GraphVerse: A Comprehensive Visual Graph Reasoning Benchmark for Multimodal Large Language Models

Chuanhao Ji; Jiajin Liu; Jiaxi Li; Kang Li; Ninghao Liu; Qiaoyu Tan; Yuanfu Sun; Yuanhang Ren

REVIEW 3 major objections 5 minor 14 references

GraphVerse: A Comprehensive Visual Graph Reasoning Benchmark for Multimodal Large Language Models

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read GraphVerse measures MLLMs' visual graph reasoning and finds them roughly 35% behind humans.

desk verdict A solid, genuinely useful VGR benchmark with programmatic ground truth; the headline accuracy findings are robust, but the process-score story leans on an LLM judge that is validated only on the five easiest tasks, and that soft spot needs referee attention. read the letter →

arxiv 2608.06769 v1 pith:GL75NDD7 submitted 2026-08-07 cs.CV

Yuanfu Sun , Yuanhang Ren , Kang Li , Chuanhao Ji , Jiaxi Li , Jiajin Liu , Ninghao Liu , Qiaoyu Tan This is my paper · ORCID

classification cs.CV

keywords visualgraphreasoningmultimodallargelanguagemodelsbenchmarkgraph-centricimageeditingprocess-sensitiveevaluationcross-imagecomputationalproblems

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

GraphVerse is a benchmark for visual graph reasoning in multimodal large language models, built from real-world graphs rendered as images and paired with programmatically verified graph problems. The paper's central claim is that prior visual graph reasoning benchmarks collapse into perception-then-text reasoning, so they never test whether a model can reason from the visual evidence itself; GraphVerse counters this with four Graph-centric Image Editing (GIE) strategies that alter graph images without changing their underlying topology, forcing models to recover and reason over the edited visual structure. It also introduces VGR-Score, which scores individual reasoning steps against programmatic graph evidence rather than only the final answer. On 11,000 samples tested with 19 MLLMs, the paper reports that even the strongest models trail human baselines by about 35% on average, with near-zero accuracy on paired-image maximum common subgraph, and that vision-based reasoning errors are the dominant failure mode. If the benchmark's measurements are right, current MLLMs are far from robust visual-structural reasoning, and training on GIE-augmented data improves both in-domain performance and transfer to broader multimodal reasoning.

What carries the argument

The load-bearing mechanism is the suite of Graph-centric Image Editing (GIE) strategies, each targeting a different cognitive demand: Image-Graph Patch Perturbation randomly flips or swaps non-empty image patches to break visual continuity; Cross-Graph Composition splits one graph into two panels and gives explicit cross-links to merge; Graph Attentional Focusing picks a target connected subgraph as the largest monochromatic component among distractor colors; and Spatially-Conditioned Recoloring recolors nodes relative to an anchor and cardinal direction. The second mechanism is VGR-Score, a process-sensitive metric built on a scoring LLM that extracts key reasoning steps from the model response and checks each against graph evidence verbalized programmatically from the ground-truth adjacency matrix and edit metadata; the final score is $\lambda R_{\text{step}} + (1-\lambda) \mathbf{1}[\hat{y} \in A^*]$ with $\lambda = 0.7$. Together these ensure that the evidence needed to verify reasoning never has to be re-read from the image by the judge, and that partial credit is assigned to individual reasoning steps rather than the final answer alone.

What would settle it

Take a fixed set of model responses, ask two independent human annotators to split them into key reasoning steps and score them under the same rubric, and compare with the LLM judge's extracted steps and VGR-Score; if step-level agreement is low, or if the judge gives a high process score to a fluent but fabricated chain that reaches the right answer through a wrong graph, the metric is measuring judge behavior rather than visual-graph reasoning.

Watch

Extended reading notes

Core claim

The paper aims to establish that visual graph reasoning is a distinct, scalable, and diagnosis-rich evaluation substrate, and that GraphVerse is a valid instrument for it. Its central design move is to keep the rendered graph image itself as the active evidence: the four GIE strategies damage, split, highlight, or recolor the visualization while preserving the semantic graph, so a correct answer requires the model to re-read and update its structural understanding from the image. The paper then reports three headline findings: current frontier MLLMs are far below human performance, with the best models losing about 35% on average and scoring below 10% on paired-image Maximum Common Subgraph; paired-image reasoning is much harder than single-image reasoning across every model family; and step-level scoring shows that vision-based reasoning errors, not perception or text errors, dominate the failures. The paper also claims that the supervision induced by GraphVerse transfers: reinforcement learning on GIE-augmented data improves accuracy on MathVista, suggesting the trained ability is general visual reasoning rather than graph knowledge.

