clinical LLM evaluations emphasize that correct answers often depend on interventions, patient state, and outcomes, not just topical overlap\(Palet al\.,[2022](https://arxiv.org/html/2607.22592#bib.bib26); Singhalet al\.,[2023](https://arxiv.org/html/2607.22592#bib.bib27)\)\. In such settings, a graph whose nodes are every extracted entity can be both large and weakly aligned with the reasoning variables that matter for retrieval\. A smaller graph can be preferable if its vocabulary is restricted to the causal quantities a domain expert would recognize\.

We ask whether this scale is necessary for strong retrieval\. Building on work showing that LLMs can efficiently discover causal structure\(Jiralersponget al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib23)\)and that causal graphs improve RAG retrieval\(Wanget al\.,[2025](https://arxiv.org/html/2607.22592#bib.bib24)\), we presentHCG\-RAG, a system that constructs*schema\-constrained hierarchical causal graphs*from unstructured corpora: an automated LLM\-driven pipeline produces a fixed, typed vocabulary of causal variables \(Definition[1](https://arxiv.org/html/2607.22592#Thmdefinition1)\), and two\-tier graph construction materializes graphs 3–20×\\timessmaller than entity\-relation baselines over the same corpus at 8×\\times–135×\\timesfewer build\-time LLM calls thanMS\-GraphRAG\(Appendix[L](https://arxiv.org/html/2607.22592#A12)\)\.*What*is put in the graph and how retrieval uses it shift the quality–efficiency frontier\.

We evaluate on three corpora: GraphRAG\-Bench medical \(2,062 Q\), GraphRAG\-Bench novel \(2,010 Q\), andEpilepsyQA, a 375\-question benchmark that we curate from two open\-access clinical epilepsy textbooks and validate with two board\-certified neurologists\. This design deliberately tests both the intended regime and a boundary case: medical and epilepsy corpora contain hierarchical causal structure, while literary narrative rewards broad entity and event tracking\. Schema\-guided causal construction matches the best entity\-relation baselines on structured\-knowledge corpora at a fraction of the graph size, while entity\-relation methods retain the advantage on literary narrative, where discoverable hierarchical causal structure is largely absent \(Section[5](https://arxiv.org/html/2607.22592#S5)\)\.

We make three contributions:111Code, evaluation scripts,EpilepsyQAquestions and annotations, and corpus reconstruction instructions are available at[https://anonymous\.4open\.science/r/hcg\-rag](https://anonymous.4open.science/r/hcg-rag)\.\(i\)compact, inspectable graphs at competitive quality: schema\-constrained construction produces graphs 3–20×\\timessmaller than entity\-relation GraphRAG on medical and epilepsy, small enough for a domain expert to audit and correct while matching answer quality, via a three\-stage automated pipeline whose query path is one LLM call plus two embedding calls; \(ii\)structure over scale on specialized domains: only retrieval methods that impose higher\-level organization outperform flat entity\-relation retrieval, and schema\-guided causal graphs are a lean, high\-precision instance; \(iii\)EpilepsyQA, a curated clinical epilepsy benchmark of 375 questions spanning six reasoning types, derived from two open\-access textbooks and validated by two board\-certified neurologists, released as a public resource for evaluating domain\-specialized retrieval systems \(Sections[5](https://arxiv.org/html/2607.22592#S5),[6](https://arxiv.org/html/2607.22592#S6)\)\.

## 2Related work

#### Retrieval\-augmented generation\.

Open\-domain QA and retrieval\-augmented language modeling established the basic pattern of retrieving external evidence before generation\(Karpukhinet al\.,[2020](https://arxiv.org/html/2607.22592#bib.bib7); Guuet al\.,[2020](https://arxiv.org/html/2607.22592#bib.bib8); Lewiset al\.,[2020](https://arxiv.org/html/2607.22592#bib.bib5)\)\. Subsequent work improved how retrieved text is consumed, from fusion\-in\-decoder architectures\(Izacard and Grave,[2021](https://arxiv.org/html/2607.22592#bib.bib9)\)to systems that decide when to retrieve, critique retrieved evidence, or interleave retrieval with multi\-step reasoning\(Jianget al\.,[2023](https://arxiv.org/html/2607.22592#bib.bib10); Trivediet al\.,[2023](https://arxiv.org/html/2607.22592#bib.bib11); Asaiet al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib12)\)\. These approaches treat the retrieval corpus primarily as text\.HCG\-RAGinstead builds a typed graph offline and uses it only to select evidence passages, leaving the answer LLM with textual support rather than graph triples\.

#### Graph\-based retrieval\-augmented generation\.

GraphRAG systems vary along three axes:*extraction strategy*\(unconstrained entity extraction vs\. schema\-guided construction\),*graph organization*\(flat entity\-relation graphs vs\. hierarchical structures such as community summaries or typed schemas\), and*retrieval mechanism*\(key\-value lookup, personalized PageRank, community\-level map\-reduce, or graph traversal\)\. We compareHCG\-RAGto three representative baselines that span these axes\.MS\-GraphRAG\(Edgeet al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib2)\)extracts entity\-relation triples and applies Leiden community detection with hierarchical summaries for local and global search;LightRAG\(Guoet al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib3)\)adds dual\-level key\-value retrieval over an LLM\-extracted entity\-relation graph; andFast\-GraphRAG\(Circlemind AI,[2024](https://arxiv.org/html/2607.22592#bib.bib4)\)replaces community detection with personalized PageRank\. All three share*unconstrained entity extraction*, producing large heterogeneous graphs whose structure mirrors surface\-level mentions\. Earlier graph\-and\-text QA systems also showed the value of traversing structured connections alongside passages\(Sunet al\.,[2019](https://arxiv.org/html/2607.22592#bib.bib16); Oguzet al\.,[2022](https://arxiv.org/html/2607.22592#bib.bib17)\), but typically assume a knowledge graph or learn a unified retriever over existing graph/text sources\.HCG\-RAGreplaces unconstrained entity extraction with schema\-guided causal construction, yielding graphs 3–20×\\timessmaller that nonetheless capture the causal structure needed for complex reasoning\. Relative to the current GraphRAG\-Bench leaders, our target is therefore a different operating point: fewer, typed, auditable graph nodes at comparable quality rather than the highest score under an unconstrained graph budget\.

#### Knowledge graphs and LLMs\.

Knowledge\-graph augmentation can improve LLM factuality and reasoning by injecting triples, subgraphs, or graph\-derived textual context into prompts\(Baeket al\.,[2023](https://arxiv.org/html/2607.22592#bib.bib14); Panet al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib13)\)\. Recent systems extend this idea to textual graph understanding, for example by retrieving graph context for generation\(Heet al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib15)\)\. These methods primarily ask how to use an available structured resource at inference time\. Our setting differs in two ways: the graph is constructed from unstructured corpora, and its schema is constrained before graph construction so that nodes denote typed variables rather than arbitrary entities\.

#### LLM\-based causal discovery and causal RAG\.

Classical causal discovery infers graph structure from data under statistical assumptions, while recent surveys emphasize both the promise and fragility of such methods in complex domains\(Glymouret al\.,[2019](https://arxiv.org/html/2607.22592#bib.bib21)\)\. LLMs add a different source of signal: they encode background knowledge that can support causal reasoning, but benchmarks also show that this ability is uneven and must be constrained\(Kıcımanet al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib22); Jinet al\.,[2023](https://arxiv.org/html/2607.22592#bib.bib25)\)\.Jiralersponget al\.\([2024](https://arxiv.org/html/2607.22592#bib.bib23)\)discover a causal directed acyclic graph \(DAG\) over a*predefined*variable set via breadth\-first search \(BFS\)–based querying, andWanget al\.\([2025](https://arxiv.org/html/2607.22592#bib.bib24)\)add per\-query LLM calls to trace causal paths within an entity\-relation graph built by standard extraction\.HCG\-RAGpushes causal reasoning to*construction time*: a typed causal schema \(Definition[1](https://arxiv.org/html/2607.22592#Thmdefinition1)\) discovers both variables and relationships, the fixed metric vocabulary constrains the graph to causally relevant concepts by design, and query\-time retrieval requires only embedding matching and BFS traversal \(no per\-query LLM causal reasoning\)\. The novelty is this combination of automated variable discovery, schema\-constrained causal graph construction, and evidence\-only retrieval; prior causal\-RAG systems either assume a predefined variable set or reason over causal paths at query time\.

## 3Method

### 3\.1Problem setup

We study retrieval\-augmented question answering over an unstructured corpus𝒟=\{di\}i=1n\\mathcal\{D\}=\\\{d\_\{i\}\\\}\_\{i=1\}^\{n\}in domains where answers often depend on causal mechanisms\. The system is given an*outcome configuration*𝒪\\mathcal\{O\}specifying graph roles, including terminal sink metrics \(e\.g\., “Patient Outcome”\) and retrieval outcome metrics that designate endpoint nodes for graph\-guided evidence selection\. Terminal metrics receive causal edges but emit none; nonterminal outcome metrics may still participate in upstream or downstream mechanisms, but are treated as retrieval endpoints when reached\. For a queryqq, the method constructs a graphG=\(𝒱,ℰ,ϕ\)G=\(\\mathcal\{V\},\\mathcal\{E\},\\phi\)with variable nodes𝒱\\mathcal\{V\}, directed causal edgesℰ\\mathcal\{E\}, and an evidence mapϕ:ℰ→2𝒞\\phi:\\mathcal\{E\}\\to 2^\{\\mathcal\{C\}\}that links each edge to supporting chunks from the chunk\-level partition𝒞=\{cj\}\\mathcal\{C\}=\\\{c\_\{j\}\\\}of𝒟\\mathcal\{D\}\. A retrieval policyRG​\(q\)⊆𝒞R\_\{G\}\(q\)\\subseteq\\mathcal\{C\}selects evidence fromGG, and the answer model returnsa=LLM​\(q,RG​\(q\)\)a=\\mathrm\{LLM\}\(q,R\_\{G\}\(q\)\)\. We evaluateHCG\-RAGby the joint trade\-off among answer correctness, graph compactness, and build/query cost: smaller graphs are human\-auditable and enable expert\-in\-the\-loop curation, while lower API cost widens the deployment envelope\.

HCG\-RAGconstructs hierarchical causal graphs from unstructured corpora and uses them for graph\-guided evidence retrieval at query time\. Given\(𝒟,𝒪\)\(\\mathcal\{D\},\\mathcal\{O\}\), it proceeds in three stages \(Figure[1](https://arxiv.org/html/2607.22592#S3.F1)\): automated domain\-specification generation \(§[3\.2](https://arxiv.org/html/2607.22592#S3.SS2)\), two\-tier graph build \(§[3\.3](https://arxiv.org/html/2607.22592#S3.SS3)\), and graph\-guided retrieval \(§[3\.4](https://arxiv.org/html/2607.22592#S3.SS4)\); Algorithm[1](https://arxiv.org/html/2607.22592#alg1)\(Appendix[A](https://arxiv.org/html/2607.22592#A1)\) gives the full formal specification\.

