LLM Reasoning with Graphs

LLM: Large Language Model

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18 papers in the last four weeks, up 350% on the four weeks before. 0.2% of all new papers.

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Jun 4, 2026cs.LG

LLM Explainability with Counterfactual Chains and Causal Graphs

Causal graphs provide a high-level language for making mechanisms transparent. Recent work uses Large Language Models (LLMs) to recover causal graphs of external-world processes. Instead, in this paper, we use causal graphs to model LLM inference itself, providing stakeholders with a transparent view of how the model perceives and organizes high-level concepts to produce a prediction. We propose a four-phase method for constructing such graphs. Given a target LLM and a set of textual examples, our method discovers class-discriminative, human-interpretable concepts and maps each input to LLM-perceived concept states. We then introduce an MCMC-inspired counterfactual augmentation procedure that expands the sparse observational data through chains of counterfactuals. This enables stable causal discovery with

σ

-CG, yielding informative, interpretable graphs. We apply our method to three LLMs across disease diagnosis, sentiment analysis, and LLM-as-a-judge classification tasks. We evaluate the learned graphs for predictive fidelity and structural stability, and the MCMC-inspired augmentation for convergence and downstream utility. Our results show that the discovered causal graphs capture meaningful dependencies consistent with LLMs' reasoning. Together, this paper provides a foundation for concept-level explainability of LLMs.

Nirit Nussbaum-Hoffer, Nitay Calderon, Liat Ein-Dor +1

Faculty of Data and Decision Sciences, Technion · IBM Research

LLM Reasoning with Graphs LLM Interpretability Causal Structure Learning Concept-Based Explanations Causal Reasoning in Language Models Counterfactual Data Augmentation+1

Jun 3, 2026cs.CL

Stepwise Reasoning Enhancement for LLMs via External Subgraph Generation

Large language models have shown strong performance in natural language generation and downstream reasoning tasks, but they still struggle with logical consistency, factual grounding, and interpretability in complex multi-step reasoning. To address these limitations, this paper proposes SGR, a stepwise reasoning enhancement framework that integrates large language models with external knowledge graphs through query-relevant subgraph generation. Given an input question, SGR first extracts key entities, relations, and constraints to construct a structured schema, then retrieves compact subgraphs from a knowledge graph using schema-guided querying. The generated subgraphs provide explicit relational evidence that guides the language model through step-by-step reasoning. In addition, SGR combines direct Cypher-based reasoning with collaborative reasoning integration, allowing candidate answers from multiple reasoning paths to be validated and aggregated according to both model confidence and graph consistency. Experiments on benchmark datasets including CWQ, WebQSP, GrailQA, and KQA Pro demonstrate that SGR improves reasoning accuracy and Hits@1 performance over standard prompting and several knowledge-enhanced baselines. Ablation studies further show that schema guidance and Neo4j-based retrieval are both crucial to the effectiveness of the framework. These results indicate that dynamically generated external subgraphs can improve the accuracy, robustness, and interpretability of LLM-based reasoning.

Xin Zhang, Yang Cao, Baoxing Wu +2

School of Information Science and Engineering, Chongqing Jiaotong University · School of Computer Science and Technology, Chongqing University of Posts and Telecommunications

LLM Grounding LLM Reasoning with Graphs Graph Retrieval-Augmented Generation Knowledge Graph Question Answering Multi-Hop Reasoning LLM Reasoning

Jun 2, 2026cs.AI

Reasoning Structure of Large Language Models

Large reasoning models (LRMs) are often evaluated using metrics such as final-answer accuracy or token count. However, identical scores on these metrics can hide fundamentally different reasoning structures. To address this limitation, we introduce a scalable LRM benchmark of logic puzzles and a pipeline that converts unstructured traces into verifiable reasoning graphs of claims and dependencies. This turns reasoning into a structured, measurable object whose topology can be quantitatively analyzed. Building on this, we define a reasoning efficiency metric that quantifies how concentrated the model's logical flow is. Our analysis on open-source reasoning models shows that structural measurements separate behaviors that token count and accuracy conflate, providing a practical tool for diagnosing failure modes and comparing how reasoning scales with puzzle difficulty.

Frédéric Berdoz, Luca A. Lanzendörfer, Fabian Farestam +1

1ETH Zurich, Switzerland.