Load-bearing premise

The benchmark's scores depend on the scoring model being able to break a free-form answer into its key reasoning steps and compare each step against the true graph facts, so if that step extraction or comparison is unreliable, the reported reasoning-error rates are not trustworthy.

Editorial extensions

If this is right

Even the strongest current MLLMs remain far from human-level visual graph reasoning: on average they trail human baselines by about 35%, and on paired-image Maximum Common Subgraph most models score below 10% accuracy.
The dominant failure mode is vision-based reasoning, not perception: across representative models, visual reasoning errors account for roughly half of all incorrect responses, and this share grows as perception improves.
Paired-image visual graph reasoning is substantially harder than single-image reasoning, with frontier models losing more than half their accuracy, suggesting cross-image structural alignment is a distinct unmet capability.
Final-answer accuracy can misrepresent reasoning quality: VGR-Score often exceeds accuracy by 30–40% on hard tasks, showing partially correct reasoning, and can fall below accuracy for strong models, revealing unstable reasoning processes.
If GraphVerse's measurements hold, GIE-augmented training data is a useful supervision source: reinforcement learning with such data improves in-domain accuracy and transfers to MathVista, with larger gains than training without GIE.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural reading is that the GIE strategies are not only evaluation tools but also a data-augmentation recipe that forces a model to update its internal graph representation after an image-level change; this could be tested by measuring whether GraphVerse-trained models become more robust to arbitrary visual corruption of relational diagrams beyond graphs.
Because VGR-Score verifies reasoning against programmatically verbalized graph evidence rather than against the rendered image, it may reward a model that states the correct graph in language while under-penalizing internally consistent-but-wrong perception; a sharper metric would additionally score the model's stated node and edge reading against the actual image content.
The paper leaves more-than-two-image and temporal graph reasoning to future work, but the large paired-image drop suggests this is a challenging frontier; extending GIE to temporal edits, such as edge insertions and deletions over time, is a natural next step.
Since task difficulty is controlled by graph size and editing type, GraphVerse's difficulty scaling is cheap and programmatic; a practical extension would be a curriculum that increases both topological and visual complexity, making visual graph reasoning a scalable training signal for general multimodal models.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

Read GraphVerse. Bottom line: it is a genuinely useful benchmark, and the headline finding survives scrutiny. The process-score story is softer than the paper's tone suggests.

What is actually new: the first visual graph reasoning benchmark with paired-image tasks, four graph-centric image editing operations that are real structural interventions rather than caption perturbations, and a process-sensitive metric built on deterministic verbalization of graph evidence. The construction is careful — ground truth comes from standard graph solvers, the evidence given to the judge is programmatic, and the accuracy numbers from 19 models clearly show MLLMs far below human level on visual graph reasoning, with near-zero MCS accuracy and a 35% average gap. That result does not depend on the LLM judge and will be cited.

The paper also earns credit for the GIE training ablation and the MathVista transfer control. Those are the right experiments to run, and they support the claim that the editing operations add something beyond simple text transcription.

The soft spots are real but localized. The VGR-Score judge is validated on only five of eleven tasks — Diameter, Shortest Distance, Cycle, Coloring, GED — and those are exactly the tasks where the judge is checking graph-traversal statements rather than certifying NP-hard optimality. TSP, MCP, MVC, and MIS, where VGR-S diverges most from accuracy and where the judge must verify optimality from a verbalized adjacency list on up to 15 nodes, are absent from the human-agreement and judge-swap studies. With only 25 samples per task and no step-level inter-annotator agreement, the claim that VGR-S "implies partially correct reasoning on hard tasks" is under-supported. The accuracy gap is solid; the process interpretation for hard tasks is not yet.

There is no circularity problem: GIE effectiveness is checked against a no-GIE control and independent transfer, and the self-citations are not load-bearing. The main fixable weakness is the missing judge validation on the optimization-heavy tasks. I would also want repeated runs before trusting the small GIE gains, but that is a minor point.

Recommendation: send it to peer review. A serious referee should push the authors to extend Appendix D to TSP, MCP, MVC, and MIS, and to report step-level agreement. The benchmark itself is worth having even if the process metric needs another round of evidence.