Informally, a specification organizes the domain along four concepts\.*Dimensions*are categorical axes that stratify the domain \(e\.g\., disease type, anatomical site\)\.*Metrics*are measurable or assessable quantities along those axes \(e\.g\., 5\-year survival rate\)\.*Variables*pair a metric with specific dimension entities to produce a concrete measurable quantity \(e\.g\., “efficacy of chemotherapy for NSCLC”\)\.*Seed edges*are directed causal relationships between variables, annotated with mechanism descriptions\.

###### Definition 1\(Domain Graph Specification\)\.

A domain graph specification is a tuple𝒮=\(𝒜,ℳ,𝒱0,ℛ0\)\\mathcal\{S\}=\(\\mathcal\{A\},\\mathcal\{M\},\\mathcal\{V\}\_\{0\},\\mathcal\{R\}\_\{0\}\)where:

- •𝒜=\{\(δi,Ei\)\}\\mathcal\{A\}=\\\{\(\\delta\_\{i\},E\_\{i\}\)\\\}is a set of dimensions, each a named axisδi\\delta\_\{i\}with entity setEiE\_\{i\};
- •ℳ\\mathcal\{M\}is afixedset of typed metrics, each with a dimension signaturesig⁡\(m\)⊆\{δi\}\\operatorname\{sig\}\(m\)\\subseteq\\\{\\delta\_\{i\}\\\}specifying the dimensions it binds;
- •𝒱0\\mathcal\{V\}\_\{0\}is anextensibleseed set of variables, where eachv=\(m,𝐞\)v=\(m,\\mathbf\{e\}\)pairs a metricm∈ℳm\\in\\mathcal\{M\}with a tuple of dimension entities𝐞∈∏δi∈sig⁡\(m\)Ei\\mathbf\{e\}\\in\\prod\_\{\\delta\_\{i\}\\in\\operatorname\{sig\}\(m\)\}E\_\{i\}, producing a concrete measurable quantity \(e\.g\.,v=\(mefficacy,\[chemo,NSCLC\]\)v=\(m\_\{\\text\{efficacy\}\},\[\\text\{chemo\},\\text\{NSCLC\}\]\)\);
- •ℛ0⊆𝒱0×𝒱0\\mathcal\{R\}\_\{0\}\\subseteq\\mathcal\{V\}\_\{0\}\\times\\mathcal\{V\}\_\{0\}is an extensible set of directed causal seed edges\.

Fixed sets are exhaustive: graph building must only reference defined members\. Extensible sets are exemplary: graph building expands them as corpus evidence warrants, constrained by the fixed vocabulary\.

Corpus𝒟\\mathcal\{D\}Outcome config𝒪\\mathcal\{O\}Stage 1Domain SpecDim\.MetricsVarsCausal Rels𝒮\\mathcal\{S\}DomainGraphSpecStage 2Graph BuildMetricEdgesNodeEdgesEvidenceLinkingTwo\-tier factorizationOffline \(per corpus\)G=\(𝒱,ℰ,ϕ\)G=\(\\mathcal\{V\},\\mathcal\{E\},\\phi\)Causal GraphStage 3RetrievalNodeMatchBFSEvidenceCollectQueryqqOnline \(per query\)Answeraa

Figure 1:TheHCG\-RAGpipeline\. The method takes a corpus and an outcome configuration specifying the causal sinks the graph should build toward \(e\.g\., “Patient Outcome”\)\.Stage 1generates a causal domain specification𝒮\\mathcal\{S\}via LLM\-driven generation of dimensions, metrics, variables, and causal relations, anchored by the configured outcome hierarchy\.Stage 2builds the causal graph through two\-tier edge discovery \(metric\-level templates then node\-level instantiation\) with evidence linking\.Stage 3answers queries via embedding\-based node matching, bounded BFS traversal, and evidence collection\. Stages 1–2 run offline per corpus; Stage 3 runs online per query\.Dimensionse\.g\. disease type, treatmentFIXEDEntitiese\.g\. NSCLC, chemotherapyEXT\.containMetricse\.g\. survival rate, treatment efficacyFIXEDVariablese\.g\. SurvivalRate\(NSCLC\),Efficacy\(NSCLC, chemo\)EXT\.typed bybound toCausal Relationse\.g\. Efficacy\(NSCLC, chemo\)→\\toSurvivalRate\(NSCLC\)EXT\.betweenCausalGraphGGnodesedgesfixed \(exhaustive vocabulary\)extensible \(expandable by graph build\)

Figure 2:Structure of the domain graph specification𝒮\\mathcal\{S\}\. Dimensions and metrics form afixedvocabulary \(solid borders\): graph building must use only defined types\. Entities, variables, and causal relations areextensible\(dashed borders\): the specification provides seed examples that graph building expands as corpus evidence warrants\.
### 3\.2Stage 1: Automated domain\-specification generation

Given corpus𝒟\\mathcal\{D\}, a chunk\-wise LLM pipeline produces𝒮\\mathcal\{S\}\(Definition[1](https://arxiv.org/html/2607.22592#Thmdefinition1); Figure[2](https://arxiv.org/html/2607.22592#S3.F2)\) that constrains all subsequent graph building\. Each metric is typed asFixed\(exhaustive\) orExtensible; the LLM discovers dimensions, metrics, variables, and directed causal seed edges from corpus chunks\. A deterministic assembly step drops invalid references, fuzzy\-matches relation endpoints to repair naming drift, and tags variables with their configured roles\.

### 3\.3Stage 2: Two\-tier causal graph build

RecallG=\(𝒱,ℰ,ϕ\)G=\(\\mathcal\{V\},\\mathcal\{E\},\\phi\)from Section[3\.1](https://arxiv.org/html/2607.22592#S3.SS1)\. Construction proceeds in two tiers \(Figure[3](https://arxiv.org/html/2607.22592#S3.F3)\)\.Tier 1evaluates each ordered metric pair\(ms,mt\)∈ℳ×ℳ\(m\_\{s\},m\_\{t\}\)\\in\\mathcal\{M\}\\times\\mathcal\{M\}\(terminals excluded as sources\) using evidence summaries and optional semantic search, producing metric\-level edge templatesℰm\\mathcal\{E\}\_\{m\}\.Tier 2instantiates each template between the concrete variables of its source and target metrics; the LLM evaluates each candidate edge, producing the final edge setℰ\\mathcal\{E\}with mechanism text and confidence scores\. Each edge is linked to corpus chunks via substring text matching plus semantic matching at thresholdτe=0\.78\\tau\_\{e\}\{=\}0\.78\(Appendix[B](https://arxiv.org/html/2607.22592#A2)\)\.

𝒱m1\\mathcal\{V\}\_\{m\_\{1\}\}𝒱m2\\mathcal\{V\}\_\{m\_\{2\}\}𝒱m3\\mathcal\{V\}\_\{m\_\{3\}\}Tier 1: Metric TemplatesO​\(\|ℳ\|2\)O\(\|\\mathcal\{M\}\|^\{2\}\)candidatesm1m\_\{1\}m2m\_\{2\}m3m\_\{3\}template\|ℳ\|\|\\mathcal\{M\}\|metricsinstantiateTier 2: Node EdgesO​\(\|ℰm\|⋅k¯2\)O\(\|\\mathcal\{E\}\_\{m\}\|\\cdot\\bar\{k\}^\{2\}\)candidatesv1v\_\{1\}v2v\_\{2\}v3v\_\{3\}v4v\_\{4\}v5v\_\{5\}v6v\_\{6\}v7v\_\{7\}\|𝒱\|\|\\mathcal\{V\}\|variables

Figure 3:Two\-tier edge construction\.Tier 1discovers causal templates between metric pairs \(left\)\.Tier 2instantiates each template between the concrete variables belonging to the source and target metrics \(right\)\. This factorization reduces LLM calls fromO​\(\|𝒱\|2\)O\(\|\\mathcal\{V\}\|^\{2\}\)candidate pairs toO​\(\|ℳ\|2\+\|ℰm\|⋅k¯2\)O\(\|\\mathcal\{M\}\|^\{2\}\+\|\\mathcal\{E\}\_\{m\}\|\\cdot\\bar\{k\}^\{2\}\)\(Remark[1](https://arxiv.org/html/2607.22592#Thmremark1)\)\.
### 3\.4Stage 3: Graph\-guided evidence retrieval

At query time, the graph acts as a*structured retrieval filter*\(Figure[4](https://arxiv.org/html/2607.22592#S3.F4)\) in three steps: \(1\)*per\-metric node matching*compares the query embedding to variable embeddings under a per\-metric cosine gate that caps matches per metric; \(2\) a*bounded BFS*\(hmax=4h\_\{\\max\}\{=\}4\) from the matched set traverses directed causal edges, collecting reachable nodes and connecting edges; \(3\)*outcome cones*, the reverse\-reachable sets of outcome/terminal nodes, are ranked by matched\-node convergence and merged by metric key, and the topCmax=6C\_\{\\max\}\{=\}6cones define the final context\. Evidence texts attached to traversed edges \(viaϕ\\phi\) are deduplicated and passed to the answer LLM; no graph structure, node names, or edge triples are included\. Formal definitions \(Defs\.[2](https://arxiv.org/html/2607.22592#Thmdefinition2)–[4](https://arxiv.org/html/2607.22592#Thmdefinition4)\) and default parameter values are in Appendix[A](https://arxiv.org/html/2607.22592#A1)\.

Query: “Reed\-Sternbergcells, diagnosis?”v1v\_\{1\}diagnosticmarkersv2v\_\{2\}cell morph\.v3v\_\{3\}lymphomasubtypev4v\_\{4\}diseasediagnosisv5v\_\{5\}histopath\.findingsv6v\_\{6\}v7v\_\{7\}cos≥τ\\operatorname\{cos\}\\geq\\tau“RS cells are pathog\- nomonic for Hodgkin lymphoma…”“Bimodal age dist\. with nodular sclerosis most common…”Hodgkin lymphomamatchedreachedoutcomenot reached

Figure 4:Graph\-guided evidence retrieval on a Hodgkin lymphoma query\. The query embeds and matches variable nodes \(green\)\. Bounded BFS traverses causal edges \(blue arrows\) to reach an outcome node \(double circle\)\. Evidence chunks attached to traversed edges are collected and passed to the LLM, which produces the correct diagnosis\. Grey nodes are not connected to matched nodes\.