Logical Reasoning LLM Evaluation LLM Reasoning with Graphs Structured Reasoning LLM Reasoning Large Reasoning Models

Jun 2, 2026cs.AI

Code-on-Graph: Iterative Programmatic Reasoning via Large Language Models on Knowledge Graphs

Knowledge Graphs (KGs) are widely used to mitigate the limitations of Large Language Models (LLMs), such as outdated knowledge and hallucinations. Existing LLM-KG integration frameworks typically rely on predefined operators to retrieve factual knowledge from KGs and inject it into prompts for answer generation. This paradigm faces two critical bottlenecks: 1) Inflexibility: The predefined operators are limited in scope and thus lack sufficient compositional expressiveness to fully capture the complex semantics required by KG questions. 2) Unscalability: Direct injection of factual knowledge into prompts limits scalability in handling large-scale factual knowledge. To address these two bottlenecks, we propose Code-on-Graph (CoG), a programmatic reasoning framework for LLM-KG integration. Specifically, given the factual knowledge retrieved at each reasoning step, CoG first identifies the corresponding KG schemas and represents these schemas as Python classes, which serve as abstract interfaces to the retrieved facts. It then generates executable code grounded in these classes, with the retrieved facts instantiated as objects of the corresponding classes during execution. This design enables flexible code-based reasoning while avoiding the direct injection of large-scale factual knowledge into prompts. Experiments on WebQSP, CWQ, and GrailQA demonstrate that CoG outperforms prior state-of-the-art models by up to 10.5%.

Weiwei Ding, Zixuan Li, Long Bai +7

1Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences · 2Shandong University · 3Shandong University-Weihai Research Institute of Industrial Technology

LLM Grounding LLM Reasoning with Graphs LLM-Based Program Synthesis Knowledge Graph Question Answering Knowledge Graphs

Jun 2, 2026cs.AI

GTBench: A Curriculum-Grounded Benchmark for Evaluating LLMs as Mathematical Research Assistants in Graph Theory

Large language models (LLMs) are increasingly used as self-study assistants in technical disciplines, yet their reliability as mathematical reasoning assistants remains poorly understood. We introduce GTBench, a curriculum-grounded benchmark for evaluating LLMs as mathematical research assistants in graph theory, comprising 63 problems organized into three groups of increasing difficulty: undergraduate definitions and basic properties (Group 1), algorithm tracing and structural reasoning (Group 2), and graduate-level proof construction (Group 3). Problems are sourced from verified academic materials including Diestel's Graph Theory. We evaluate five frontier models -- GPT-5, Claude Sonnet 4.6, Gemini 2.5 Flash-Lite, Llama 3.3 70B, and Mistral Large 3 -- under zero-shot and chain-of-thought prompting, using exact-match and LLM-as-judge evaluation for Groups 1 and 2, and a hybrid human expert and LLM-as-judge protocol for Group 3. Our results reveal a pronounced performance hierarchy: GPT-5 approaches ceiling on Group 1 (95.8% zero-shot) and maintains meaningful accuracy on graduate proofs (82%), while all other models degrade substantially with difficulty, with Llama achieving 0% under human evaluation on Group 3 zero-shot. Failure mode analysis shows that correct algorithm, wrong execution errors dominate Groups 1 and 2, while Group 3 additionally surfaces incomplete reasoning failures and reveals systematic disagreement between human evaluators and the automated judge, particularly on verbose or near-complete proofs (kappa = 0.48-0.83 across human pairs). GTBench provides the first curriculum-grounded evaluation framework for graph-theoretic reasoning in LLMs, with direct implications for the governance of AI tools in mathematical education and scientific research.

Noujoud Nader, Ibrahem Aljabea, Patrick Diehl +1

Louisiana State University, USA · Los Alamos National Laboratory, USA · Texas A&M-Central Texas, USA

Mathematical Reasoning Benchmarks LLM Reasoning with Graphs Graph Reasoning LLM Mathematical Reasoning

Jun 1, 2026cs.AI

Visual Graph Scaffolds for Structural Reasoning in Large Language Models

Graphs have been used to enhance large language models (LLMs) for structured reasoning, mostly as external knowledge sources are provided to models at test time. In this paper, we take a different view: the value of graphs for LLMs lie not only in supplying information, but also in organizing reasoning. Inspired by how humans use graph-structured mind maps to organize branching and converging thoughts, we ask whether graphs can serve as an internal form of reasoning assistance. We study this question on multi-hop question answering tasks, where teacher-provided reasoning traces are rewritten as graph mind maps and used to guide a student model. Our experiments reveal a clear modality gap. When graph structures are flattened into text, their benefits become limited once direct answer hints are removed. Under this abstract guidance setting, both reasoning efficiency and answer quality degrade substantially. In contrast, visual graph guidance remains effective without direct answer clues, and its advantage persists after supervised fine-tuning and KL-based distillation. The above findings support the claim that graphs should be studied not only as external knowledge structures for LLMs, but also as visual scaffolds for organizing reasoning.

