Dear Dr. Sun,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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Kind regards,

Giridhar Maji, Ph.D.

Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Yes

Reviewer #2: Partly

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2. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: Yes

Reviewer #2: Yes

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3. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #1: Yes

Reviewer #2: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: In this study, the authors propose a novel method for identifying influential nodes that are effective for diffusion in complex networks. This method introduces the concept of exclusive neighboring nodes in addition to conventional neighboring nodes. Numerical experiments demonstrate that this approach can identify nodes that facilitate diffusion more effectively than existing methods.

The introduction of exclusive neighborhoods presents a fresh and intriguing perspective. The effectiveness of this concept has also been validated through numerical experiments.

However, several aspects of the study are not fully explained, which necessitates a major revision.

Major Comments:

1. Clarification of logarithm usage in Equations (4) and (5)

Please provide a detailed explanation of why logarithms are used in these equations. At a minimum, state the advantages of this approach and the reason behind its implementation.

2. Interpretation of the final formula (Equation 9)

The study introduces "exclusive neighboring nodes" as a new perspective for identifying influencers. However, the calculation of this index is quite complex, making it unclear what the final metric truly represents. While specific calculation examples are provided (lines 274–302), it would be more informative to illustrate the network structure of high-ranking influencers based on this metric. In other words, the paper should explicitly clarify which nodes are identified as influencers and how their evaluation is influenced by the introduction of exclusive neighborhoods.

3. Clarification of red and blue numbers in the tables

I could not find an explanation for the meaning of the red and blue numbers in Tables 1, 3, 4, and 5. Please specify what these color distinctions represent.

Minor Comments:

4. Notation consistency in Equation (5)

The term EN(v_j) should be written as EN(v_i, v_j) to maintain consistency with the notation used in Equation (3).

5. Notation clarification in line 285

The term max ND appears to refer to max k_{max}, but the notation should be aligned for consistency throughout the manuscript.

Reviewer #2: This is a really interesting method and a fantastic introduction to the general subject matter. I really enjoyed the introduction and background sections. The method is clearly described; although I think it could be made more concise without losing clarity, I prefer the longer explanation. Small comment there is that the notation "Ks value" for "k-shell" was never introduced.

My main concern with this work is the level of claims for every result section that this method is "superior", "more consistent", etc. I think a little bit more humility would still leave the method looking great (it seems like a great method!), while acknowledging that other methods out-perform it at times. It was a bit tedious to read an enthusiastic claim at the end of every results paragraph. Highlighting some areas where other models out-perform MNEN would seem appropriate, and generally listing comparison metrics for the other models would seem like better use of space than simply listing all the top nodes for each model.

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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.

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Reviewer #1: Yes:  Masaki Chujyo

Reviewer #2: No

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Influential node identification method based on multi-order neighbors and exclusive neighborhood

PONE-D-25-05440R1

Dear Dr. Sun,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Giridhar Maji, Ph.D.

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

Reviewer #1: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions??>

Reviewer #1: Yes

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3. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #1: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

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Reviewer #1: The authors have responded sincerely to the reviewers' comments, and as a result, the paper has been improved. I therefore recommend acceptance.

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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

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