## 4Experimental setup

### 4\.1Benchmarks

GraphRAG\-Bench:We evaluate on the Medical \(2,062 questions\) and Novel \(2,010 questions\) subsets of GraphRAG\-Bench\. Medical tests structured domain reasoning, while Novel provides a literary boundary case where entity\-relation structure differs substantially from the intended setting\. See details in Appendix[C](https://arxiv.org/html/2607.22592#A3)\.EpilepsyQA:We curate a 375\-question epilepsy benchmark from a clinical corpus derived from two open\-access textbooks\. Candidate Q–A pairs were LLM\-generated and then reviewed by two board\-certified neurologists, who corrected reference answers and removed inaccurate or off\-topic items\. All retained questions target epilepsy specifically\. The final benchmark spans six question types; see details in Appendix[C](https://arxiv.org/html/2607.22592#A3)\.

### 4\.2Baselines

All systems use the same LLM \(gpt\-5\.4\-mini\) for generation and the same embedding model \(text\-embedding\-3\-small\) for retrieval, to ensure fair comparison\.HCG\-RAGadditionally usesgpt\-5\.4\-minifor all graph\-construction steps\. The LLM\-as\-judge\(Zhenget al\.,[2023](https://arxiv.org/html/2607.22592#bib.bib30)\)is held constant across systems atGLM\-4\.7\(Z\.ai,[2025](https://arxiv.org/html/2607.22592#bib.bib31)\), accessed through a LiteLLM proxy\(BerriAI,[2023](https://arxiv.org/html/2607.22592#bib.bib32)\)fronting AWS Bedrock with multi\-region routing\. Graph baselines areMS\-GraphRAG\(Edgeet al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib2)\),LightRAG\(Guoet al\.,[2024](https://arxiv.org/html/2607.22592#bib.bib3)\), andFast\-GraphRAG\(Circlemind AI,[2024](https://arxiv.org/html/2607.22592#bib.bib4)\)\(Section[2](https://arxiv.org/html/2607.22592#S2)\)\.NaiveRAGretrieves the top\-5 chunks \(1,200 words, 200\-word overlap\) by embedding similarity without a graph\.In\-contextpasses the full corpus in the answer LLM’s context window with no retrieval\.HCG\-RAG\(ours\)is specified in Section[3](https://arxiv.org/html/2607.22592#S3); ablations appear in Section[6](https://arxiv.org/html/2607.22592#S6)\.

### 4\.3Evaluation metrics

Following GraphRAG\-Bench, we report LLM\-judge metrics per question type:Answer correctness\(weighted combination of atomic\-factF1F\_\{1\}at 0\.75 and embedding similarity at 0\.25\);ROUGE\-L\(lexical overlap with ground truth\);Coverage\(fraction of ground\-truth facts attributed\); andFaithfulness\(fraction of answer statements supported by retrieved context\)\.

### 4\.4Graph scaling tiers and reproducibility

We construct up to fourHCG\-RAGvariants per corpus by capping the specification’s metric/dimension counts: medical yields XS \(333 nodes\)/S \(902\)/M \(1,064\)/L \(1,583\), and epilepsy XS \(218\)/S \(427\)/M \(468\)/L \(624\) under the same cap sequence \(node counts differ across corpora because the same cap produces different graphs on corpora of different size and density\)\. Node counts forHCG\-RAGare typed variables; for baselines they are extracted entities, so edge counts are not directly comparable across paradigms\. All experiments use isolated per\-framework virtual environments, temperature 0, and report means±\\pmstandard deviations over five independent runs \(run 0 builds the graph; subsequent runs reuse it\)\.

## 5Results

### 5\.1Graph compactification

The Nodes column of Table[1](https://arxiv.org/html/2607.22592#S5.T1)shows the compactness gap:HCG\-RAGachieves a 3–17×\\timesnode reduction over entity\-relation baselines on medical\. The smallest tier \(XS, 333 nodes\) is∼\{\\sim\}17×\\timessmaller thanFast\-GraphRAG, and even the largest tier \(L, 1,583 nodes\) uses 3–4×\\timesfewer nodes\. Edge counts and wiring density are in Table[6](https://arxiv.org/html/2607.22592#A5.T6)\(Appendix[E](https://arxiv.org/html/2607.22592#A5)\)\.

Beyond node count, compactness has practical consequences\. At 333–1,064 nodes, the full variable vocabulary fits in a single editor pane \(the medical schema is 173 metrics; Appendix[A](https://arxiv.org/html/2607.22592#A1)\): a domain expert can read every node, correct a mislabeled edge, and have the fix propagate deterministically through graph build and retrieval\. Entity\-relation graphs of 5k\+ nodes offer no such affordance\. The compactness also constrains query\-time cost: eachHCG\-RAGquery makes a single LLM call \(answer generation from retrieved evidence\), versus 2 forLightRAG/Fast\-GraphRAGand∼\{\\sim\}196 forMS\-GraphRAGglobal\. Per\-query latency ranges from 3\.2 s \(XS\) to 12\.6 s \(L\), comparable toFast\-GraphRAG\(2\.7 s\) at the XS tier; full build and query cost details are in Appendix[L](https://arxiv.org/html/2607.22592#A12)\.

### 5\.2Overall answer quality

On medical \(Table[1](https://arxiv.org/html/2607.22592#S5.T1); 5\-run means±\\pmstd\),MS\-GraphRAGglobal search leads on coverage \(0\.649\) but has the lowest correctness \(0\.573\) and ROUGE \(0\.139\): community\-level abstractions lose factual specificity\.HCG\-RAGM is statistically indistinguishable fromLightRAGon correctness \(0\.679 vs\. 0\.673;p=\.27p\{=\}\.27, Appendix[H](https://arxiv.org/html/2607.22592#A8)\) and trailsFast\-GraphRAG\(0\.690\) by 1\.1 pp, while using∼\{\\sim\}5×\\timesfewer nodes\. Treating answer quality and graph size jointly, the smallerHCG\-RAGtiers \(XS, S, M\) lie on the medical \(correctness, coverage, nodes\) Pareto frontier; the L tier is dominated by M, signalling diminishing returns past 1k nodes\.Fast\-GraphRAGachieves the highest medical correctness \(0\.6900\.690\) but at5×5\\timesthe node count;HCG\-RAGM sacrifices 1\.1 pp in correctness to gain\+9\.1\+9\.1pp in coverage with a5×5\\timessmaller graph \(Figure[6](https://arxiv.org/html/2607.22592#A7.F6), Appendix[G](https://arxiv.org/html/2607.22592#A7)\)\. Paired\-bootstrap significance for every headline pair, plus the cross\-stratum hop\-heavy/lookup\-heavy slice analysis on epilepsy, is reported in Appendix[H](https://arxiv.org/html/2607.22592#A8); cross\-family judge robustness \(Kimi\-K2\.5\) is in Appendix[I](https://arxiv.org/html/2607.22592#A9)\.

Table 1:Answer quality and graph size on GraphRAG\-Bench medical \(2,062 questions, 5 runs, GLM\-4\.7 judge\)\.HCG\-RAGtiers use 3–17×\\timesfewer nodes than entity\-relation baselines while landing within 2\.6 pp of the best system on answer correctness\.Boldmarks the best value per column;underlinemarks the bestHCG\-RAGvalue, which in every case is Pareto\-optimal \(no baseline achieves both higher quality and fewer nodes\)\. ROUGE averaged over Fact Retrieval and Complex Reasoning; Coverage over Contextual Summarization and Creative Generation\. Faithfulness \(Creative Generation only\) is reported in Appendix[E](https://arxiv.org/html/2607.22592#A5)\.Four qualitative case studies on medical Complex Reasoning \(multi\-hop causal chains whereHCG\-RAGbeatsFast\-GraphRAGby\>\>0\.3 correctness\) appear in Appendix[J](https://arxiv.org/html/2607.22592#A10)\.

On the literary novel benchmark \(Appendix[D](https://arxiv.org/html/2607.22592#A4), Table[5](https://arxiv.org/html/2607.22592#A4.T5)\), entity\-relation systems have an advantage:Fast\-GraphRAGleads correctness \(0\.596\),HCG\-RAGtrailsNaiveRAG\(0\.524 vs\. 0\.544\) but is comparable on coverage \(0\.462 vs\. 0\.488\); the In\-context ablation \(Table[3](https://arxiv.org/html/2607.22592#S6.T3)\) reaches 0\.591 here, the only benchmark where removing the graph helps\.222Only the S tier is reported on novel because the medical and epilepsy scaling curves \(Section[5\.3](https://arxiv.org/html/2607.22592#S5.SS3)\) show that tier choice has minimal effect on answer correctness \(≤0\.015\\leq 0\.015pp spread\); given the additional build cost for a corpus of 20 novels and the clear domain mismatch, we report a single representative tier rather than all four\.

OnEpilepsyQA\(Table[2](https://arxiv.org/html/2607.22592#S5.T2)\), the structural separation is stark: all fourHCG\-RAGtiers \(0\.6040\.604–0\.6110\.611\) andMS\-GraphRAGlocal \(0\.6060\.606\) cluster at the top, well aboveFast\-GraphRAG\(0\.5690\.569\),NaiveRAG\(0\.3970\.397\), andLightRAG\(0\.3340\.334\)\. The two methods that beat flat entity\-relation retrieval are the two that impose higher\-level organization, namelyMS\-GraphRAG\(hierarchical community summaries\) andHCG\-RAG\(typed causal schema\)\. The wider gap relative to medical is consistent with the benchmark’s question distribution: 80% ofEpilepsyQAquestions require multi\-step reasoning \(Mechanistic, Multi\-hop, Counterfactual, Clinical Reasoning\), while Fact Retrieval the category where flat entity co\-occurrence suffices accounts for only 1\.6%, compared with 53% on medical\. The underlying corpus \(two focused clinical textbooks\) is also more tightly covered by the typed schema than the broader medical corpus, so the graph captures a larger share of the relationships the questions test\.HCG\-RAGachieves this clustering with graphs77–20×20\\timessmaller thanMS\-GraphRAG’s \(218218–624624vs\.4,3354\{,\}335nodes; Table[2](https://arxiv.org/html/2607.22592#S5.T2)\)\. The structural separation is robust to a cross\-family second judge \(Kimi\-K2\.5; bothHCG\-RAGandMS\-GraphRAGlocal significantly outperform every flat entity\-relation baseline under both judges,q<\.001q\{<\}\.001; Appendix[I](https://arxiv.org/html/2607.22592#A9)\)\. On secondary metrics,HCG\-RAG’s top tiers lead aggregate ROUGE \(0\.206 vs\. 0\.201Fast\-GraphRAG, 0\.170MS\-GraphRAGlocal\) andHCG\-RAGXS leads Fact Retrieval \(\+10\.7\+10\.7pp overMS\-GraphRAGlocal; Appendix[F](https://arxiv.org/html/2607.22592#A6)\)\. The separation is structural rather than graph\-size driven:MS\-GraphRAGadds Leiden communities and multi\-resolution summaries on top of its entity\-relation graph, so the two systems that beat flat entity\-relation retrieval are the two that impose higher\-level organization \(Fast\-GraphRAG’s entity\-relation graph trails by 3\.7 pp at comparable size toMS\-GraphRAG’s\)\. Per\-question\-type breakdowns are in Appendices[E](https://arxiv.org/html/2607.22592#A5)and[F](https://arxiv.org/html/2607.22592#A6)\.