Runlin Lei, Xiaokui Xiao, Zhewei Wei

Renmin University of China · National University of Singapore

LLM Reasoning with Graphs LLM Prompting LLM Reasoning

Jun 1, 2026cs.CL

PlanarBench: Evaluating LLM Spatial Reasoning via Planar Graph Drawing

Existing LLM graph benchmarks typically ask models to answer graph-theoretic questions or compute symbolic solutions rather than construct spatial layouts. Within-task difficulty is also primarily stratified by vertex count. However, existing research also suggests that task difficulty is more closely related to the number of constraints imposed by the edges than to the number of vertices being arranged. We introduce PlanarBench, a benchmark that asks models to produce crossing-free ASCII drawings of planar graphs given only an edge list. Across 91 model configurations and 199 non-isomorphic connected planar graphs with 2-7 vertices, edge count is more strongly associated with mean task score than vertex count (

r=-0.85

) versus (

r=-0.47

) and remains strongly associated after controlling for vertex count (

r_p=-0.80

). PlanarBench provides a controlled setting for separating these two difficulty axes. In addition, neither drawing area nor total response length demonstrated a meaningful correlation with score, which is evidence against a simple output-size explanation. Performance varies widely: the best model scores 159.5 out of 199, most models below 30B parameters score under 25, and substantial failures remain among frontier systems.

Oleksandr Nikitin, Anna Kravchenko

Spatial Reasoning Benchmarks LLM Evaluation LLM Reasoning with Graphs Spatial Reasoning

May 29, 2026cs.AI

GraphARC: A Comprehensive Benchmark for Graph-Based Abstract Reasoning

Relational reasoning lies at the heart of intelligence, but existing benchmarks are typically confined to formats such as grids or text. We introduce GraphARC, a benchmark for abstract reasoning on graph-structured data. GraphARC generalizes the few-shot transformation learning paradigm of the Abstraction and Reasoning Corpus (ARC). Each task requires inferring a transformation rule from a few input-output pairs and applying it to a new test graph, covering local, global, and hierarchical graph transformations. Unlike grid-based ARC, GraphARC instances can be generated at scale across diverse graph families and sizes, enabling systematic evaluation of generalization abilities. We evaluate state-of-the-art language models on GraphARC and observe clear limitations. Models can answer questions about graph properties but often fail to solve the full graph transformation task, revealing a comprehension-execution gap. Performance further degrades on larger instances, exposing scaling barriers. More broadly, by combining aspects of node classification, link prediction, and graph generation within a single framework, GraphARC provides a promising testbed for future graph foundation models.

Saku Peltonen, August Bøgh Rønberg, Andreas Plesner +1

ETH Zürich Zürich, Switzerland

LLM Reasoning with Graphs Synthetic Benchmark Generation Graph Foundation Models Graph Reasoning

May 26, 2026cs.AI

The Compressive Knowledge Graph Hypothesis: Which Graph Facts Matter for Scientific Hypothesis Generation?

Knowledge graphs (KGs) can provide structured scientific context to language models, but it remains unclear which graph facts actually shape the generated hypotheses. We study KG-guided hypothesis generation for battery materials across Mistral-7B, Llama-3.1-70B, and Gemini 2.5 Flash. We perturb local KGs by varying density, ontology richness, topology, and control structure, and evaluate outputs with both provided-graph and fixed-reference metrics. Across models, KG utility is selective and model-dependent: graph context changes outputs, but no-KG outputs also recover substantial graph content from model priors. Compact top-k subgraphs often approximate full-KG behavior, including when claimed-outcome triples are held out. At the same time, compression is not unique to one semantic ranking rule, random and topology-based subsets can also recover much of the signal. These results support a redundancy-aware Compressive KG hypothesis: useful KG signal is often recoverable from compact, scientifically structured subgraphs rather than requiring the full local graph.

Shashwat Sourav, Viktoriia Baibakova, Sanjay Das +4

1Washington University in St. Louis · 2Oak Ridge National Laboratory · 3Lawrence Berkeley National Laboratory +1

LLM Grounding LLM Reasoning with Graphs Scientific Hypothesis Generation Large Language Model-Guided Scientific Discovery Knowledge Graphs

May 26, 2026cs.CL

Bounded Path Context: A Controlled Study of Visible Path History in LLM-Based Knowledge Graph Question Answering

LLM-based knowledge-graph question answering (KGQA) delegates graph traversal to language models, turning each question into a sequence of local relation-selection decisions repeated across beams and hops. A common but untested default is to serialize the complete partial path into every routing prompt, even though the controller already maintains this path as exact symbolic state. Bounded Path Context (BPC) decouples these two roles: the controller retains full paths in symbolic memory for answer extraction and audit, while the relation-selection prompt exposes only the question, the current entity, outgoing relation candidates, and at most the last K hops. A controlled sweep over K -- fixing graph neighborhoods, beam budget, depth, decoding, and answer-extraction format -- shows that bounded histories match or exceed full-history prompting on complete WebQSP and CWQ test sets with Qwen3.5-9B-AWQ: K=1 achieves 0.487 answer-set F1 on WebQSP versus 0.472 for full history, and K=0 reaches 0.287 on CWQ versus 0.274, with 9.7% and 12.1% fewer input tokens respectively. At the 4B scale, K=1 remains the strongest setting on both benchmarks. Per-example analysis reveals that 71-84% of examples are unaffected by history length, while the affected cases expose when prior hops disambiguate versus distract. These results suggest that path serialization length is better treated as a tunable interface variable than as a default assumption in LLM-based graph controllers.