For my own use: I would bring it to reading group and cite the accuracy findings, not the process metric as it stands.

Referee Report

3 major / 5 minor

Summary. The paper introduces GraphVerse, a benchmark for visual graph reasoning in multimodal large language models, comprising 11,000 samples (with a 1,060-sample testmini) across nine single-image tasks and two paired-image tasks grounded in real-world graph sources. The benchmark contributes four graph-centric image editing (GIE) strategies that modify graph images while preserving semantic structure, and VGR-Score, a process-sensitive metric computed by an LLM judge that scores extracted reasoning steps against programmatically verbalized graph evidence. Experiments on 19 MLLMs and three text-only description-to-LLM baselines report large gaps between current MLLMs and human annotators, substantially higher VGR-Score than accuracy on many NP-hard tasks, improvements from PoT prompting and from SFT/RL training with GIE-augmented data, and transfer gains on MathVista.

Significance. If the central claims hold, GraphVerse would be a valuable addition to MLLM evaluation: the ground-truth answers come from standard graph solvers, the GIE strategies are well-motivated and target distinct reasoning faculties, and the ablation design includes a no-GIE training control and an independent MathVista transfer check. The programmatic verbalization of graph evidence is a genuinely useful design choice because it removes the need for a vision-capable judge. The main contribution at risk is VGR-Score as a diagnostic of partial reasoning: its human-agreement and judge-robustness evidence covers only five of the eleven tasks, and the largest VGR-Score/accuracy divergences occur precisely in the excluded NP-hard tasks. The accuracy-based findings, including the large MLLM-human gaps and the paired-image difficulty, are programmatically verifiable and do not depend on the judge. The paper ships code and detailed prompts, which strengthens reproducibility.

major comments (3)

[Sec. 4.4 / Algorithm 5; Appendix D.1-D.2; Sec. 5.2] The central diagnostic claim that VGR-Score reveals 'partially correct reasoning despite incorrect final answers' (Sec. 5.2) is load-bearing for the paper, but the VGR-Score validation covers only five tasks: Diameter, SD, Cycle, Coloring, and GED. The excluded tasks TSP, MCP, MVC, MIS, and MCS are exactly those where the judge must certify NP-hard optimality or subgraph isomorphism from a verbalized adjacency list, and where Table 1 shows the largest VGR-S minus Acc gaps (e.g., DeepSeek-V4-Pro TSP: 3.9 Acc vs. 34.2 VGR-S; Gemini-3-Pro MCS: 6.0 Acc vs. 34.3 VGR-S). Without human-agreement or judge-swap evidence on these tasks, and with only 25 samples per task, the claim that VGR-S exceeds accuracy by 30-40% and thereby implies partially correct reasoning is unverified for precisely the tasks on which the metric's added value rests. I recommend either extending the Appendix D studies to TSP, MCP, MVC, MIS, and MCS, or explicitly restricting the process-sensitivity claims to the five validated tasks.
[Sec. 5.1 / Table 6; Sec. 5.3 / Table 3] All experimental comparisons are based on a single run, and the testmini uses only 25 samples per task-GIE cell (Table 6). Several headline improvements are therefore within the range of ordinary sampling noise: for example, Table 3 reports an RL paired-image improvement of 16.1 absolute points on Qwen3-VL-8B, which corresponds to about four samples, and Table 4 reports overall MathVista gains of 0.31 and 1.10 points. Without confidence intervals, bootstrap estimates, or multiple seeds, claims such as 'RL brings a 13.6% gain over SFT' and 'What transfers from GraphVerse is not graph knowledge, but reasoning itself' are not statistically supported. I request error bars or a statistical test for the main comparative claims, or a softening of the quantitative language.
[Sec. 5.3 / Table 3; Sec. E.3 / Table 13] The claim that 'post-training with GIE-augmented data yields larger gains than a matched no-GIE training set' is not consistently supported across settings. In Table 3, for Qwen3-VL-8B, RL with GIE achieves 16.1 on Paired Image while RL w/o GIE achieves 17.5; for Qwen3-VL-2B, RL with GIE achieves 1.8 on Paired Image while RL w/o GIE achieves 2.2. The aggregate averages favor GIE, but the paired-image subcategory shows a negative or null effect of GIE. Because GIE effectiveness is a central contribution, the paper should either explain this per-setting inconsistency, report the comparison with error bars, or qualify the aggregate claim.