Table 2:Answer quality and graph size onEpilepsyQA\(375 neurologist\-validated questions, 5 runs, GLM\-4\.7 judge\)\. All fourHCG\-RAGtiers \(0\.604–0\.611\) andMS\-GraphRAGlocal \(0\.606\) cluster at the top, significantly above flat entity\-relation methods, while using 7–20×\\timesfewer nodes\. Emphasis conventions follow Table[1](https://arxiv.org/html/2607.22592#S5.T1)\. ROUGE averaged over all non\-synthesis types; Coverage over Synthesis only\.
### 5\.3Scaling analysis

Quality vs\. graph size shows*diminishing returns past M on medical*: XS→\\toS→\\toM improves monotonically, but expanding to L yields no net gain on the headline metric and slight regressions on Complex Reasoning \(−\-1\.3 pp\) and Creative Generation faithfulness \(−\-2\.8 pp\), consistent with schema saturation\. M and S have similar edge counts \(8,455 vs\. 8,846\) despite differing node counts because both tiers’ metric\-level caps produced comparable Tier\-1 edge templates on this corpus; the node difference reflects variable instantiation, not edge discovery\. On epilepsy the curve is flatter still, with all four tiers within 0\.010 answer correctness; even the XS tier \(218 nodes\) captures the domain’s causal structure\. Full tier\-by\-tier breakdowns are in Appendices[E](https://arxiv.org/html/2607.22592#A5)\(medical\) and[F](https://arxiv.org/html/2607.22592#A6)\(epilepsy\)\.

## 6Ablation study

Two ablations on the S tier isolate the role of the graph \(Table[3](https://arxiv.org/html/2607.22592#S6.T3)\)\.*Nodes only*runs the same BFS over the same graph but feeds the LLM only the matched node names and edge triples\.*In\-context*removes the graph entirely and passes the full corpus to the LLM\.

Table 3:Ablation: medical answer correctness \(5\-run mean±\\pmsample std across runs, computed from count\-weighted answer correctness in evaluation exports\)\.HCG\-RAG\(default\) provides only graph\-selected evidence to the answer LLM; the per\-question\-type breakdown \(including ablation rows\) is in Appendix[E](https://arxiv.org/html/2607.22592#A5), Table[7](https://arxiv.org/html/2607.22592#A5.T7)\.Nodes only: same BFS, LLM receives node names and edge triples instead of evidence passages\.In\-context: no retrieval; LLM receives the full corpus\.

#### The graph is a retrieval filter, not a reasoning substrate\.

DefaultHCG\-RAGfeeds only evidence passages to the answer LLM and reaches 0\.668 on medical, within 2\.2 pp ofFast\-GraphRAG\(0\.690\) and statistically indistinguishable fromLightRAG\(0\.673\)\.*Nodes only*inverts this and drops to 0\.480 \(−18\.8\-18\.8pp\), confirming that the LLM relies on retrieved text rather than graph structure itself\. The gap toNaiveRAG\(0\.608\) is\+6\.0\+6\.0pp \(p<\.001p\{<\}\.001, paired bootstrap; Appendix[H](https://arxiv.org/html/2607.22592#A8)\)\. BothNaiveRAGandHCG\-RAGfeed only text to the LLM, so the graph’s role is to*select*evidence via BFS, a structured filter distinct from top\-kksearch and PageRank\. Removing retrieval entirely \(*In\-context*\) costs−16\.3\-16\.3pp on medical and−15\.9\-15\.9pp on epilepsy, but reaches 0\.591 on novel, consistent with the finding that the causal graph’s retrieval advantage is strongest on structured domains\.

## 7Limitations

Graph correctness scope\.Neurologists validated theEpilepsyQAquestions \(Table[2](https://arxiv.org/html/2607.22592#S5.T2)\), and the compact typed graph is small enough to inspect in a single editor pane, a deliberate design goal\. Every causal edge stores mechanism text and chunk\-level provenance, so a domain expert can verify or correct individual claims without re\-running the pipeline\. A systematic edge\-by\-edge audit was beyond the scope of this study; we view it as a natural next step enabled precisely by the graph’s compactness\.Precision–coverage trade\-off\.Schema\-constrained construction deliberately favors precision over broad lexical coverage, which is the appropriate trade\-off for fact\-heavy, causally structured domains\. On summarization\-heavy tasks \(Contextual Summarization, Creative Generation, epilepsy Synthesis\),MS\-GraphRAGglobal’s community summaries achieve higher aggregate coverage\.Domain scope\.HCG\-RAGis designed for corpora with discoverable hierarchical causal structure \(e\.g\., medical and scientific text\)\. On literary narrative, where such structure is largely absent, the causal graph may offer less benefit, as the novel benchmark suggests\. This is consistent with the paper’s central thesis that graph topology should match the domain’s knowledge structure rather than default to a single paradigm\.

## 8Conclusion

We presentedHCG\-RAG, a system that constructs schema\-constrained hierarchical causal graphs via an automated domain\-specification pipeline and uses them as a graph\-guided retrieval filter\. The headline finding is*compactness without sacrifice*: schema\-constrained causal graphs match entity\-relation GraphRAG with 3–20×\\timesfewer nodes, producing graphs small enough for a domain expert to audit, correct, and extend\. Ablations attribute the gain to the causal graph itself, which serves as a*structured retrieval filter*\. The second finding is structural: on specialized domains with discoverable hierarchical causal structure \(epilepsy\), only methods that impose higher\-level organization \(MS\-GraphRAG’s community summaries andHCG\-RAG’s typed causal schema\) outperform flat entity\-relation retrieval; on literary narrative, where such structure is largely absent, entity\-relation graphs lead\. Because the pipeline produces inspectable artifacts \(YAML schema, typed nodes, per\-edge mechanism text\) over a graph that fits in a single editor pane, our fully automated numbers are a*zero\-shot lower bound*on what the approach can achieve with expert\-in\-the\-loop curation\. The broader design lesson is to ask*what*to put in the graph and*how*to use it, not only how many nodes to extract\.

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## Appendix AMethod details

This appendix collects the algorithmic specification, the retrieval\-stage definitions \(per\-metric node matching, bounded BFS, outcome cone\), and the derivation for Remark[1](https://arxiv.org/html/2607.22592#Thmremark1), all referenced from Section[3](https://arxiv.org/html/2607.22592#S3)\.

#### Derivation for Remark[1](https://arxiv.org/html/2607.22592#Thmremark1)\.

Tier 1 evaluates at most\|ℳ\|2−\|ℳ\|\|\\mathcal\{M\}\|^\{2\}\-\|\\mathcal\{M\}\|ordered metric pairs \(after excluding self\-loops and terminal sources\)\. Tier 2 evaluates node pairs only for templates inℰm\\mathcal\{E\}\_\{m\}: each template\(ms,mt\)\(m\_\{s\},m\_\{t\}\)contributes\|𝒱ms\|⋅\|𝒱mt\|≤k¯2\|\\mathcal\{V\}\_\{m\_\{s\}\}\|\\cdot\|\\mathcal\{V\}\_\{m\_\{t\}\}\|\\leq\\bar\{k\}^\{2\}candidates\. Summing over templates,

Total calls≤\|ℳ\|​\(\|ℳ\|−1\)⏟Tier 1\+∑\(ms,mt\)∈ℰm\|𝒱ms\|⋅\|𝒱mt\|⏟Tier 2≤\|ℳ\|2\+\|ℰm\|⋅k¯2\.\\text\{Total calls\}\\leq\\underbrace\{\|\\mathcal\{M\}\|\(\|\\mathcal\{M\}\|\-1\)\}\_\{\\text\{Tier 1\}\}\+\\underbrace\{\\sum\_\{\(m\_\{s\},m\_\{t\}\)\\in\\mathcal\{E\}\_\{m\}\}\|\\mathcal\{V\}\_\{m\_\{s\}\}\|\\cdot\|\\mathcal\{V\}\_\{m\_\{t\}\}\|\}\_\{\\text\{Tier 2\}\}\\leq\|\\mathcal\{M\}\|^\{2\}\+\|\\mathcal\{E\}\_\{m\}\|\\cdot\\bar\{k\}^\{2\}\.For exhaustive pairwise evaluation, all\|𝒱\|2\|\\mathcal\{V\}\|^\{2\}pairs must be considered\. The two\-tier bound never exceeds this: in the worst case where every metric pair yields a template \(\|ℰm\|=\|ℳ\|2\|\\mathcal\{E\}\_\{m\}\|=\|\\mathcal\{M\}\|^\{2\}\), the Tier 2 sum becomes∑ms,mt\|𝒱ms\|⋅\|𝒱mt\|=\(∑m\|𝒱m\|\)2=\|𝒱\|2\\sum\_\{m\_\{s\},m\_\{t\}\}\|\\mathcal\{V\}\_\{m\_\{s\}\}\|\\cdot\|\\mathcal\{V\}\_\{m\_\{t\}\}\|=\\bigl\(\\sum\_\{m\}\|\\mathcal\{V\}\_\{m\}\|\\bigr\)^\{2\}=\|\\mathcal\{V\}\|^\{2\}, recovering the naive bound\. In practice\|ℰm\|≪\|ℳ\|2\|\\mathcal\{E\}\_\{m\}\|\\ll\|\\mathcal\{M\}\|^\{2\}since Tier 1 filters most metric pairs, yielding a strict reduction\.□\\square

#### Inspectability: a representative schema excerpt\.

The fixed metric/dimension vocabulary \(FIXED in Figure[2](https://arxiv.org/html/2607.22592#S3.F2)\) is small enough to print and read in a sitting\. Figure[5](https://arxiv.org/html/2607.22592#A1.F5)shows a 28\-line excerpt from the medical schema’s metrics block: each metric is named with its dimension signature, has a one\-paragraph mechanism description, and carries a graph role\. The full medical schema is 173 metrics across 9 categories; the full epilepsy schema is 91 metrics across 8 categories\. Both fit in a single text editor pane and are human\-editable; corrections propagate deterministically through graph build \(Stage 2\) and retrieval \(Stage 3\)\.