Xihang Shan, Ye Luo

School of Mathematical Sciences Xiamen University · School of Informatics Xiamen University

Multi-Hop QA LLM Reasoning with Graphs Knowledge Graph Question Answering LLM Context Management Prompt Engineering

May 24, 2026cs.CL

Knowledge Graph-Driven Expert-Level Reasoning for Neuroscience

Knowledge graph (KG) is an abstraction that can be extracted from text corpora and used for in-depth reasoning. Prior work has leveraged KGs to fine-tune language models (LMs), enabling domain-specific superintelligence. In this work, we explore whether KG-driven in-depth reasoning capabilities can emerge in neuroscience using only information contained within a single authoritative textbook. The central hypothesis is that structured knowledge, when distilled into a high-quality KG and converted into KG-grounded question-answer (QA) supervision, is sufficient to produce expert-level reasoning through a fine-tuned LM that surpasses large language models (LLMs) in accuracy, while employing orders of magnitude fewer parameters. We construct a textbook-derived KG via a dual-LLM validation pipeline, expand it with a masked LM trained on the KG topology, generate multi-hop QA items, which include QA pairs and reasoning traces, to fine-tune an LM exclusively on KG-derived supervision, and apply reinforcement learning using path-derived KG signals as implicit reward models. Our results demonstrate that deep, mechanistic neuroscience understanding can be induced in the model without reliance on large, heterogeneous web-scale corpora. The KG-based synthetic neuroscience curriculum that readers can quiz themselves on, and the fine-tuned LM, are available at the following GitHub location: https://kg-bottom-up-superintelligence.github.io/neuro-bench.

Jake Stephen, Niraj K. Jha

Department of Electrical and Computer Engineering, Princeton University

Knowledge Augmentation for Language Models LLM Reasoning with Graphs Knowledge Graph Question Answering

May 21, 2026cs.LG

Reinforced Graph of Thoughts: RL-Driven Adaptive Prompting for LLMs

Graph of Thoughts (GoT), a generalized form of recent prompting paradigms for large language models (LLMs), has been shown to be useful for elaborate problem solving. By executing a graph of operations, thoughts of the LLM are structured as an arbitrary graph, forming the actual graph of thoughts. Originally, the graph of operations is defined manually, which requires in-depth knowledge about the solution of the problem to solve. Such a static graph of operations is rigid and therefore lacks adaptability. We propose Reinforced Graph of Thoughts (RGoT), an automated approach to the GoT prompting paradigm that leverages reinforcement learning (RL) to adaptively generate a graph of operations from a human-defined set. Results indicate that, under certain constraints, it is possible to construct graphs of operations adaptively to the task's complexity in an automated way.

Manuel Noah Riesen, Peter Alfred von Niederhäusern

School of Engineering and Computer Science Bern University of Applied Sciences Bern, Switzerland

LLM Reasoning with Graphs LLM Prompting CoT Reasoning RL for Language Model Reasoning

May 21, 2026cs.LG

Ex-GraphRAG: Interpretable Evidence Routing for Graph-Augmented LLMs

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.

Yoav Kor Sade, Arvindh Arun, Rishi Puri +2

Tel Aviv University · Institute for AI, University of Stuttgart · NVIDIA +1

Graph Neural Networks LLM Reasoning with Graphs Graph Retrieval-Augmented Generation Knowledge Graph Question Answering GNN Explainability

May 11, 2026cs.AI

SLASH the Sink: Sharpening Structural Attention Inside LLMs

Large Language Models (LLMs) show remarkable semantic understanding but often struggle with structural understanding when processing graph topologies in a serialized format. Existing solutions rely on training external graph-based adapters or fine-tuning, which incur high costs and lost generalizability. In this work, we investigate the internal mechanisms of LLMs and present a critical finding: LLMs spontaneously reconstruct the graph's topology internally, evidenced by a distinct "sawtooth" pattern in their attention maps that structurally aligns with the "token-level adjacency matrix". However, this intrinsic structural understanding is diluted by the attention sink. We theoretically formalize this dilution as a representation bottleneck, stemming from a fundamental conflict: the model's anisotropic bias, essential for language tasks, suppresses the topology-aware local aggregation required for graph reasoning. To address this, we propose a training-free solution, named StructuraL Attention SHarpening (SLASH), which amplifies this internal structural understanding via a plug-and-play attention redistribution. Experiments on pure graph tasks and molecular prediction validate that SLASH delivers significant and consistent performance gains across diverse LLMs.

