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REVIEW 3 major objections 6 minor 52 references

Visual Graph Arena: Evaluating Visual Conceptualization of Vision and Multimodal Large Language Models

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read On Visual Graph Arena, humans score 88–100 percent while vision and multimodal LLMs fail at graph isomorphism and most other tasks.

desk verdict A useful new benchmark for layout-shift visual graph reasoning, but the headline claim about missing conceptualization is not established because the design never rules out vision-encoder parsing failure. read the letter →

arxiv 2506.06242 v1 pith:7UULODPI submitted 2025-06-06 cs.CV cs.AI

Zahra Babaiee , Peyman M. Kiasari , Daniela Rus , Radu Grosu This is my paper
classification cs.CVcs.AI
keywords VisualGraphArenaconceptualizationisomorphismmultimodallargelanguagemodelsreasoninglayouttransferHamiltonianpathchordlesscycle
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

The paper introduces Visual Graph Arena, a set of six image-based graph tasks that ask whether a model can recognize the same underlying concept when the drawing changes. It claims that humans do this almost without effort—88 to 100 percent accuracy across tasks—while state-of-the-art vision models and multimodal LLMs mostly fail, particularly at graph isomorphism. The paper interprets these failures as evidence that current models rely on pattern matching rather than representation-invariant conceptual understanding. The contribution is a benchmark that isolates this ability, plus a set of behavioral anomalies that expose when a model's above-chance score is actually a shortcut.

What carries the argument

The load-bearing mechanism is the training/test layout split: graphs are rendered in one layout (Kamada-Kawai or random) for training and in a different layout (planar, Kamada-Kawai, or random) for testing, so any above-chance performance requires recognizing the concept rather than memorizing pixel patterns. The six tasks operationalize conceptualization as classification problems: yes/no isomorphism with an easy random-foil and hard degree-equivalent-foil version, yes/no Hamiltonian path and Hamiltonian cycle presence, and four-choice shortest-path and biggest-chordless-cycle lengths. Human performance on the same images supplies the reference level that defines what conceptualization should look like.

What would settle it

Train the same vision encoders on VGA for substantially more than 10 epochs, or provide them with explicit node and edge coordinate supervision, and test on the planar-layout splits. If accuracy on isomorphism jumps to near-human levels, the reported failure is a layout-parsing or training-budget problem rather than a missing conceptual invariant.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that visual conceptualization—recognizing a graph property regardless of how the graph is drawn—is present in human subjects and largely absent from current AI systems. Across the six VGA tasks, vision models fine-tuned for ten epochs performed at chance on easy and hard isomorphism, and only modestly above chance on Hamiltonian path, shortest path, Hamiltonian cycle, and chordless cycle tasks. Multimodal LLMs, including GPT-o1, GPT-4o, and Claude 3.5 Sonnet, mostly performed at or near random, with GPT-o1's partial success on Hamiltonian cycles traceable to leaf-node detection rather than graph reasoning. The paper frames these results as showing that models display pseudo-intelligent pattern matching rather than genuine understanding.

Load-bearing premise

The load-bearing premise is that near-random accuracy on test graphs drawn in a new layout reflects a lack of conceptual understanding, rather than an inability to parse that unfamiliar drawing style.

Editorial extensions

If this is right

  • Any model trained on VGA's training splits can be scored for layout transfer by comparing its accuracy on the different-layout test splits, giving a direct measure of representation-invariant visual reasoning.
  • Because humans reach 88–100 percent accuracy, the benchmark supplies a concrete performance target that current models do not meet.
  • GPT-o1's Hamiltonian-cycle accuracy being tied to leaf-node detection means above-chance scores on graph tasks should not be taken as genuine understanding without checking for shortcut cues.
  • Datasets and training schemes aimed at human-like visual understanding can use VGA's layout split as a curriculum signal, since the bottleneck appears to be transfer across visual form rather than graph-problem difficulty.