Figure 5:Excerpt from the medicalgraph\_spec\.yaml\(3 of 173 metrics shown\)\. The vocabulary is closed at construction time: new entities and variables are admitted only if they fit an existing metric template, which is what bounds graph size\.metrics:

\-name:DiagnosticApproach\(disease,diagnostic\_modality,biomarker\)

description:Methodsusedtodetectandconfirmdisease,including

imagingmodalities,biopsies,bloodtests,urinetests,biomarker

panels,pathologyreview,genetictesting,flowcytometry,and

endoscopicprocedures\.Drivenbysymptoms,riskfactors,anatomy

involved,andpriortestresults;influencesstagingaccuracy,

treatmentselection,andsurveillanceplanning\.

attributes:

category:diagnostics

graph\_role:outcome

\-name:AnatomicalInvolvement\(disease,anatomy,outcome\_horizon\)

description:Bodysitesandtissuestructuresinvolvedbythe

diseaseovertime,includingprimarysites,tissuelayers,

nerves,lymphnodes,marrow,andmetastaticorgans\.Shapedby

localinvasionandmetastaticspread;influencessymptoms,

staging,treatmentoptions,andprognosis\.

attributes:

category:anatomy

graph\_role:outcome

\-name:StagingClassification\(disease,stage,subtype\)

description:Clinicalorpathologicseverityclassification

reflectingdiseaseextent,grade,phase,molecularsubgroup,or

riskcategory,includingTNMstage,local/regional/metastatic

extent,leukemiaphase,andlow/high/very\-high\-riskgroupings\.

Determinedbydiagnosticfindings,invasionextent,metastatic

burden,andbiomarkerstatus;directlydrivestherapychoice

andprognosis\.

attributes:

category:staging

graph\_role:outcome

Algorithm 1HCG\-RAGpipeline0:Corpus

𝒟=\{d1,…,dn\}\\mathcal\{D\}=\\\{d\_\{1\},\\ldots,d\_\{n\}\\\}, outcome config

𝒪\\mathcal\{O\}, query

qq
0:Answer

aa
1:Stage 1: Domain Specification

2:

𝒜←GenerateDimensions​\(𝒟\)\\mathcal\{A\}\\leftarrow\\textsc\{GenerateDimensions\}\(\\mathcal\{D\}\)\{axes

\(δi,Ei\)\(\\delta\_\{i\},E\_\{i\}\); Definition[1](https://arxiv.org/html/2607.22592#Thmdefinition1)\}

3:

ℳ←GenerateMetrics​\(𝒟,𝒜\)\\mathcal\{M\}\\leftarrow\\textsc\{GenerateMetrics\}\(\\mathcal\{D\},\\mathcal\{A\}\)\{fixed metrics and signatures

sig⁡\(m\)\\operatorname\{sig\}\(m\)\}

4:

𝒱0←GenerateVariables​\(𝒟,𝒜,ℳ\)\\mathcal\{V\}\_\{0\}\\leftarrow\\textsc\{GenerateVariables\}\(\\mathcal\{D\},\\mathcal\{A\},\\mathcal\{M\}\)\{seed variables

v=\(m,𝐞\)v=\(m,\\mathbf\{e\}\)\(extensible\)\}

5:

ℛ0←GenerateCausalRelations​\(𝒟,𝒜,ℳ,𝒱0\)\\mathcal\{R\}\_\{0\}\\leftarrow\\textsc\{GenerateCausalRelations\}\(\\mathcal\{D\},\\mathcal\{A\},\\mathcal\{M\},\\mathcal\{V\}\_\{0\}\)\{seed edges on

𝒱0\\mathcal\{V\}\_\{0\}\(extensible\)\}

6:Stage 2: Graph Build

7:

ℰm←MetricEdges​\(ℳ,ℛ0,𝒟\)\\mathcal\{E\}\_\{m\}\\leftarrow\\textsc\{MetricEdges\}\(\\mathcal\{M\},\\mathcal\{R\}\_\{0\},\\mathcal\{D\}\)\{metric\-level templates\}

8:

\(𝒱,ℰn\)←NodeEdges​\(𝒱0,ℰm,𝒟\)\(\\mathcal\{V\},\\mathcal\{E\}\_\{n\}\)\\leftarrow\\textsc\{NodeEdges\}\(\\mathcal\{V\}\_\{0\},\\mathcal\{E\}\_\{m\},\\mathcal\{D\}\)\{tier\-2 instantiation; may extend

𝒱\\mathcal\{V\}beyond

𝒱0\\mathcal\{V\}\_\{0\}\}

9:

G←LinkEvidence​\(\(𝒱,ℰn\),𝒟\)G\\leftarrow\\textsc\{LinkEvidence\}\(\(\\mathcal\{V\},\\mathcal\{E\}\_\{n\}\),\\mathcal\{D\}\)\{attach evidence chunks\}

10:Stage 3: Query\-Time Retrieval

11:

Vq←MatchNodes​\(q,𝒱\)V\_\{q\}\\leftarrow\\textsc\{MatchNodes\}\(q,\\mathcal\{V\}\)\{per\-metric cosine gating\}

12:

Gq←BFS​\(G,Vq,hmax\)G\_\{q\}\\leftarrow\\textsc\{BFS\}\(G,V\_\{q\},h\_\{\\max\}\)\{bounded causal subgraph\}

13:

Cq←CollectEvidence​\(Gq\)C\_\{q\}\\leftarrow\\textsc\{CollectEvidence\}\(G\_\{q\}\)\{evidence from traversed edges\}

14:

a←LLM​\(q,Cq\)a\\leftarrow\\textsc\{LLM\}\(q,C\_\{q\}\)

#### Retrieval\-stage definitions\.

The three\-step retrieval procedure summarized in Section[3\.4](https://arxiv.org/html/2607.22592#S3.SS4)is defined formally as follows\.

###### Definition 2\(Per\-Metric Node Matching\)\.

Given query embedding𝐪\\mathbf\{q\}, pre\-computed variable embeddings\{𝐯i\}\\\{\\mathbf\{v\}\_\{i\}\\\}, and metric assignmentμ:𝒱→ℳ\\mu:\\mathcal\{V\}\\to\\mathcal\{M\}, the match setVqV\_\{q\}is constructed via a per\-metric gating procedure that prevents any single metric from dominating:

1. 1\.For each metricmjm\_\{j\}, compute the top similarityσj∗=maxvi:μ​\(vi\)=mj⁡cos⁡\(𝐪,𝐯i\)\\sigma\_\{j\}^\{\*\}=\\max\_\{v\_\{i\}:\\,\\mu\(v\_\{i\}\)=m\_\{j\}\}\\operatorname\{cos\}\(\\mathbf\{q\},\\mathbf\{v\}\_\{i\}\)\.
2. 2\.Retain metricmjm\_\{j\}iffσj∗≥τmin\\sigma\_\{j\}^\{\*\}\\geq\\tau\_\{\\min\}\(admission floor on the metric’s best variable, default0\.350\.35\)\. Keep the topKKmetrics byσj∗\\sigma\_\{j\}^\{\*\}\(defaultK=5K=5\)\.
3. 3\.For each retained metric, compute the per\-variable admission thresholdτj=min⁡\(τmin,σj∗​\(1−β\)\)\\tau\_\{j\}=\\min\(\\tau\_\{\\min\},\\;\\sigma\_\{j\}^\{\*\}\(1\-\\beta\)\)with bandβ=0\.20\\beta=0\.20\. The relative termσj∗​\(1−β\)\\sigma\_\{j\}^\{\*\}\(1\-\\beta\)enforces a band below the metric’s best match;τmin\\tau\_\{\\min\}then caps that threshold so a single very\-highσj∗\\sigma\_\{j\}^\{\*\}does not exclude moderately\-similar variables\. The effective threshold is thusτj≤τmin\\tau\_\{j\}\\leq\\tau\_\{\\min\}\.
4. 4\.Vq=\{vi∣μ​\(vi\)=mj,cos⁡\(𝐪,𝐯i\)≥τj\}V\_\{q\}=\\\{v\_\{i\}\\mid\\mu\(v\_\{i\}\)=m\_\{j\},\\;\\operatorname\{cos\}\(\\mathbf\{q\},\\mathbf\{v\}\_\{i\}\)\\geq\\tau\_\{j\}\\\}, capped atP=3P=3per metric, sorted by similarity\.

###### Definition 3\(Bounded BFS Subgraph\)\.

Given causal graphG=\(𝒱,ℰ,ϕ\)G=\(\\mathcal\{V\},\\mathcal\{E\},\\phi\), match setVqV\_\{q\}, and depth boundhmaxh\_\{\\max\}\(default 4\), the reachable subgraphGq=\(Vr,Er\)G\_\{q\}=\(V\_\{r\},E\_\{r\}\)is constructed by running forward BFS from every matched node inVqV\_\{q\}along directed causal edges for at mosthmaxh\_\{\\max\}hops:

Vr=\{v∈𝒱∣∃v0∈Vq​s\.t\.​v0→⋯→v​in​G,path length≤hmax\}\.V\_\{r\}=\\bigl\\\{v\\in\\mathcal\{V\}\\mid\\exists\\,v\_\{0\}\\in V\_\{q\}\\text\{ s\.t\.\\ \}v\_\{0\}\\to\\cdots\\to v\\text\{ in \}G,\\;\\text\{path length\}\\leq h\_\{\\max\}\\bigr\\\}\.ErE\_\{r\}is the set of edges inGGbetween nodes inVrV\_\{r\}, and each edge carries its linked evidence viaϕ\\phi\.

###### Definition 4\(Outcome Cone\)\.

For outcome nodeo∈Vro\\in V\_\{r\}\(identified by role∈\{terminal,outcome\}\\in\\\{\\text\{terminal\},\\text\{outcome\}\\\}\), the*outcome cone*𝒦o\\mathcal\{K\}\_\{o\}is the set of nodes inGqG\_\{q\}from whichoois reachable via reverse BFS onGqG\_\{q\}:

𝒦o=\{v∈Vr∣v→⋯→o​in​Gq\}\.\\mathcal\{K\}\_\{o\}=\\\{v\\in V\_\{r\}\\mid v\\to\\cdots\\to o\\text\{ in \}G\_\{q\}\\\}\.Cones are ranked by convergence count\|𝒦o∩Vq\|\|\\mathcal\{K\}\_\{o\}\\cap V\_\{q\}\|\(how many matched query nodes reach this outcome\)\. When multiple outcome nodes share the same metric key \(e\.g\., twoPatientOutcomevariables for different entities\), their cones are merged into a single combined cone to avoid redundant causal chains\. The final set is capped atCmax=6C\_\{\\max\}=6cones\.