Yiming Liu, Bin Lu, Xinbing Wang +2

Shanghai Jiao Tong University, Shanghai, China · Institute of Geographical Science and Natural Resources Research, Chinese Academy of Sciences, Beijing, China

LLM Reasoning with Graphs LLM Interpretability Attention Sinks Attention Mechanisms LLM Reasoning LLMs for Graph Learning

May 11, 2026cs.LG

Teaching LLMs to See Graphs: Unifying Text and Structural Reasoning

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.

Dario Vajda

Faculty of Computer and Information Science University of Ljubljana

LLM Reasoning with Graphs Text-Attributed Graph Learning Graph Transformer LLM Reasoning LLMs for Graph Learning

May 10, 2026cs.AI

LLM-Guided Monte Carlo Tree Search over Knowledge Graphs: Composing Mechanistic Explanations for Drug-Disease Pairs

Extracting multi-step explanations from knowledge graphs poses a combinatorial challenge requiring both heuristic guidance (as candidates proliferate with depth) and credit assignment (as path quality emerges over extended sequences). Frontier LLMs, strong on knowledge/reasoning benchmarks, offer a compelling source of such heuristics, yet their knowledge comes sans guarantees and compositional performance degrades as chains lengthen. We thus present TESSERA, a 3-part neuro-symbolic framework that uses LLMs in a circumscribed role: for local discriminative judgement rather than autonomous multi-step generation; the knowledge graph then defines the hypothesis space enforcing hard structural constraints, and MCTS coordinates the long-horizon search with principled credit assignment via backpropagation. LLMs perform dual roles as a prior policy biasing exploration and a comparative state evaluator supplying reward signals. Evaluation on drug mechanism elucidation across two complementary knowledge graphs demonstrates fidelity to curated biology while surfacing coherent alternative mechanisms, with ablations confirming discriminative contribution from both LLM components. Beyond its current application, our framework offers a general paradigm for compositional reasoning over structured knowledge.

Rishabh Jakhar, Michel Dumontier, Remzi Celebi

Institute of Data Science, Department of Advanced Computing Sciences, Maastricht University, The Netherlands

LLM Reasoning with Graphs Scientific Discovery Monte Carlo Tree Search Neuro-Symbolic Reasoning Knowledge Graph Question Answering Large Language Model-Guided Scientific Discovery+1

May 8, 2026cs.AI

Belief or Circuitry? Causal Evidence for In-Context Graph Learning

How do LLMs learn in-context? Is it by pattern-matching recent tokens, or by inferring latent structure? We probe this question using a toy graph random-walk across two competing graph structures. This task's answer is, in principle, decidable: either the model tracks global topology, or it copies local transitions. We present two lines of evidence that neither account alone is sufficient. First, reconstructing the internal representation structure via PCA reveals that at intermediate mixture ratios, both graph topologies are encoded in orthogonal principal subspaces simultaneously. This pattern is difficult to reconcile with purely local transition copying. Second, residual-stream activation patching and graph-difference steering causally intervene on this graph-family signal: late-layer patching almost fully transfers the clean graph preference, while linear steering moves predictions in the intended direction and fails under norm-matched and label-shuffled controls. Taken together, our findings are most consistent with a dual-mechanism account in which genuine structure inference and induction circuits operate in parallel.

Katharine Kowalyshyn, Timothy Duggan, Daniel Little +1

Department of Computer Science, Tufts University, Medford, United States

Transformer Interpretability LLM Reasoning with Graphs In-Context Learning

May 5, 2026cs.CL

Revisiting Graph-Tokenizing Large Language Models: A Systematic Evaluation of Graph Token Understanding

The remarkable success of large language models (LLMs) has motivated researchers to adapt them as universal predictors for various graph tasks. As a widely recognized paradigm, Graph-Tokenizing LLMs (GTokenLLMs) compress complex graph data into graph tokens and treat them as prefix tokens for querying LLMs, leading many to believe that LLMs can understand graphs more effectively and efficiently. In this paper, we challenge this belief: \textit{Do GTokenLLMs fully understand graph tokens in the natural-language embedding space?} Motivated by this question, we formalize a unified framework for GTokenLLMs and propose an evaluation pipeline, \textbf{GTEval}, to assess graph-token understanding via instruction transformations at the format and content levels. We conduct extensive experiments on 6 representative GTokenLLMs with GTEval. The primary findings are as follows: (1) Existing GTokenLLMs do not fully understand graph tokens. They exhibit over-sensitivity or over-insensitivity to instruction changes, and rely heavily on text for reasoning; (2) Although graph tokens preserve task-relevant graph information and receive attention across LLM layers, their utilization varies across models and instruction variants; (3) Additional instruction tuning can improve performance on the original and seen instructions, but it does not fully address the challenge of graph-token understanding, calling for further improvement.