Reading between the lines

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

  • A natural next experiment would apply the same layout-split protocol to molecular drawings and circuit diagrams; the paper's own framing suggests the failure pattern should recur wherever the same structure can be drawn in many ways.
  • The two anomalies (middle scores and easier-worse) can be used as a general diagnostic: any atomic perceptual task where a model scores in the middle and does worse on easy items is likely being solved via shortcut features rather than concept knowledge.
  • The 10-epoch fine-tuning budget leaves open that stronger encoders, higher-resolution input, or explicit layout augmentation might narrow or close the gap, which would shift the explanation from missing conceptualization to insufficient invariance training.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper introduces the Visual Graph Arena (VGA), a benchmark of six graph tasks (easy and hard isomorphism, Hamiltonian path, shortest path, Hamiltonian cycle, biggest chordless cycle) in which the training and test images use different graph layouts (e.g., Kamada-Kawai vs. planar) to test whether models recognize the same graph concept across visual form. The authors fine-tune several vision models (ViT, Swin, ConvNeXt, SigLIP, DINOv2) on the tasks and evaluate MLLMs (GPT-4o, GPT-o1, Claude 3.5 Sonnet, etc.) in zero-shot settings. The reported results show that humans achieve 88–100% accuracy, while vision models fail or perform modestly on cross-layout tests, and most MLLMs perform near chance. The paper interprets these failures as evidence of a lack of 'conceptualization' and of 'pseudo-intelligent pattern matching' rather than genuine understanding.

Significance. If the benchmark is a valid operationalization of visual conceptualization, the results are striking and would constitute a useful diagnostic dataset for layout-invariant visual reasoning. The dataset is large (27k–150k training samples per task) and the layout-shift protocol is a reasonable way to test representation-invariant reasoning. The inclusion of a human baseline is a strength, as is the attempt to isolate path, cycle, and isomorphism concepts. The central negative findings—near-chance performance on cross-layout isomorphism and limited success on other tasks—are broadly consistent across architectures and are likely to be of interest to the vision and multimodal LLM communities. However, the paper's stronger interpretive claims (absence of conceptualization, pseudo-intelligence) rest on assumptions that are not explicitly validated by the experiments as reported.

major comments (3)
  1. [§3.2, §4.1, Appendix C] The central inference—that near-chance cross-layout accuracy demonstrates a lack of representation-invariant conceptualization—requires that the vision models can actually parse the test-layout graphs into nodes and edges. The paper never reports a same-layout control: no model is trained on planar-rendered graphs and tested on planar-rendered graphs, or trained on Kamada-Kawai and tested on Kamada-Kawai. Without such a control, the failure could be attributed to the vision encoder's inability to extract nodes and edges from planar drawings (different edge lengths, crossing patterns, and white-space statistics) rather than to an absence of abstract graph reasoning. Please add the missing control experiments or explicitly weaken the conceptualization claim to a claim about layout-transfer robustness.
  2. [§4.1 and Appendix C] The evaluation protocol violates test-set independence: the paper states that 'we report the best validation accuracy achieved during the training epochs' and that 'the best-performing model on the test set was selected for each task and architecture combination.' Tuning model selection on the test set inflates the reported numbers and makes the benchmark results not reproducible as unbiased estimates. The authors should either use a held-out validation set for early stopping and model selection, or report the last-epoch model's test accuracy, and then report a single, unselected test evaluation.
  3. [§5.1 and §5.3, Table 3] The interpretation of the confusion pattern in Table 3 as evidence of 'pseudo-intelligent pattern matching' is not supported by the data. The 'atomic-task' framing in §5.1 is not justified: shortest-path length is not an atomic skill that an agent either knows completely or not at all, so intermediate accuracy is not anomalous. Moreover, the confusion between lengths 1 and 2 could plausibly arise from a partial ability to count edges or from perceptual errors in the provided graph drawings. The paper should either provide additional control experiments (e.g., testing GPT-o1 on the same planar graph without the node-marking task) or temper the pseudo-intelligence claim to a more descriptive statement about the observed failure modes.
minor comments (6)
  1. [§4, 'Humans'] The human baseline uses only 15 subjects and 24 questions total (four per task). Please report the standard errors or confidence intervals and clarify whether each subject answered all 24 questions; the current sentence is ambiguous.
  2. [Table 2] The 'FAIL' entries are said to indicate near-random performance, but exact numbers are not reported. Please replace the label with the actual accuracy (or a range) so readers can verify that the performance is at chance.
  3. [§5.1] The examples used to motivate the 'Middle-Score Anomaly' (e.g., recognizing numbers ending in zero) are not analogous to the graph tasks, since the graph tasks admit degrees of partial knowledge. Clarify the scope of the anomaly definition.
  4. [§3.2, §4.1, Figure 8, Conclusions] Several typos appear: 'Haminltonian' in §3.2, 'Visaul' in §4.1, 'cordless' in Figure 8, and 'designed designed' in the Conclusions. Please correct these.
  5. [Figure 10 caption] The caption of Figure 10 says 'examples of the easy isomorphism task' but the figure is in the Hard Isomorphism subsection and likely shows hard examples. Please correct the caption.
  6. [Appendix A and Abstract] The dataset URL is given as vga.csail.mit.edu in the abstract but visualgrapharena.com in Appendix A. Please unify the URL and verify that both lead to the same resource.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper reports measured benchmark performance rather than deriving predictions from fitted inputs.