#### Hyperparameters\.

The per\-metric matching and BFS defaults are in Table[4](https://arxiv.org/html/2607.22592#A1.T4)\. The effective per\-metric thresholdτj=min⁡\(τmin,σj∗​\(1−β\)\)\\tau\_\{j\}=\\min\(\\tau\_\{\\min\},\\;\\sigma\_\{j\}^\{\*\}\(1\-\\beta\)\)adapts to each metric’s best match quality: whenσj∗=0\.65\\sigma\_\{j\}^\{\*\}=0\.65,τj=min⁡\(0\.35,0\.52\)=0\.35\\tau\_\{j\}=\\min\(0\.35,0\.52\)=0\.35; for a weaker matchσj∗=0\.40\\sigma\_\{j\}^\{\*\}=0\.40,τj=min⁡\(0\.35,0\.32\)=0\.32\\tau\_\{j\}=\\min\(0\.35,0\.32\)=0\.32, admitting variables with slightly lower similarity when the overall signal is weaker\. Defaults were determined empirically on the medical benchmark and are likely domain\-dependent; corpora with different vocabulary density or embedding characteristics may require re\-tuning, particularlyτmin\\tau\_\{\\min\},τe\\tau\_\{e\}, andKK\.

Table 4:Node matching and retrieval hyperparameters\.

## Appendix BEvidence linking details

Evidence linking \(Section[3\.3](https://arxiv.org/html/2607.22592#S3.SS3)\) employs two complementary strategies:

1. 1\.Text matching\.For edges with document\-sourced evidence, the first 200 characters of each evidence text are matched against corpus chunks via substring search\. This captures exact textual provenance when the LLM quotes source material during graph building\.
2. 2\.Semantic matching\.The edge context string “source→\\totarget:mechanism” is embedded and compared to pre\-embedded corpus chunks via cosine similarity\. Chunks with similarity≥τe=0\.78\\geq\\tau\_\{e\}=0\.78are linked, keeping at most 2 chunks per edge\.

The hybrid approach ensures coverage: substring matching captures direct textual evidence, while semantic matching links edges to paraphrased or summarized corpus content\.

## Appendix CBenchmark details

This appendix collects corpus and dataset details omitted from Section 4\.1 for space\.

#### GraphRAG\-Bench\.

We use the Medical and Novel subsets of GraphRAG\-Bench\(Xianget al\.,[2026](https://arxiv.org/html/2607.22592#bib.bib1)\)\. Medical contains 2,062 expert\-authored questions across Fact Retrieval \(1,098\), Complex Reasoning \(509\), Contextual Summarization \(289\), and Creative Generation \(166\)\. Novel contains 2,010 questions across 20 novels with the same four question types\. Each item is paired with a ground\-truth answer and source corpus documents\.

#### EpilepsyQA\.

Our epilepsy evaluation set is derived from a clinical corpus built from two open\-access textbooks\(Bromfieldet al\.,[2006](https://arxiv.org/html/2607.22592#bib.bib28); Czuczwar,[2022](https://arxiv.org/html/2607.22592#bib.bib29)\), one under Creative Commons Attribution and one under Creative Commons Attribution–NonCommercial terms\. We first generated 700 candidate Q–A pairs with Claude Opus 4\.6 \(extended thinking enabled\), then had two board\-certified neurologists from a U\.S\. medical school independently review the full set, correcting reference answers and removing inaccurate or off\-topic items\. The final set contains 375 questions spanning six types: Mechanistic \(102\), Multi\-hop Causal \(102\), Synthesis \(69\), Clinical Reasoning \(57\), Counterfactual \(39\), and Fact Retrieval \(6\)\. The release will include benchmark questions, reference answers, neurologist annotations, and corpus reconstruction instructions\.

## Appendix DNovel benchmark results

Table[5](https://arxiv.org/html/2607.22592#A4.T5)reports aggregate answer quality on the GraphRAG\-Bench novel subset \(2,010 questions, five runs\)\. Only the S tier is reported here: medical and epilepsy scaling curves \(Section[5\.3](https://arxiv.org/html/2607.22592#S5.SS3)\) show that tier choice has minimal impact on answer correctness \(≤0\.015\\leq 0\.015pp spread across four tiers\), and the novel corpus represents a known boundary case where hierarchical causal structure is largely absent, so evaluating additional tiers would not change the qualitative conclusion\.Fast\-GraphRAGleads across all metrics;HCG\-RAGtrailsNaiveRAGon correctness but is comparable on coverage\. The In\-context ablation \(Table[3](https://arxiv.org/html/2607.22592#S6.T3)\) reaches 0\.591 correctness on novel compared to 0\.505 on medical and 0\.445 on epilepsy: removing the graph helps only on novel, confirming that the causal graph’s advantage is domain\-dependent and strongest on structured knowledge rather than literary narrative\.

Table 5:Answer quality on GraphRAG\-Bench novel \(2,010 questions, 5 runs, GLM\-4\.7 judge\)\.†*In\-context*feeds the full corpus to the answer LLM with no graph retrieval \(the In\-context ablation; Section[6](https://arxiv.org/html/2607.22592#S6)\); included here because it is the only system to surpassNaiveRAGon novel\.
## Appendix EMedical detailed results

Table[6](https://arxiv.org/html/2607.22592#A5.T6)lists edge counts and wiring density for the medical graphs \(node counts appear in the main results table, Table[1](https://arxiv.org/html/2607.22592#S5.T1)\)\. Tables[7](https://arxiv.org/html/2607.22592#A5.T7)and[8](https://arxiv.org/html/2607.22592#A5.T8)report per\-question\-type breakdowns on GraphRAG\-Bench medical \(2,062 questions, 5 runs\)\. Table[7](https://arxiv.org/html/2607.22592#A5.T7)stratifies all baselines, allHCG\-RAGtiers, and the two ablations from Section[6](https://arxiv.org/html/2607.22592#S6)by question type\. Table[8](https://arxiv.org/html/2607.22592#A5.T8)breaks all metrics out across the fourHCG\-RAGtiers, exposing the scaling curve underlying the headline numbers\.

Table 6:Edge counts and wiring density on GraphRAG\-Bench medical\. Edge semantics differ across paradigms \(entity co\-mention vs\. typed causal\), so the compactness comparison is primarily about node vocabulary \(Table[1](https://arxiv.org/html/2607.22592#S5.T1)\); Edges/Node illustrates wiring density, not cross\-paradigm comparability\.Table 7:Stratified results on GraphRAG\-Bench medical \(5 runs\)\. Correctness for all four question types \(FR: Fact Retrieval; CR: Complex Reasoning; CS: Contextual Summary; CG: Creative Generation\)\. Coverage for CS and CG; Faithfulness for CG only\. Ablations \(Nodes only,In\-context\) defined in Section[6](https://arxiv.org/html/2607.22592#S6)\.Table 8:Scaling analysis on medical: all metrics by question type andHCG\-RAGtier \(5\-run means\)\. ROUGE reported for FR/CR; Coverage for CS/CG; Faithfulness for CG only\.
## Appendix FEpilepsyQAdetailed results

Table[9](https://arxiv.org/html/2607.22592#A6.T9)lists graph footprints on the epilepsy corpus; Tables[10](https://arxiv.org/html/2607.22592#A6.T10)and[11](https://arxiv.org/html/2607.22592#A6.T11)report per\-question\-type breakdowns and tier scaling onEpilepsyQA\(375 questions, 5 runs\)\. Unlike the medical benchmark where quality peaks at the M tier, epilepsy exhibits a flat scaling curve: L \(0\.611\) leads with XS \(0\.607\), M \(0\.604\), and S \(0\.604\) all within 0\.007 answer correctness\. Even the smallest tier captures sufficient causal structure for effective retrieval\.

Table 9:Graph sizes on the epilepsy corpus \(same tier labels as Table[11](https://arxiv.org/html/2607.22592#A6.T11)\)\.MS\-GraphRAGlocal and global search share one extracted entity graph\. Edge semantics differ across paradigms \(entity co\-mention vs\. typed causal\), so the compactness comparison is primarily about node vocabulary; Edges/Node illustrates wiring density, not cross\-paradigm comparability\. Baseline counts are taken from each framework’s built epilepsy index \(Microsoft GraphRAGentities/relationshipstables, LightRAG entity and relation stores, Fast\-GraphRAG serialized graph\);HCG\-RAGcounts are typed variables and causal edges in the stored graph build\.Table 10:Stratified results on epilepsy \(5 runs\)\. Correctness for all six question types; Coverage for Synthesis only\. Mech: Mechanistic; CF: Counterfactual; MHC: Multi\-hop Causal; Syn: Synthesis; FR: Fact Retrieval; ClinR: Clinical Reasoning\.Table 11:Scaling analysis on epilepsy \(5\-run means\)\.
## Appendix GPareto frontier on medical

Figure[6](https://arxiv.org/html/2607.22592#A7.F6)visualizes the quality–size trade\-off on GraphRAG\-Bench medical, using node count as a graph\-footprint proxy and projecting the \(correctness, coverage, nodes\) space onto two 2\-D planes \(correctness vs\. nodes and coverage vs\. nodes\)\.Fast\-GraphRAGsits on the frontier as the high\-correctness extreme \(0\.690 correctness, 0\.525 coverage, 5,807 nodes\);HCG\-RAGM occupies the high\-coverage, low\-node trade\-off \(0\.679 correctness, 0\.616 coverage, 1,064 nodes\), trading 1\.1 pp correctness for\+9\.1\+9\.1pp coverage and a5\.5×5\.5\\timessmaller graph\.LightRAGis strictly dominated byHCG\-RAGM on all three axes \(\+0\.6\+0\.6pp correctness,\+15\.0\+15\.0pp coverage,4\.6×4\.6\\timesfewer nodes\)\. The three smallerHCG\-RAGtiers \(XS, S, M\) sit on the frontier in both projections, occupying the low\-node arc that no other system reaches;MS\-GraphRAGoccupies a complementary high\-coverage, high\-node regime \(0\.649 coverage, 5,130 nodes for global\)\. The L tier \(1,583 nodes\) is dominated by M on correctness \(−\-1\.0 pp\) and coverage \(−\-1\.5 pp\), signalling diminishing returns past 1k nodes\.

1,0001\{,\}00010,00010\{,\}0000\.60\.60\.650\.650\.70\.7XSSMLLGRFGRMSGR\-LMSGR\-GGraph nodes \(log scale\)Answer correctness\(a\) Correctness vs\. nodes1,0001\{,\}00010,00010\{,\}0000\.450\.450\.50\.50\.550\.550\.60\.60\.650\.65XSSMLLGRFGRMSGR\-LMSGR\-GGraph nodes \(log scale\)Coverage\(b\) Coverage vs\. nodesPareto frontierHCG\-RAGLightRAG / Fast\-GraphRAGMS\-GraphRAG \(local / global\)Figure 6:Quality–size frontier on GraphRAG\-Bench medical \(5\-run means, GLM\-4\.7 judge\)\. Dashed lines trace the non\-dominated set in each 2\-D projection of the \(correctness, coverage, nodes\) space, using node count as a graph\-footprint proxy\.*Top*:HCG\-RAGXS, S, and M form the low\-node arc of the correctness–nodes frontier;Fast\-GraphRAGanchors the high\-correctness end \(0\.690\)\.LightRAGis strictly dominated byHCG\-RAGM \(lower correctness, lower coverage, more nodes\);HCG\-RAGL is dominated byHCG\-RAGM on both axes, signaling diminishing returns past M\.*Bottom*:HCG\-RAGXS, S, M form the low\-node portion of the coverage–nodes frontier, transitioning toMS\-GraphRAG’s higher\-coverage, higher\-node regime;LightRAG,Fast\-GraphRAG, andHCG\-RAGL are dominated on this projection\.
## Appendix HPaired bootstrap significance

Run\-to\-run standard deviation in Tables[1](https://arxiv.org/html/2607.22592#S5.T1)and[2](https://arxiv.org/html/2607.22592#S5.T2)reflects API/decoding noise across the five inference runs at temperature 0; it is not a test of significance across the benchmark\. To address that gap, we compute paired bootstrap confidence intervals on per\-question answer correctness, using the per\-question scores already produced by the GLM\-4\.7 judge for every system on every benchmark\.