Zhongjian Zhang, Yue Yu, Mengmei Zhang +3

Beijing University of Posts and Telecommunications · China Telecom Bestpay · Beihang University

LLM Evaluation LLM Reasoning with Graphs Graph Foundation Models LLMs for Graph Learning

May 4, 2026cs.AI

SCPRM: A Schema-aware Cumulative Process Reward Model for Knowledge Graph Question Answering

Large language models excel at complex reasoning, yet evaluating their intermediate steps remains challenging. Although process reward models provide step-wise supervision, they often suffer from a risk compensation effect, where incorrect steps are offset by later correct ones, assigning high rewards to flawed reasoning paths. This issue is further exacerbated in knowledge graph (KG) reasoning, as there may exist multiple paths between the start and end entities in the KGs, and a risky step can make the reasoning path flawed. Those limitations are problematic in risk-sensitive tasks such as medical and legal KG reasoning. To address the issues, we propose a Schema-aware Cumulative Process Reward Model (SCPRM) that evaluates reasoning paths by conditioning on the reasoning prefix , and incorporating schema distance between current reasoning step and the implicit target parsed from the query, which provides cumulative and future rewards to guide the path explorations. We further integrate SCPRM into Monte Carlo Tree Search (MCTS) as SCPRM-MCTS to conduct multi-hop reasoning on KGs for question answering (QA) tasks. Across medical and legal KGQA and CWQ, SCPRM-MCTS improves the performance of Hits@k by an average of 1.18% over strong baselines, demonstrating more accurate and risk-sensitive reasoning evaluation.

Jiujiu Chen, Yazheng Liu, Sihong Xie +1

HKUST (GZ)

LLM Reasoning with Graphs Process Reward Models Knowledge Graph Question Answering Multi-Hop Reasoning

May 4, 2026cs.AI

Position: How can Graphs Help Large Language Models?

With the rapid advancement of large language models (LLMs), classic graph learning tasks have greatly benefited from LLMs, including improved encoding of textual features, more efficient construction of graphs from text, and enhanced reasoning over knowledge graphs. In this paper, we ask a complementary question: How can graphs help LLMs? We address this question from three perspectives: 1) graphs provide an up-to-date knowledge source that helps reduce LLM hallucinations, 2) graph-based prompting techniques-such as Chain-of-Thought (CoT), Tree-of-Thought (ToT), and Graph-of-Thought (GoT)-enhance LLM reasoning capabilities, and 3) integrating graphs into LLMs improves their understanding of structured data, expanding their applicability to domains such as e-commerce, code, and relational databases (RDBs). We further outlook some future directions including designing sparse LLM architectures based on graphs and brain-inspired memory systems.

Xiyuan Wang, Yi Hu, Yanbo Wang +2

Institute for Artificial Intelligence, Peking University, Beijing 100871, China · School of Computer Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China

LLM Grounding Knowledge Augmentation for Language Models LLM Reasoning with Graphs LLM Prompting

May 2, 2026cs.LG

Evaluating LLMs on Large-Scale Graph Property Estimation via Random Walks

With the rapidly improving reasoning abilities of Large Language Models (LLMs), there is also a rising demand to use them in a wide variety of domains. This brings about the need to carefully evaluate the limits of the capabilities of these models with various tests and benchmarks. Graph structures are ubiquitous in real-world data, and are often used to represent and analyze relationship patterns within data. Many benchmarks have already been proposed in the graph literature to test the reasoning ability of LLMs to follow and execute graph algorithms. However, due to the limited context length of LLMs, these benchmarks consist of very small graphs. In real-world data, the size of graphs can be significantly larger, and in many cases, not fully accessible. In this paper, we examine a class of problems that arises with very large graphs having limited accessibility. We propose a large graph benchmark dataset, EstGraph, and introduce four distinct tasks designed to estimate large graph properties. We evaluate the reasoning abilities of LLMs on these tasks using a wide variety of graph datasets. In addition, we provide task-specific prompt constructions based on random walk sampling of large graphs (up to millions of nodes) that effectively convey sufficient information to LLMs within the limits of context length.