minor comments (5)

[Appendix D.1 / Table 9] The human-agreement study uses two annotators and reports only the mean difference between LLM-judge and manual scores; no inter-annotator agreement (e.g., Cohen's kappa) is provided, making it hard to interpret whether the 'strong agreement' is between the judge and humans or merely between the two humans.
[Appendix E.6] The human reference baselines in Table 1 appear to come from two PhD annotators, but no per-task variance or inter-annotator reliability is reported for the NP-hard tasks, despite those tasks having the largest model-human gaps.
[Sec. 5.1 / Table 1] The row 'MLLM Description=>LLMs' is difficult to interpret in Table 1 because the number of models differs from the main MLLM list and the procedure is only fully described in Appendix E.3; a one-sentence pointer in the main text would help.
[Appendix G / Figure 12] There is a typo in the Figure 12 prompt: 'patch-fliped' should be 'patch-flipped'.
[Sec. 4.2 / Table 7] The task labels 'Poly' and 'NPH' are not defined in a table or glossary; the reader must infer them from the text in Sec. 4.2. A short definition or table footnote would improve accessibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No material circularity: benchmark answers are programmatically verified, VGR-Score is a metric rather than a fitted prediction, and GIE validation includes an external MathVista transfer control.

full rationale

GraphVerse's central claims—that MLLMs underperform on visual graph reasoning and that VGR-Score exposes process-level failures—do not reduce to their inputs. Final-answer accuracy is computed by programmatic solvers on the underlying graph (Sec. 4.1, Problem 3.1), not fitted to any model output. VGR-Score (Sec. 4.4, Algorithm 5) is a weighted combination of a step-consistency check against deterministically verbalized graph evidence E* and a final-answer match; it is a metric, not a prediction, and no parameter is fitted to the quantities it later 'predicts.' The GIE effectiveness claim is supported by a matched no-GIE training control and by out-of-domain transfer on MathVista (Sec. 5.5, Table 4), which is external to the benchmark. Self-citations (e.g., Sun et al. 2025, 2026a,b; Yang et al. 2026) appear only in related-work context and are not load-bearing. The App. D robustness study covers only five of eleven tasks, leaving the judge-based metric less validated on the hardest NP-hard tasks (TSP, MCP, MVC, MIS); this is a limitation of evidence, not a circular reduction, because the metric's definition does not presuppose the conclusion it is used to draw.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The benchmark introduces no fitted physical parameters. The main hand-chosen constants are the VGR-Score weight lambda=0.7, the 3x3 patch grid, and per-task node ranges. The central claims rest on domain assumptions about rendering completeness, semantic preservation of edits, and the fidelity of an LLM judge to human reasoning quality. No new physical entities are proposed.

free parameters (3)

lambda (VGR-Score weight) = 0.7
Hand-set weight in VGR-Score between step correctness R_step and final answer correctness. Chosen following prior work (Sec. 4.4). Scores shift with lambda, so the metric is not parameter-free, though the paper's main conclusions are only reported under lambda=0.7.
patch grid size r = 3 (3x3 tiles)
GIE patch perturbation uses an r x r grid with r=3 in all prompts. Chosen by the authors; affects task difficulty but is not fitted to data.
node count ranges per task = e.g., TSP 7-9, Cycle 6-10, GED 4-8 (Table 7)
Sampled graph sizes are hand-chosen to keep tasks tractable and comparable to prior text-based graph benchmarks. The difficulty-scaling claims in Appendix F rest on these ranges.

assumptions (5)

standard math Programmatic graph solvers on the known underlying graph produce correct gold answers for all tasks, including NP-hard ones on small node ranges.
Problem 3.1 defines y=S(G) and gold labels are computed by Python solvers (Sec. C.3). Exact solvers are tractable because Table 7 caps nodes at 15.
domain assumption GraphViz rendering is information-complete and unambiguous: all structure and attributes needed to solve the task are visually decodable, and no graph evidence is duplicated in the text prompt.
Sec. 4.1 Principle (b). If rendering were ambiguous, low model scores could be perception artifacts, not reasoning failures.
domain assumption The GIE operations preserve the underlying graph semantics: after the required mental reconstruction, the edited image still determines the same graph and task answer.
Sec. 4.3. Patch flip/swap assumes unique recovery, attentional focusing assumes the highlighted component is identifiable, and recoloring assumes spatial directions are computable from circle centers. If false, tasks test restoration rather than reasoning.
domain assumption An LLM judge, given deterministic verbalized graph evidence, can accurately extract key reasoning steps and judge their consistency with the evidence.
Sec. 4.4 and Algorithm 5. All process-level claims rest on this, mitigated only by Appendix D robustness analyses on a few tasks.
domain assumption The two Ph.D. volunteer annotators provide an unbiased human reference score for each task.
Sec. E.6 and Table 9. No inter-annotator agreement or full annotation protocol is reported, yet human numbers anchor the claim that models trail humans.