#### Procedure\.

For each pair\(A,B\)\(A,B\)on a benchmark, we average each system’s per\-question correctness over the five runs to obtain a paired score vector, restrict to the intersection of question IDs, and take a paired bootstrap on the per\-question differenceΔq=sqA−sqB\\Delta\_\{q\}=s^\{A\}\_\{q\}\-s^\{B\}\_\{q\}\(B=10,000B=10\{,\}000resamples, seed=42=42\)\. We report meanΔ\\Delta, the 2\.5/97\.5 percentile interval, and a two\-sidedpp\-value \(twice the smaller bootstrap\-mean tail mass\)\.

#### Headline comparisons\.

Table[12](https://arxiv.org/html/2607.22592#A8.T12)reports significance for the comparisons referenced in the main text\. The pattern reinforces a more calibrated reading:HCG\-RAG’s wins over flat entity\-relation methods \(Fast\-GraphRAGon epilepsy,LightRAGon epilepsy and medical,NaiveRAGon medical\) are statistically significant; the closest pairs in the top cluster \(HCG\-RAGtiers vs\.MS\-GraphRAGlocal on epilepsy\) are statistical ties; andHCG\-RAG’s 1\.1 pp medical gap behindFast\-GraphRAGis significant rather than within noise, supporting the framing of the medical result as a5×5\\times\-graph\-size trade rather than parity\.

Table 12:Paired bootstrap on per\-question answer correctness \(B=10,000\{=\}10\{,\}000resamples, seed=42\{=\}42\)\.Δ\\Deltais the mean per\-question differenceA−BA\-B; CI is the 95% percentile interval;ppis two\-sided\. Per\-pairnnis the size of the question\-ID intersection across the five runs; the medicalHCG\-RAGM vs\.LightRAGpair drops to 2061 because one question has noLightRAGoutput across all five runs and is excluded from that pair only\. Non\-significant ties \(HCG\-RAGtiers vs\.MS\-GraphRAGlocal on epilepsy\) indicate failure to reject the null atα=\.05\\alpha\{=\}\.05, not formal equivalence; tightness of the 95% CI \(e\.g\.HCG\-RAGL vs\.MS\-GraphRAGlocal:\[−\.006,\+\.016\]\[\-\.006,\+\.016\]\) bounds the practical magnitude of any remaining effect\.BenchmarkA vs\. BΔ\\Delta95% CIppnnSig\. @ \.05medicalHCG\-RAGM vs\.NaiveRAG\+\.070\+\.070\[\+\.059,\+\.082\]\[\+\.059,\+\.082\]<\.001<\.0012062yesmedicalHCG\-RAGM vs\.MS\-GraphRAGlocal\+\.025\+\.025\[\+\.016,\+\.034\]\[\+\.016,\+\.034\]<\.001<\.0012062yesmedicalHCG\-RAGM vs\.LightRAG\+\.006\+\.006\[−\.005,\+\.018\]\[\-\.005,\+\.018\]\.27\.272061nomedicalHCG\-RAGM vs\.Fast\-GraphRAG−\.011\-\.011\[−\.020,−\.002\]\[\-\.020,\-\.002\]\.02\.022062yesmedicalHCG\-RAGL vs\.Fast\-GraphRAG−\.020\-\.020\[−\.030,−\.011\]\[\-\.030,\-\.011\]<\.001<\.0012062yesmedicalHCG\-RAGXS vs\.Fast\-GraphRAG−\.025\-\.025\[−\.035,−\.015\]\[\-\.035,\-\.015\]<\.001<\.0012062yesepilepsyHCG\-RAGL vs\.LightRAG\+\.277\+\.277\[\+\.256,\+\.299\]\[\+\.256,\+\.299\]<\.001<\.001375yesepilepsyHCG\-RAGL vs\.Fast\-GraphRAG\+\.041\+\.041\[\+\.030,\+\.053\]\[\+\.030,\+\.053\]<\.001<\.001375yesepilepsyHCG\-RAGL vs\.MS\-GraphRAGlocal\+\.005\+\.005\[−\.006,\+\.016\]\[\-\.006,\+\.016\]\.41\.41375noepilepsyHCG\-RAGXS vs\.MS\-GraphRAGlocal\+\.001\+\.001\[−\.010,\+\.013\]\[\-\.010,\+\.013\]\.82\.82375noepilepsyHCG\-RAGM vs\.MS\-GraphRAGlocal−\.002\-\.002\[−\.013,\+\.010\]\[\-\.013,\+\.010\]\.77\.77375noepilepsyHCG\-RAGL vs\.HCG\-RAGXS\+\.003\+\.003\[−\.004,\+\.011\]\[\-\.004,\+\.011\]\.38\.38375nonovelHCG\-RAGS vs\.Fast\-GraphRAG−\.072\-\.072\[−\.083,−\.061\]\[\-\.083,\-\.061\]<\.001<\.0012009yesnovelHCG\-RAGS vs\.LightRAG−\.055\-\.055\[−\.067,−\.043\]\[\-\.067,\-\.043\]<\.001<\.0012009yesnovelHCG\-RAGS vs\.NaiveRAG−\.019\-\.019\[−\.031,−\.008\]\[\-\.031,\-\.008\]\.001\.0012009yes
#### Cross\-stratum stability on epilepsy \(hop\-heavy vs\. lookup\-heavy\)\.

To test whetherHCG\-RAG’s advantage over flat entity\-relation retrieval concentrates on multi\-hop questions, we group epilepsy questions into a hop\-heavy slice \(Multi\-hop Causal, Counterfactual, Synthesis;n=210n\{=\}210\) and a lookup\-heavy slice \(Fact Retrieval, Mechanistic;n=108n\{=\}108\) and run paired bootstrap on each\.HCG\-RAGL significantly outperformsFast\-GraphRAGon both slices \(Δ=\+\.038\\Delta\{=\}\{\+\}\.038and\+\.044\{\+\}\.044; bothp<\.001p\{<\}\.001\) andLightRAGon both \(Δ\>\+\.28\\Delta\{\>\}\{\+\}\.28;p<\.001p\{<\}\.001\)\. VersusMS\-GraphRAGlocal it is tied on both \(p=\.51p\{=\}\.51andp=\.94p\{=\}\.94\)\. The advantage of structured retrieval over flat entity\-relation methods holds whether the question requires chained mechanism reasoning or a typed\-vocabulary lookup \(it is not concentrated on a single question type\)\.

## Appendix ICross\-family judge robustness \(Kimi\-K2\.5\)

To validate that the GLM\-4\.7 judge column is not a single\-judge artefact, we re\-evaluate every paper\-era inference prediction under a second judge from a different vendor family:Kimi\-K2\.5\(Moonshot AI, on AWS Bedrock\)\.

#### Per\-system rank correlation \(GLM↔\\leftrightarrowKimi\)\.

Table 13:Spearmanρ\\rhoand Kendallτ\\taubetween GLM\-4\.7 and Kimi\-K2\.5 on per\-system mean answer correctness, per benchmark\. Paired bootstrap, B=10,000\{=\}10\{,\}000, seed=42\{=\}42\.
#### Side\-by\-side per\-system means\.

Table[14](https://arxiv.org/html/2607.22592#A9.T14)reports per\-system means under both judges on each benchmark\. Kimi is on average stricter than GLM \(Δ¯=−0\.012\\bar\{\\Delta\}\{=\}\-0\.012medical,−0\.014\-0\.014novel\), with epilepsy as an exception where Kimi rates several systems more leniently \(Δ¯=\+0\.014\\bar\{\\Delta\}\{=\}\+0\.014, withMS\-GraphRAGvariants gaining the most\)\.

Table 14:Per\-system answer correctness under GLM\-4\.7 vs\. Kimi\-K2\.5\.Δ=\\Delta=Kimi−\-GLM; positive==Kimi more lenient\.
#### Significance\-flag survival\.

Replicating the paired bootstrap of Table[12](https://arxiv.org/html/2607.22592#A8.T12)under Kimi \(same per\-question procedure, BH\-FDR\-adjustedqq\-values within family\) preserves the headline verdict on five of seven pairs: on medical,HCG\-RAGM vs\.LightRAGstays a tie and vs\.MS\-GraphRAGlocal andNaiveRAGstay wins \(q<\.001q\{<\}\.001\); on epilepsy,HCG\-RAGL vs\.Fast\-GraphRAGand vs\.LightRAGstay wins \(q<\.001q\{<\}\.001under both judges\)\. The two shifts pull in opposite directions: medicalHCG\-RAGM vs\.Fast\-GraphRAGsoftens from lose \(q=\.025q\{=\}\.025GLM\) to tie \(q=\.44q\{=\}\.44Kimi\), while epilepsyHCG\-RAGL vs\.MS\-GraphRAGlocal moves from tie \(q=\.42q\{=\}\.42\) to a Kimi loss \(q<\.001q\{<\}\.001\), leaving the aggregate narrative roughly neutral\.

#### What survives, what shifts\.

The categorical claim that organized methods \(HCG\-RAGandMS\-GraphRAG\) significantly outperform flat entity\-relation retrieval on epilepsy is robust under both judges \(HCG\-RAGL vs\.Fast\-GraphRAGΔ=\+\.041\\Delta\{=\}\+\.041GLM,\+\.045\+\.045Kimi, bothq<\.001q\{<\}\.001\)\. On medical,HCG\-RAGM’s competitive position with the strongest entity\-relation system is*strengthened*under Kimi \(M vs\.Fast\-GraphRAGmoves fromq=\.025q\{=\}\.025toq=\.44q\{=\}\.44\)\. The single result that does not survive Kimi as worded is the epilepsy tie betweenHCG\-RAGL andMS\-GraphRAGlocal: under Kimi,MS\-GraphRAGlocal leads by2\.32\.3pp \(q<\.001q\{<\}\.001\)\. Notably,HCG\-RAG’s epilepsy scores are judge\-stable across all four tiers \(\|Δ\|≤\.007\|\\Delta\|\{\\leq\}\.007\), whileMS\-GraphRAGlocal’s score swings\+\.029\+\.029, indicating the cross\-judge disagreement reflects judge\-dependent generosity towardMS\-GraphRAG’s community\-summary outputs rather than instability inHCG\-RAG\.