Sunil Kumar Maurya, Xin Liu

University of Tokyo Tokyo, Japan · AIST Tokyo, Japan

LLM Evaluation LLM Reasoning with Graphs Graph Reasoning LLM Reasoning

Apr 27, 2026cs.CL

Detecting Hallucinations for Large Language Model-based Knowledge Graph Reasoning

Knowledge graph (KG) reasoning infers new knowledge from existing facts and is widely applied in question answering, recommendation, and decision support. With the rapid development of large language models (LLMs), LLM-based KG reasoning frameworks have become increasingly popular by leveraging retrieved KG information. However, hallucinations in LLMs remain a critical issue. Even when relevant KG knowledge is incorporated, models may still generate incorrect outputs, leading to misinformation and unreliable decisions. Existing hallucination detection methods either focus on LLM internal states or verify consistency with retrieved contexts, but both overlook the structural information in KGs, resulting in suboptimal performance. To address this gap, we propose LUCID, the first halLUcination deteCtIon method for LLM-based knowleDge graph reasoning frameworks. LUCID jointly leverages LLM attention scores, KG semantics, and structural information. Specifically, it extracts node and edge features from attention scores and semantic similarities, and integrates them with KG structure using a graph neural network. We also construct manually annotated benchmark datasets for evaluation. Experiments on nine datasets show that LUCID achieves state of the art performance compared to 15 baselines.

Xinyan Zhu, Yaoqi Liu, Yue Gao +3

Beijing University of Posts and Telecommunications · Tsinghua University

LLM Reasoning with Graphs Hallucination in Language Models LLM Hallucination Detection Knowledge Graphs

Apr 24, 2026cs.AI

Don't Make the LLM Read the Graph: Make the Graph Think

We investigate whether explicit belief graphs improve LLM performance in cooperative multi-agent reasoning. Through 3,000+ controlled trials across four LLM families in the cooperative card game Hanabi, we establish four findings. First, integration architecture determines whether belief graphs provide value: as prompt context, graphs are decorative for strong models and beneficial only for weak models on 2nd-order Theory of Mind (80% vs 10%, p<0.0001, OR=36.0); when graphs gate action selection through ranked shortlists, they become structurally essential even for strong models (100% vs 20% on 2nd-order ToM, p<0.001). Second, we identify "Planner Defiance," a model-family-specific failure where LLMs override correct planner recommendations at partial competence (90% override, replicated N=20); Gemini models show near-zero defiance while Llama 70B shows 90%, and models distinguish factual context (deferred to) from advisory recommendations (overridden). Third, full-game evidence confirms inter-agent conventions (+128% over baseline, p=0.003) outperform all single-agent interventions, and individual belief-graph components must be combined to produce gains. Fourth, preliminary scaling analysis (N=10/cell, exploratory) suggests graph depth has diminishing returns: shallow graphs provide the best cost-benefit ratio, while deeper ToM graphs appear harmful at larger player counts (-1.5 pts at 5-player, p=0.029).

Yuqi Sun, Tianqin Meng, George Liu +4

Mindoverflow · University of Waterloo · Carnegie Mellon University +4

Multi-Agent Coordination Game-Playing Agents LLM Reasoning with Graphs Theory of Mind Graph Reasoning Multi-Agent Reasoning

Apr 21, 2026cs.CL

TRN-R1-Zero: Text-rich Network Reasoning via LLMs with Reinforcement Learning Only

Zero-shot reasoning on text-rich networks (TRNs) remains a challenging frontier, as models must integrate textual semantics with relational structure without task-specific supervision. While graph neural networks rely on fixed label spaces and supervised objectives, recent large language model (LLM)-based approaches often overlook graph context or depend on distillation from larger models, limiting generalisation. We propose TRN-R1-Zero, a post-training framework for TRN reasoning trained solely via reinforcement learning. TRN-R1-Zero directly optimises base LLMs using a Neighbour-aware Group Relative Policy Optimisation objective that dynamically adjusts rewards based on a novel margin gain metric for the informativeness of neighbouring signals, effectively guiding the model toward relational reasoning. Unlike prior methods, TRN-R1-Zero requires no supervised fine-tuning or chain-of-thought data generated from large reasoning models. Extensive experiments across citation, hyperlink, social and co-purchase TRN benchmarks demonstrate the superiority and robustness of TRN-R1-Zero. Moreover, relying strictly on node-level training, TRN-R1-Zero achieves zero-shot inference on edge- and graph-level tasks, extending beyond cross-domain transfer. The codebase is publicly available at https://github.com/superallen13/TRN-R1-Zero.

Yilun Liu, Ruihong Qiu, Zi Huang

School of Electrical Engineering and Computer Science The University of Queensland Brisbane, Queensland, Australia

Zero-Shot Learning LLM Reasoning with Graphs RL for Language Model Reasoning Text-Attributed Graph Learning LLMs for Graph Learning

Apr 21, 2026cs.AI

DW-Bench: Benchmarking LLMs on Data Warehouse Graph Topology Reasoning

This paper introduces DW-Bench, a new benchmark that evaluates large language models (LLMs) on graph-topology reasoning over data warehouse schemas, explicitly integrating both foreign-key (FK) and data-lineage edges. The benchmark comprises 1,046 automatically generated, verifiably correct questions across five schemas. Experiments show that tool-augmented methods substantially outperform static approaches but plateau on hard compositional subtypes.