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Cite this review

Pith. "Pith review of GraphVerse: A Comprehensive Visual Graph Reasoning Benchmark for Multimodal Large Language Models." pith.science (2026). https://pith.science/paper/GL75NDD7

@misc{pith2026260806769,
  author       = {Pith},
  title        = {Pith review of: GraphVerse: A Comprehensive Visual Graph Reasoning Benchmark for Multimodal Large Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GL75NDD7}},
  note         = {Machine review of arXiv:2608.06769}
}

read the original abstract

Recent Multimodal Large Language Models (MLLMs) have achieved remarkable progress across diverse vision-language tasks, creating an urgent need for more challenging benchmarks. Yet existing evaluations still provide limited insight into whether these models can truly reason over structured visual information. Visual Graph Reasoning (VGR) offers a compelling testbed for this challenge, requiring models to integrate perception, structural understanding, and multi-step reasoning over graph-based visual inputs. However, prior VGR benchmarks often reduce the task to visual perception followed by text-based reasoning, restrict evaluation to single-image settings, rely on answer-only metrics, and underrepresent realistic graph-centric scenarios. To bridge the gap, we introduce GraphVerse, a unified benchmark that jointly evaluates perception, visual reasoning, and text-based graph reasoning in MLLMs under both single-image and paired-image settings. At its core is a suite of Graph-centric Image Editing (GIE) strategies that modify graph images while preserving their semantics, turning them into active tests of visual reasoning. We further propose VGR-Score, a process-sensitive metric that evaluates reasoning quality beyond final-answer accuracy. Extensive experiments reveal several key limitations of current MLLMs in VGR, while also validating the effectiveness of GIE strategies and the transferability of GraphVerse to broader multimodal reasoning capabilities. The code is available at https://github.com/sunyuanfu/GraphVerse.

Figures

Figures reproduced from arXiv: 2608.06769 by the authors.

**Figure 2.** Radar chart of model performance on VGR under different GIE operations. P- and S- denote PairedImage and Single-Image VGR, respectively. 5.2 Overall Results ▶ Visual graph reasoning remains a major challenge for MLLMs. Even the strongest current models, including Gemini-3-Pro and GPT-5.2, still leave substantial room for improvement on many VGR tasks. For example, on MCS, their accuracy remains below 10%, and they… view at source ↗

**Figure 3.** Pie Chart of Failure Mode Analysis for Rep [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (11 more)

**Figure 4.** Figure 4: Visualization examples of four graph-centric image editing operations across different graph sizes. Within [PITH_FULL_IMAGE:figures/full_fig_p023_4.png]

**Figure 5.** Figure 5: A visual graph reasoning case under spatially-conditioned recoloring, where the model identifies a [PITH_FULL_IMAGE:figures/full_fig_p025_5.png]

**Figure 6.** Figure 6: Rendered Graph of Figure [PITH_FULL_IMAGE:figures/full_fig_p026_6.png]

**Figure 8.** Figure 8: A visual graph reasoning case under spatially-conditioned recoloring, where the model identifies a [PITH_FULL_IMAGE:figures/full_fig_p027_8.png]

**Figure 9.** Figure 9: A graph edit distance prompt for molecular graph alignment under restored visualization layouts [PITH_FULL_IMAGE:figures/full_fig_p027_9.png]

**Figure 10.** Figure 10: Graph Edit Evidence Image-Pair [PITH_FULL_IMAGE:figures/full_fig_p028_10.png]

**Figure 12.** Figure 12: Prompt: Longest Relationship Chain - DBPedia Knowledge Graph [PITH_FULL_IMAGE:figures/full_fig_p029_12.png]

**Figure 13.** Figure 13: Prompt: Shortest Relationship Chain in Knowledge Graph [PITH_FULL_IMAGE:figures/full_fig_p030_13.png]