full rationale

This paper is an empirical benchmark paper, not a derivation. Its central claims are statements about measured model performance on a newly constructed dataset, and no predicted quantity is produced by fitting a parameter and then renaming that fit as a prediction. The vision models are fine-tuned on rendered graphs in one layout and tested on held-out graphs in another layout; the reported accuracies are test-set measurements, not quantities forced by construction. The 'conceptualization' construct is explicitly defined as the ability to recognize and reason about the same concept across representational variations, so using layout variation as the test condition is an operationalization of that definition rather than a circular reduction. There are no load-bearing self-citations: references to Kamada-Kawai and Tay et al. are used only for graph-drawing layouts and for the term 'FAIL', respectively. The later 'pseudo-intelligent pattern matching' interpretation is an abductive reading of the observed confusion-matrix anomalies, not a step that reduces to the paper's own inputs. Even if the operationalization is debatable, no equation or fitted parameter makes the conclusion equivalent to the input by construction. The benchmark is also self-contained against external human baselines, which provide independent empirical content. I therefore find no specific circular step that can be quoted and exhibited as a reduction.

Assumptions & free parameters 6 free parameters · 5 assumptions · 1 invented entities

The benchmark's validity rests on hand-selected design choices and several domain assumptions about the meaning of layout transfer, the adequacy of the human baseline, and the sufficiency of the MLLM sample size. The paper provides no sensitivity analysis for these choices, and the pseudo-intelligence construct is an invented explanation without independent falsifiable evidence.

free parameters (6)
  • Number of nodes per graph = 8-9
    Chosen to keep graphs visually readable for humans while generating enough distinct graphs; affects all tasks and the interpretation of failure.
  • Shortest path answer classes = 1, 2, 3, 4
    Chosen to maintain a balanced 4-class dataset; this truncation shapes the confusion matrix used to claim the Easier-Worse Anomaly.
  • Chordless cycle answer classes = 3, 4, 5, 6
    Chosen to keep classes balanced; trees and longer cycles are excluded, affecting task difficulty.
  • Train/test layout pairing = Kamada-Kawai (train) vs planar (test) for path and cycle tasks; random (train) vs random/KK/planar (test) for shortest…
    The central manipulation; the observed failure rates are contingent on this pairing and would change under other pairings.
  • Degree-equivalent false pairs in hard isomorphism = degree-equivalent
    Chosen to remove trivial degree-sequence cues; directly defines what 'hard' means.
  • Training set size per task = 25,000 to 140,000
    Varies across tasks due to graph availability; unequal training budgets could affect whether failure reflects task difficulty or data quantity.
assumptions (5)
  • domain assumption Graph isomorphism, Hamiltonian path/cycle, and chordless-cycle concepts are visually recognizable in 8-9 node drawings at levels humans can solve.
    The entire benchmark assumes human readability; validated only by a 15-subject study with 4 questions per task (Section 4, Humans).
  • domain assumption A vision model that understands a concept should transfer across layouts when fine-tuned on one layout.
    This is the interpretive link from layout-transfer accuracy to conceptualization (Section 3.2). If layout shift introduces a distribution shift that is not part of the 'concept', the inference is unsupported.
  • domain assumption The train/test splits prevent graph overlap (no graph appears in both splits).
    The paper describes this for isomorphism and implicitly for other tasks, but does not provide a formal check; if any training graph appears in test, memorization could contaminate results (Appendix B).
  • domain assumption The MLLM evaluation with 100 samples per task is sufficient to detect conceptual ability.
    The anomaly analysis and the 55% vs 67% accuracies are based on 100 samples; sampling noise can explain the anomalous pattern (Section 4.1).
  • domain assumption Pre-trained vision backbones can learn graph visual reasoning from 10 epochs of fine-tuning on up to 140,000 images.
    The paper does not explore longer training, data augmentation, or alternative architectures; the failure might be a training budget issue (Appendix C).
invented entities (1)
  • pseudo-intelligence
    purpose: Explains GPT-o1's above-random but anomalous performance as imitative-probabilistic reasoning rather than genuine understanding.
    Introduced in Section 5.3 to interpret the Middle-Score and Easier-Worse Anomalies; no independent measurement or falsifiable prediction is given beyond the same confusion matrix used to define the anomalies.

