Dear Dr. Vestergaard,

Thank you very much for submitting your manuscript "Compression-based inference of network motif sets" for consideration at PLOS Computational Biology.

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Fabrizio De Vico Fallani

Guest Editor

PLOS Computational Biology

Thomas Serre

Section Editor

PLOS Computational Biology

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Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: see attached file

Reviewer #2: In the manuscript "Compression-based inference of network motif sets", A. Benichou and colleagues propose a framework for motif mining based on lossless network compression using subgraph contractions. They applied this framework to synthetic benchmark and neural connectomes, which allow the evaluation of the collective significance of motif sets in terms of a null model inferred from the data.

Altogether, this represents a valuable contribution to the network and neuroscientific communities. However, certain sections need rephrasing and clarification before acceptance. Below are my comments and suggestions:

- While most of the manuscript is well-written, the abstract, introduction and part of the method could benefit from being more concise. Also, in the introduction and abstract, explicitly mentioning that the approach was first assessed on numerical benchmarks and then applied to neural connectomes would enhance clarity.

- I believe that it would be important to expand on the time and space complexity of the proposed approach, including information about some of the cases reported in the manuscript (e.g. the authors mention the need of storing 1.3 TB of data for the Drosophila connectome). This will offer valuable insights into usability and complexity in practical cases.

- Although the code and scripts used in the manuscript are available on GitHub, providing additional documentation and example cases on how to use the code and perform simple analyses would increase its usability among scientists working on these topics.

- Even though the approach does not allow for overlapping contractions, the motifs identified in the C.elegans connectome could be also linked to recent works on symmetric motifs in C.elegans (e.g. https://www.nature.com/articles/s41467-019-12675-8). Are there any commonalities in the motifs obtained in the manuscript and the symmetric building blocks reported in the paper? If so, this could be useful to strengthen the importance of some of motifs identified in the empirical datasets.

- In addition to the recent work on bayesian stochastic block modeling, the authors might consider exploring parallels with the hierarchical block model discussed in another study (https://journals.aps.org/prx/abstract/10.1103/PhysRevX.4).

Minor Comments:

- Caption Figure 1: "In this example," instead of "In this eample,"

- Figure 2D: Adding a legend explaining the meaning of the colors would improve interpretation.

- Line 210: Correcting "m_{max.}" to "m_{max}"

- Lines 211-213: The paragraph appears to be redundant or repeated.

- Figure labels in Figure 3: Placing them on the side of the figure, as done in other figures, would be ideal.

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: No

Reviewer #2: No

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Attachments

Attachment

Submitted filename: benichou.pdf

Dear Dr. Vestergaard,

We are pleased to inform you that your manuscript 'Compression-based inference of network motif sets' has been provisionally accepted for publication in PLOS Computational Biology.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.

Should you, your institution's press office or the journal office choose to press release your paper, you will automatically be opted out of early publication. We ask that you notify us now if you or your institution is planning to press release the article. All press must be co-ordinated with PLOS.

Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology. 

Best regards,

Fabrizio De Vico Fallani

Guest Editor

PLOS Computational Biology

Thomas Serre

Section Editor

PLOS Computational Biology

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Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: Than you for addressing all the comments and concerns of the reviewers in a constructive manner. I think that this version of the manuscript is an improvement with respect to the previous one that is suitable for publication in PLoS Computational Biology.

Reviewer #2: The authors have successfully addressed all of my concerns. The revised version of the manuscript shows significant improvement compared to the previous version. The manuscript is now much more concise and contains the necessary information to fully comprehend the work they have conducted. As such, I have no further comments on this version of the manuscript.

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: None

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PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No