**Figure 14.** Figure 14: Prompt: Maximum Independent Set for Social Influence Network [PITH_FULL_IMAGE:figures/full_fig_p031_14.png]

**Figure 15.** Figure 15: Prompt: Common Neighbors in Co-authorship Network [PITH_FULL_IMAGE:figures/full_fig_p032_15.png]

**Figure 16.** Figure 16: Prompt: Airline Route Optimization (TSP) [PITH_FULL_IMAGE:figures/full_fig_p033_16.png]

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Reference graph

Works this paper leans on

14 extracted references · 8 canonical work pages

[1]

patch-swap

Structural Analysis.Molecule A (Image 1):Based on the visual cues and “patch-swap” description, the image consists of patches containing nodes labeled 0(C), 1(C), 2(C), 3(C), 4(O), and 5(O). For connectivity tracing, in the top-right region, 1(C) (blue) is connected to 0(C) (pink). In the middle region, 0(C) connects to 3(C) (green), and 3(C) connects to ...

work page
[2]

For node mapping, the only perfect match is A0 (C, Pink) with B2 (C, Pink), so mapping A0 -> B2 has cost 0

Graph Edit Distance Calculation.We assume a cost of 1 for any node substitution if the element or color differs, and a cost of 1 for any edge insertion or deletion. For node mapping, the only perfect match is A0 (C, Pink) with B2 (C, Pink), so mapping A0 -> B2 has cost 0. All other mappings involve a mismatch in element, color, or both, so A1, A2, A3, A4,...

work page
[3]

edit_distance:␣{min_cost};␣mapping:␣{best_mapping}

Python Solution. import networkx as nx import itertools def solve_ged(): nodes_A = { 0: {'elem':'C','color':'Pink'}, 1: {'elem':'C','color':'Blue'}, 2: {'elem':'C','color':'Yellow'}, 3: {'elem':'C','color':'Green'}, 4: {'elem':'O','color':'Pink'}, 5: {'elem':'O','color':'Blue'} } edges_A = [(1,0), (0,3), (3,2), (2,5), (5,4)] nodes_B = { 0: {'elem':'Cl','c...

work page
[4]

The optimal mapping aligns the single matching Carbon atom (A0 -> B2) and maps the rest to minimize structural disruption

Result.Running the analysis confirms the minimum edit distance is 7. The optimal mapping aligns the single matching Carbon atom (A0 -> B2) and maps the rest to minimize structural disruption. Final Answer:edit_distance: 7; mapping: [2, 3, 0, 1, 4, 5] 26 Figure 8: A visual graph reasoning case under spatially-conditioned recoloring, where the model identif...

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Qwen Team

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(2) Claimed Molecule A connectivity: chain 1–0–3–2–5–4 (edges (1,0), (0,3), (3,2), (2,5), (5,4))

Key Operations:(1) Claimed Molecule A node labels/elements: nodes 0–5 are 0:C, 1:C, 2:C, 3:C, 4:O, 5:O. (2) Claimed Molecule A connectivity: chain 1–0–3–2–5–4 (edges (1,0), (0,3), (3,2), (2,5), (5,4)). (3) Stated Structure A is the linear chain 1–0–3–2–5–4. (4) Listed Molecule A node attributes (colors) for nodes 0–5. (5) Claimed Molecule B node labels/el...

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Therefore, steps (1), (4), and (5) are unsupported

Judge Analysis:The model’s node labels/elements and colors for both graphs are invented and do not match the provided Graph A and Graph B descriptions, which use the color roles mint, lemon, sky, rose, peach, etc., together with specific edge lists. Therefore, steps (1), (4), and (5) are unsupported. The true Graph A is a 6-node path 0–1–2–3–4–5, with edg...

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Judge Feedback Question Prompt:You are comparing two molecular graphs to brief medicinal chemists on structural alignment

Final Judge Result:Reasoning Steps: [0,0,0,0,0,0,0,0,0,0,0,0]; Final Answer: 0/1 Figure 9: A graph edit distance prompt for molecular graph alignment under restored visualization layouts (Question). Judge Feedback Question Prompt:You are comparing two molecular graphs to brief...
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OpenReview.net. Gemini Team, Rohan Anil, Sebastian Borgeaud, Jean- Baptiste Alayrac, Jiahui Yu, Radu Soricut, Johan Schalkwyk, Andrew M Dai, Anja Hauth, Katie Mil- lican, and 1 others. 2023. Gemini: a family of highly capable multimodal models.arXiv preprint arXiv:2312.11805. ...