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Cite this review

Pith. "Pith review of Visual Graph Arena: Evaluating Visual Conceptualization of Vision and Multimodal Large Language Models." pith.science (2026). https://pith.science/paper/7UULODPI

@misc{pith2026250606242,
  author       = {Pith},
  title        = {Pith review of: Visual Graph Arena: Evaluating Visual Conceptualization of Vision and Multimodal Large Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7UULODPI}},
  note         = {Machine review of arXiv:2506.06242}
}
read the original abstract

Recent advancements in multimodal large language models have driven breakthroughs in visual question answering. Yet, a critical gap persists, `conceptualization'-the ability to recognize and reason about the same concept despite variations in visual form, a basic ability of human reasoning. To address this challenge, we introduce the Visual Graph Arena (VGA), a dataset featuring six graph-based tasks designed to evaluate and improve AI systems' capacity for visual abstraction. VGA uses diverse graph layouts (e.g., Kamada-Kawai vs. planar) to test reasoning independent of visual form. Experiments with state-of-the-art vision models and multimodal LLMs reveal a striking divide: humans achieved near-perfect accuracy across tasks, while models totally failed on isomorphism detection and showed limited success in path/cycle tasks. We further identify behavioral anomalies suggesting pseudo-intelligent pattern matching rather than genuine understanding. These findings underscore fundamental limitations in current AI models for visual understanding. By isolating the challenge of representation-invariant reasoning, the VGA provides a framework to drive progress toward human-like conceptualization in AI visual models. The Visual Graph Arena is available at: \href{https://vga.csail.mit.edu/}{vga.csail.mit.edu}

Figures

Figures reproduced from arXiv: 2506.06242 by the authors.