Ahmed G. A. H Ahmed, C. Okan Sakar

Innosol / Bahçe¸sehir University · Department of Computer Engineering, Bahcesehir University, Turkey

LLM Evaluation LLM Reasoning with Graphs Graph Reasoning

Apr 18, 2026cs.AI

GraphDC: A Divide-and-Conquer Multi-Agent System for Scalable Graph Algorithm Reasoning

Large Language Models (LLMs) have demonstrated strong potential for many mathematical problems. However, their performance on graph algorithmic tasks is still unsatisfying, since graphs are naturally more complex in topology and often require systematic multi-step reasoning, especially on larger graphs. Motivated by this gap, we propose GraphDC, a Divide-and-Conquer multi-agent framework for scalable graph algorithm reasoning. Specifically, inspired by Divide-and-Conquer design, GraphDC decomposes an input graph into smaller subgraphs, assigns each subgraph to a specialized agent for local reasoning, and uses a master agent to integrate the local outputs with inter-subgraph information to produce the final solution. This hierarchical design reduces the reasoning burden on individual agents, alleviates computational bottlenecks, and improves robustness on large graph instances. Extensive experiments show that GraphDC consistently outperforms existing methods on graph algorithm reasoning across diverse tasks and scales, especially on larger instances where direct end-to-end reasoning is less reliable.

Wenjin Li, Jiaming Cui

Department of Computer Science, Virginia Tech

Multi-Agent LLM Systems LLM Reasoning with Graphs Graph Reasoning Algorithmic Reasoning

Apr 18, 2026cs.IR

RLM-on-KG: Heuristics First, LLMs When Needed: Adaptive Retrieval Control over Mention Graphs for Scattered Evidence

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.

Andrea Volpini, Elie Raad

WordLift

Multi-Hop QA LLM Reasoning with Graphs Graph Retrieval-Augmented Generation Graph-Based Retrieval Knowledge Graph Question Answering

Apr 17, 2026cs.AI

Integrating Graphs, Large Language Models, and Agents: Reasoning and Retrieval

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.

Hamed Jelodar, Samita Bai, Mohammad Meymani +3

Canadian Institute for Cybersecurity, Faculty of Computer Science, University of New Brunswick, Fredericton, NB E3B 9W4, Canada

LLM Reasoning with Graphs Graph Retrieval-Augmented Generation Graph-Based Retrieval LLM Reasoning

Mar 20, 2026cs.AI

Learning Dynamic Belief Graphs for Theory-of-mind Reasoning

Theory of Mind (ToM) reasoning with Large Language Models (LLMs) requires inferring how people's implicit, evolving beliefs shape what they seek and how they act under uncertainty -- especially in high-stakes settings such as disaster response, emergency medicine, and human-in-the-loop autonomy. Prior approaches either prompt LLMs directly or use latent-state models that treat beliefs as static and independent, often producing incoherent mental models over time and weak reasoning in dynamic contexts. We introduce a structured cognitive trajectory model for LLM-based ToM that represents mental state as a dynamic belief graph, jointly inferring latent beliefs, learning their time-varying dependencies, and linking belief evolution to information seeking and decisions. Our model contributes (i) a novel projection from textualized probabilistic statements to consistent probabilistic graphical model updates, (ii) an energy-based factor graph representation of belief interdependencies, and (iii) an ELBO-based objective that captures belief accumulation and delayed decisions. Across multiple real-world disaster evacuation datasets, our model significantly improves action prediction and recovers interpretable belief trajectories consistent with human reasoning, providing a principled module for augmenting LLMs with ToM in high-uncertainty environment. https://anonymous.4open.science/r/ICML_submission-6373/

Ruxiao Chen, Xilei Zhao, Thomas J. Cova +2

Department of Civil and Systems Engineering, Johns Hopkins University, Baltimore, MD, USA · Civil and Coastal Engineering, University of Florida, Gainesville, FL, USA · School of the Environment, Society & Sustainability, University of Utah, Salt Lake City, UT, USA +1

Computational Cognitive Modeling LLM Reasoning with Graphs Theory of Mind Probabilistic Graphical Models Disaster Response LLM Reasoning

Feb 4, 2026cs.AI

CausalRAG2: Hierarchical Causal Knowledge Graph Design for RAG

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.

Nengbo Wang, Tuo Liang, Vikash Singh +6

Department of Computer and Data Sciences, Case Western Reserve University, Cleveland, OH, USA · Design and Innovation Department, Case Western Reserve University, Cleveland, OH, USA

KG Construction Retrieval-Augmented Generation LLM Reasoning with Graphs Graph Retrieval-Augmented Generation Knowledge Graphs