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

patch-swap

Structural Analysis.Molecule A (Image 1):Based on the visual cues and “patch-swap” description, the image consists of patches containing nodes labeled 0(C), 1(C), 2(C), 3(C), 4(O), and 5(O). For connectivity tracing, in the top-right region, 1(C) (blue) is connected to 0(C) (pink). In the middle region, 0(C) connects to 3(C) (green), and 3(C) connects to ...

work page

[2] [2]

For node mapping, the only perfect match is A0 (C, Pink) with B2 (C, Pink), so mapping A0 -> B2 has cost 0

Graph Edit Distance Calculation.We assume a cost of 1 for any node substitution if the element or color differs, and a cost of 1 for any edge insertion or deletion. For node mapping, the only perfect match is A0 (C, Pink) with B2 (C, Pink), so mapping A0 -> B2 has cost 0. All other mappings involve a mismatch in element, color, or both, so A1, A2, A3, A4,...

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[3] [3]

edit_distance:␣{min_cost};␣mapping:␣{best_mapping}

Python Solution. import networkx as nx import itertools def solve_ged(): nodes_A = { 0: {'elem':'C','color':'Pink'}, 1: {'elem':'C','color':'Blue'}, 2: {'elem':'C','color':'Yellow'}, 3: {'elem':'C','color':'Green'}, 4: {'elem':'O','color':'Pink'}, 5: {'elem':'O','color':'Blue'} } edges_A = [(1,0), (0,3), (3,2), (2,5), (5,4)] nodes_B = { 0: {'elem':'Cl','c...

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[4] [4]

The optimal mapping aligns the single matching Carbon atom (A0 -> B2) and maps the rest to minimize structural disruption

Result.Running the analysis confirms the minimum edit distance is 7. The optimal mapping aligns the single matching Carbon atom (A0 -> B2) and maps the rest to minimize structural disruption. Final Answer:edit_distance: 7; mapping: [2, 3, 0, 1, 4, 5] 26 Figure 8: A visual graph reasoning case under spatially-conditioned recoloring, where the model identif...

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[5] [5]

Qwen Team

Kimi-vl technical report.arXiv preprint arXiv:2504.07491. Qwen Team. 2025. Qwq-32b: Embracing the power of reinforcement learning. 10 Fei Wang, Xingyu Fu, James Y Huang, Zekun Li, Qin Liu, Xiaogeng Liu, Mingyu Derek Ma, Nan Xu, Wenxuan Zhou, Kai Zhang, and 1 others. 2024a. Muirbench: A comprehensive benchmark for ro- bust multi-image understanding.arXiv p...

arXiv 2025

[6] [7]

type": "color_swap

Mme-reasoning: A comprehensive bench- mark for logical reasoning in mllms.arXiv preprint arXiv:2505.21327. Xiang Yue, Yuansheng Ni, Kai Zhang, Tianyu Zheng, Ruoqi Liu, Ge Zhang, Samuel Stevens, Dongfu Jiang, Weiming Ren, Yuxuan Sun, and 1 others. 2024. Mmmu: A massive multi-discipline multimodal un- derstanding and reasoning benchmark for expert agi. InPr...

arXiv 2024

[7] [12]

(2) Claimed Molecule A connectivity: chain 1–0–3–2–5–4 (edges (1,0), (0,3), (3,2), (2,5), (5,4))

Key Operations:(1) Claimed Molecule A node labels/elements: nodes 0–5 are 0:C, 1:C, 2:C, 3:C, 4:O, 5:O. (2) Claimed Molecule A connectivity: chain 1–0–3–2–5–4 (edges (1,0), (0,3), (3,2), (2,5), (5,4)). (3) Stated Structure A is the linear chain 1–0–3–2–5–4. (4) Listed Molecule A node attributes (colors) for nodes 0–5. (5) Claimed Molecule B node labels/el...

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Therefore, steps (1), (4), and (5) are unsupported

Judge Analysis:The model’s node labels/elements and colors for both graphs are invented and do not match the provided Graph A and Graph B descriptions, which use the color roles mint, lemon, sky, rose, peach, etc., together with specific edge lists. Therefore, steps (1), (4), and (5) are unsupported. The true Graph A is a 6-node path 0–1–2–3–4–5, with edg...

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