## Appendix JQualitative case studies

We examine four medical Complex\-Reasoning questions where the causal graph produces qualitatively different answers from entity\-relation baselines\. These are representative of the 32 questions whereHCG\-RAGexceedsFast\-GraphRAGby more than 0\.3 answer correctness; all involve multi\-hop causal chains that flat entity retrieval cannot reconstruct\.

#### Hodgkin lymphoma diagnosis \(visualized in Figure[4](https://arxiv.org/html/2607.22592#S3.F4)\)\.

*Q: A 25\-year\-old presents with swollen lymph nodes in the upper body\. What cancer is most likely?*Ground truth: Hodgkin lymphoma \(common ages 15–30, starts in upper body nodes\)\.HCG\-RAGanswers “Hodgkin lymphoma, because in a 25\-year\-old, swollen upper\-body lymph nodes are a classic presentation” \(0\.969\)\.Fast\-GraphRAGanswers “breast cancer” \(0\.380\), retrieving passages about breast masses rather than following the age\-presentation\-diagnosis chain\. The causal graph connects age\-stratified risk factors to lymphoma subtypes via directed edges, enabling the correct differential\.

#### Bladder cancer treatment\.

*Q: Which treatments are used for non\-muscle\-invasive bladder cancer?*Ground truth: TURBT and intravesical therapy \(BCG or chemotherapy\)\.HCG\-RAGanswers “treated with transurethral resection of the bladder tumor \(TURBT\), often followed by intravesical therapy such as chemotherapy or BCG” \(0\.982\)\.Fast\-GraphRAGanswers “commonly treated with surgery, chemotherapy, radiation therapy, immunotherapy” \(0\.366\), a generic oncology response that misses the stage\-specific protocol\. The causal graph links cancer staging variables to treatment response variables, retrieving evidence about the specific TURBT pathway\.

#### Biomarker interpretation\.

*Q: What is the role of p16 protein in oropharyngeal squamous cell carcinoma?*Ground truth: p16 overexpression identifies HPV\-mediated SCC\.HCG\-RAGanswers “p16 is a surrogate biomarker used to identify HPV\-positive oropharyngeal squamous cell carcinoma” \(0\.983\)\.Fast\-GraphRAGdescribes p16 vaguely as a “biomarker test” without connecting it to the HPV mechanism \(0\.394\)\. The causal graph encodes the biomarker→\\tosubtype→\\toprognosis chain, so BFS from a p16\-matched node retrieves the HPV connection\.

#### Treatment decision reasoning\.

*Q: Why don’t all follicular lymphoma patients need immediate treatment?*HCG\-RAGanswers “because many cases are indolent and low\-risk, so they can be safely monitored with watchful waiting” \(0\.879\)\.Fast\-GraphRAGproduces a generic statement about treatment decisions \(0\.346\)\. The causal graph links disease aggressiveness to treatment urgency, retrieving evidence about the indolent subtype\.

Across these cases,HCG\-RAG’s advantage stems from the same mechanism: BFS traversal follows causal pathways \(risk factor→\\todiagnosis, staging→\\totreatment, biomarker→\\tosubtype\) and collects evidence along the chain\. Entity\-relation retrieval surfaces topically related passages but cannot reconstruct the multi\-hop reasoning path\. Qualitative case studies fromEpilepsyQAare deferred to future work pending expert clinical review of retrieved causal chains\.

## Appendix KExperimental details

#### Model configuration\.

All frameworks usegpt\-5\.4\-minifor generation andtext\-embedding\-3\-smallfor embeddings, accessed via the OpenAI API\. Temperature is set to 0 for reproducibility\.

#### Competitor configuration\.

Fast\-GraphRAGandLightRAGare run in isolated Python virtual environments to avoid dependency conflicts \(they pin different versions of theopenaipackage\)\.MS\-GraphRAGis run via direct import\. All competitors use their default configurations except for the model and embedding model, which are standardized\.

#### Evaluation\.

The LLM\-as\-judge evaluator uses GLM\-4\.7\(Z\.ai,[2025](https://arxiv.org/html/2607.22592#bib.bib31)\)via a LiteLLM proxy\(BerriAI,[2023](https://arxiv.org/html/2607.22592#bib.bib32)\)fronting AWS Bedrock; metrics are from GraphRAG\-Bench\(Xianget al\.,[2026](https://arxiv.org/html/2607.22592#bib.bib1)\): answer correctness, coverage score, faithfulness, and ROUGE score\. Metrics are computed per\-question and aggregated per question type\. We use a non\-OpenAI judge to avoid same\-family bias when evaluatinggpt\-5\.4\-mini–extracted answers; the embedding component of answer correctness remainstext\-embedding\-3\-smallfor direct comparability with prior GraphRAG\-Bench results\.

#### Hardware\.

All experiments were executed on an AWSc6a\.4xlargeinstance \(16 vCPUs, AMD EPYC 7R13; 32 GB RAM; 200 GB EBS; Ubuntu 24\.04\) inus\-east\-1\. No GPU was used: graph construction and answer generation are API\-bound \(OpenAI\), so local computation is minimal\.

#### Domain specification provenance\.

All domain specifications used in the benchmark \(outcome configuration and generated schemas\) were produced end\-to\-end by the automated pipeline \(§[3\.2](https://arxiv.org/html/2607.22592#S3.SS2)\) with no human review or editing\.HCG\-RAG’s domain\-specification stage thus produces usable causal schemas without expert intervention\. The pipeline is also designed to be human\-editable: a domain expert can revise or author the outcome configuration to encode prior causal knowledge, potentially improving graph quality beyond what fully automated generation achieves\.

## Appendix LGraph construction and query cost

Table[15](https://arxiv.org/html/2607.22592#A12.T15)summarizes one\-time build cost and recurringGraphRAG\-Benchquery cost on medical \(2,0622\{,\}062questions\)\. ForHCG\-RAGAPI columns we reportoneembedding per answered question plusoneextractor LLM\.

Table 15:Build and query cost on the medical benchmark \(2,062 questions\)\. Token counts are per query\.LightRAGcaches LLM responses after the first run, reducing subsequent query latency to<<1 s; uncached numbers are shown\.MS\-GraphRAGlocal and global share a single build phase; global search map\-reduces over all community reports, yielding∼\\sim196 LLM calls per query\.Build \(one\-time\)QueryAPI calls/qTokens/qFrameworkTime↓\\downarrowLLM↓\\downarrowEmb\.↓\\downarrowBatch↓\\downarrowLatency↓\\downarrowEmb↓\\downarrowLLM↓\\downarrowEmb↓\\downarrowLLM↓\\downarrow\(min\)callscalls\(s/q\)\(s/q\)calls/qcalls/qtok/qprompt tok/qNaiveRAG<<1030\.31\.611107,500LightRAG344,42315,8890\.32\.5124526,545Fast\-GraphRAG132,8821820\.82\.712279,054MS\-GraphRAGlocal2817,638331\.23\.8222118,664MS\-GraphRAGglobal9\.542\.8019602,339,848HCG\-RAG\(ours\) L422,2141,34410\.812\.6111110,730HCG\-RAG\(ours\) M271,1673873\.45\.8111112,080HCG\-RAG\(ours\) S26833904\.06\.3111111,430HCG\-RAG\(ours\) XS8131530\.23\.2111112,700MS\-GraphRAG’s build is the most LLM\-intensive: 17,638 calls in 28 min, dominated by 16,354 entity/relationship description summarizations and 1,085 community reports across five hierarchy levels\. This is4×4\\timesmore LLM calls thanLightRAG\(4,423\) and6×6\\timesmore thanFast\-GraphRAG\(2,882\)\.HCG\-RAG’s build cost is comparable to the lighter competitors: 26 minutes and 833 LLM calls for the S tier; the XS tier builds in 8 minutes with only 131 LLM calls, strictly cheaper thanFast\-GraphRAG\(13 min, 2,882 calls\)\. The L tier \(42 min\) trades longer build time for richer graph structure but is dominated by M on the quality–size Pareto frontier \(Section[5\.3](https://arxiv.org/html/2607.22592#S5.SS3)\); the M/S/XS tiers are the recommended operating points\. Beyond raw counts, the qualitative difference matters:∼\{\\sim\}1k typed, human\-readable nodes versus 5\.8k opaque entities enables expert audit and correction, and on epilepsyHCG\-RAGoutperformsFast\-GraphRAGby 3\.5–4\.2 pp despite far fewer nodes \(Table[2](https://arxiv.org/html/2607.22592#S5.T2)\)\. Per\-query API cost is*lower*forHCG\-RAG: a single LLM call \(answer generation from retrieved evidence\), whileLightRAGandFast\-GraphRAGeach make 2, andMS\-GraphRAGlocal makes 2\.MS\-GraphRAGglobal is an outlier at∼\\sim196 LLM calls per query \(map\-reduce over all community reports\), yielding the highest per\-query latency \(42\.8 s\) but also the highest coverage \(Table[1](https://arxiv.org/html/2607.22592#S5.T1)\)\.

#### Per\-query token cost\.

Among entity\-relation systems,Fast\-GraphRAGis the most token\-efficient \(9\.0k prompt tok/q\) whileLightRAGsends the most \(26\.5k\) due to a large entity\-store context window\.HCG\-RAGfalls between them \(11–13k for S/M tiers\), with the L tier slightly lower because BFS retrieves fewer evidence chunks per query\.MS\-GraphRAG’s two methods sit at the extremes:MS\-GraphRAGlocal at 18\.7k tok/q is comparable toHCG\-RAGM andLightRAG;MS\-GraphRAGglobal is the outlier at≈2\.34\\approx 2\.34M tok/q, roughly𝟐𝟎𝟎×\\mathbf\{200\\times\}more prompt tokens per query thanHCG\-RAGM and260×260\\timesmore thanFast\-GraphRAG\. The inflation comes from map\-reducing over∼\\sim196 community reports \(≈\\approx12k tokens each\) for every query, which also produces the 42\.8 s/q latency in the same row\.

The key query\-time cost difference forHCG\-RAGis*latency*rather than API spend\. A singleHCG\-RAGquery takes 3\.2–12\.6 s depending on graph size, with only≈\\approx1\.5–2\.0 s spent on the API call; the rest is graph traversal and cone merging \(CPU\-bound\)\. The XS tier \(3\.2 s\) is comparable toFast\-GraphRAG\(2\.7 s\) at similar quality \(Table[1](https://arxiv.org/html/2607.22592#S5.T1)\), while larger tiers trade latency for richer evidence retrieval\.