Figure 1
Figure 1. Examples of different visual representations of identical concepts across different scientific and technical domains. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Illustration of a single graph displayed in three distinct visualization layouts to highlight the impact of graphical [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Overview of the ’Visual Graph Arena Benchmark’ detailing the division of tasks into categories of Graph [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (22 more)
Figure 4
Figure 4. Figure 4: Two non-isomorphic degree-equivalent graphs with the degree sequence of {3, 3, 2, 2, 1, 1}. Hard: The hard category intensifies the challenge by se￾lecting graph pairs that are degree-equivalent. These pairs are visually different but share identical numbers of edges a…
Figure 6
Figure 6. Figure 6: An example for the biggest-chordless-cycle prob [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 5
Figure 5. Figure 5: Example of a Hamiltonian path, a path that visits [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 7
Figure 7. Figure 7: Breakdown of the performance comparison of [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Overview of the directory structure of the Visual Graph Arena benchmark. [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: Examples of the easy isomorphism task with true and false labels. [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Examples of the easy isomorphism task with true and false labels. [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]
Figure 11
Figure 11. Figure 11: Examples of the shortest path task between marked nodes. [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]
Figure 12
Figure 12. Figure 12: Examples of the Hamiltonian path task with true and false labels. [PITH_FULL_IMAGE:figures/full_fig_p015_12.png]
Figure 13
Figure 13. Figure 13: Examples of the Hamiltonian cycle task with true and false labels. [PITH_FULL_IMAGE:figures/full_fig_p016_13.png]
Figure 14
Figure 14. Figure 14: Examples of the biggest chordless cycle task. [PITH_FULL_IMAGE:figures/full_fig_p016_14.png]
Figure 15
Figure 15. Figure 15: The three graphs we asked the LLMs to generate the adjacency matrix. [PITH_FULL_IMAGE:figures/full_fig_p017_15.png]
Figure 16
Figure 16. Figure 16: reconstructed graphs from the generated adjacency matrix by GPT-4o. [PITH_FULL_IMAGE:figures/full_fig_p017_16.png]
Figure 17
Figure 17. Figure 17: reconstructed graphs from the generated adjacency matrix by Claude 3.5 Sonnet. [PITH_FULL_IMAGE:figures/full_fig_p018_17.png]
Figure 18
Figure 18. Figure 18: reconstructed graphs from the generated adjacency matrix by Claude 3 Opus. [PITH_FULL_IMAGE:figures/full_fig_p018_18.png]
Figure 19
Figure 19. Figure 19: reconstructed graphs from the generated adjacency matrix by GPT o1. [PITH_FULL_IMAGE:figures/full_fig_p019_19.png]
Figure 20
Figure 20. Figure 20: The input image, the answer is ’Yes’ Claude 3.5 Sonnet Output: To determine if these graphs are isomorphic, I’ll analyze their structures: Left graph: • 9 vertices • 10 edges • Degree sequence: 3, 3, 3, 2, 2, 2, 2, 2, 1 Right graph: • 9 vertices • 10 edges • Degree se…
Figure 21
Figure 21. Figure 21: The input image, the answer is ’No’ GPT-4o Output: To determine if the two graphs are isomorphic, I will analyze the structural properties of each graph, such as the number of vertices, edges, and the degree of each vertex, and compare them. Step 1: Count the vertices…
Figure 22
Figure 22. Figure 22: The input image, the answer is ’Yes’ GPT-4o Output: To determine whether the graph has a Hamiltonian cycle (a cycle that visits every vertex exactly once and returns to the starting vertex), we need to consider the structure of the graph and see if such a cycle can be…
Figure 23
Figure 23. Figure 23: The input image, the answer is ’3’ 27 [PITH_FULL_IMAGE:figures/full_fig_p027_23.png]
Figure 24
Figure 24. Figure 24: The input image, the answer is ’Yes’ GPT-4o Output: To determine if the given graph has a Hamiltonian path, I will visually inspect the graph. A Hamiltonian path is a path in a graph that visits each vertex exactly once. Upon inspecting the graph: 1. I identified the …
Figure 25
Figure 25. Figure 25: The input image, the answer is ’1’ GPT-4o Output: To find the shortest path between the two square nodes in the graph, we can visually inspect the connections between the nodes. Looking at the image: 1. Start from the square node on the left side of the graph. 2. Ther…

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Reference graph

Works this paper leans on

52 extracted references · 49 canonical work pages

  1. [1]

    Number of vertices: Both graphs have the same number of vertices

    work page

  2. [2]

    Goyal, Y ., Khot, T., Summers-Stay, D., Batra, D., and Parikh, D

    URL https://openreview.net/forum? id=LdRZ9SFBku. Goyal, Y ., Khot, T., Summers-Stay, D., Batra, D., and Parikh, D. Making the v in vqa matter: Elevating the role of image understanding in visual question answer- ing. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 6904–6913, 2017. Guetta, N. B., Slobodkin, A., Maimon,...

    work page 2017

  3. [3]

    Gupta, T

    URL https://openreview.net/forum? id=hwbRjslR5N. Gupta, T. and Kembhavi, A. Visual programming: Compo- sitional visual reasoning without training. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 14953–14962, 2023. Han, C., Mao, J., Gan, C., Tenenbaum, J., and Wu, J. Vi- sual concept-metaconcept learning. Advances ...

    arXiv 2023

  4. [4]

    Morris, C., Kriege, N

    URL https://openreview.net/forum? id=loJM1acwzf. Morris, C., Kriege, N. M., Bause, F., Kersting, K., Mutzel, P., and Neumann, M. Tudataset: A collection of bench- mark datasets for learning with graphs. arXiv preprint arXiv:2007.08663, 2020. Murphy, R., Srinivasan, B., Rao, V ., and Ribeiro, B. Re- lational pooling for graph representations. In Interna- t...

    arXiv 2007

  5. [5]

    Go down to the bottom point of the rightmost triangle

    work page

  6. [6]

    Move up to the right point of that triangle

    work page

  7. [7]

    Number of edges: Both graphs also have the same number of edges

    work page

  8. [8]

    tree-like

    Vertex degrees: The degrees of corresponding vertices (number of edges connected to each vertex) should be the same. However, upon visual inspection, the structure of the graphs seems to differ significantly. The graph on the right has a more symmetrical structure, while the graph on the left appears more irregular. Specifically, the arrangement of connec...

    work page

Show all 52 references
  1. [9]

    The left graph is more densely interconnected, with multiple triangles and a more compact shape

  2. [10]

    The right graph has a more stretched out, less symmetrical structure

  3. [11]

    The degree distribution (number of edges connected to each vertex) seems different between the two graphs

  4. [12]

    These structural differences suggest that there is no one-to-one mapping that could transform one graph into the other while preserving all connections

    The left graph appears to have more cycles than the right graph. These structural differences suggest that there is no one-to-one mapping that could transform one graph into the other while preserving all connections. Given these observations, my conclusion is that these graph...

  5. [13]

    The same number of vertices

  6. [14]

    The same number of edges

  7. [15]

    Equivalent connectivity between corresponding pairs of vertices Comparing the two given graphs:

  8. [16]

    So this condition is satisfied

    Number of vertices: Both graphs appear to have 6 vertices each. So this condition is satisfied

  9. [17]

    Edge count matches

    Number of edges: I count 9 edges in the graph on the left, and 9 edges in the graph on the right as well. Edge count matches

  10. [18]

    We’d need to find a one-to-one mapping between the vertices of the two graphs, such that the edge connections are preserved

    Vertex connectivity: This is trickier to verify visually. We’d need to find a one-to-one mapping between the vertices of the two graphs, such that the edge connections are preserved. One potential mapping: Left graph vertex (from top) 1 → 1, 2 → 2, 3 → 6, 4 → 5, 5 → 4, 6 → 3 o...

  11. [19]

    Visit all 9 vertices

  12. [20]

    Use only existing edges

  13. [21]

    Return to the starting point

  14. [22]

    • The graph is not fully connected - it has a “pinched” middle section

    Visit each vertex only once (except the start/end) Looking at the graph structure: • There are several vertices with only two connections, which limits path options. • The graph is not fully connected - it has a “pinched” middle section. • There’s no obvious circular path that...

  15. [23]

    The graph has 6 vertices

  16. [24]

    Each vertex has a degree (number of edges connected to it) of at least 2

  17. [25]

    induced cycle,

    It appears that we can trace a path that visits each vertex exactly once and returns to the starting point. One possible Hamiltonian cycle in this graph could be: Start at any vertex, move to an adjacent vertex, then continue moving to unvisited adjacent vertices until all ver...

  18. [26]

    Identify all cycles: We need to identify all the possible cycles in the graph

  19. [27]

    Determine if they are chordless: For each cycle, check if there are any extra edges (chords) connecting non-consecutive vertices in the cycle. Observation from the Image: Looking at the graph, a few potential cycles stand out: • Cycle 1: Going through five points that seem to ...

  20. [28]

    The cycle involving the five vertices appears to be the largest cycle

  21. [29]

    Conclusion: The biggest chordless cycle in this graph consists of 5 vertices

    There are no additional edges (chords) connecting non-consecutive vertices in this cycle, making it a chordless cycle. Conclusion: The biggest chordless cycle in this graph consists of 5 vertices. Thus, the final answer is 5 . Claude 3.5 Sonnet Output: To find the biggest chor...

  22. [30]

    First, I’ll identify all cycles in the graph

  23. [31]

    Then, I’ll check each cycle to see if it has any chords (edges connecting non-adjacent vertices within the cycle)

  24. [32]

    induced”) cycle is to look around the “outer rim

    Among the chordless cycles, I’ll determine the largest one. After analyzing the graph: • There are several triangles (3-cycles), but these are too small to be the answer. • I can see a few 4-cycles, but upon closer inspection, they all have chords. • The largest cycle I can fi...

  25. [33]

    I identified the vertices and observed the connections between them

  26. [34]

    Given the structure of the graph, it appears that there is no such path that visits every vertex exactly once without retracing any edge or missing any vertex

    I checked if there’s a path that visits every vertex exactly once. Given the structure of the graph, it appears that there is no such path that visits every vertex exactly once without retracing any edge or missing any vertex. Final answer: No 30 Visual Graph Arena Claude 3.5 ...

  27. [35]

    Begin at the leftmost point

  28. [36]

    Move right to the next point

  29. [37]

    Go up to the top of the leftmost triangle

  30. [38]

    Move right to the center point of the graph

  31. [41]

    Go to the top point of the rightmost triangle

  32. [42]

    Therefore, the graph does have a Hamiltonian path

    End at the uppermost point of the graph This path visits all 8 vertices exactly once, without repeating any vertex. Therefore, the graph does have a Hamiltonian path. Yes Claude 3 Opus Output: To determine whether the given graph has a Hamiltonian path, I’ll analyze its struct...

  33. [43]

    Start from the square node on the left side of the graph

  34. [44]

    There is a direct connection to the node above it

  35. [45]

    Therefore, the shortest path consists of two edges

    From this node, there is a connection to the square node on the right side. Therefore, the shortest path consists of two edges. The final answer is 2 . 32 Visual Graph Arena Claude 3.5 Sonnet Output: To find the shortest path between the two square nodes in this graph, I’ll co...

  36. [46]

    A direct path that goes through the center node of the graph

  37. [47]

    The direct path through the center is clearly shorter

    A path that follows the outer edges of the graph. The direct path through the center is clearly shorter. It requires traversing only 2 edges:

  38. [48]

    From the first square node to the center node

  39. [49]

    Therefore, the shortest path between the two square nodes in this graph is 2

    From the center node to the second square node The path along the outer edges would require traversing at least 3 edges. Therefore, the shortest path between the two square nodes in this graph is 2 . Claude 3 Opus Output: The image shows a graph with 6 nodes, where 2 nodes are...

  40. [50]

    Starting from the top square node, there are two possible paths: down-left or down-right

  41. [51]

    Following the down-left path: Square → Circle → Square This path has a length of 2 edges

  42. [52]

    Therefore, the shortest path between the two square nodes goes through the down-left path, with a length of 2 edges

    Following the down-right path: Square → Circle → Circle → Circle → Square This path has a length of 4 edges. Therefore, the shortest path between the two square nodes goes through the down-left path, with a length of 2 edges. The shortest path between the two square nodes is 2...

  43. [2021]

    The image presented contains a graph. Please transcribe this graph’s adjacency matrix

    URL https://openreview.net/forum? id=qVyeW-grC2k. Wang, K., Pan, J., Shi, W., Lu, Z., Ren, H., Zhou, A., Zhan, M., and Li, H. Measuring multimodal mathematical reasoning with MATH-vision dataset. In The Thirty-eight Conference on Neural Information Processing Systems Datasets ...

    2024 arXiv

  44. [2024]

    Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., and Houlsby, N

    URL https://openreview.net/forum? id=YMAU2kJgzY. Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., and Houlsby, N. An image is worth 16x16 words: Transformers for image rec...

    2020

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.