Content of review 1, reviewed on December 23, 2022

The authors analyze the problem of influential spreaders in networks in terms of Trophic Analysis. They show that a network's directionality is fundamental to information spreading and is associated with localization.
The paper is well written, and the results are essential to understand the evolution of dynamic processes in directed networks. Therefore, I suggest publication after the authors address some minor issues.
Equation 2 has no reference. Do the authors propose it in the paper? If it does, please clarify.
In equation 2, how v is defined? Please clarify the relation's motivation in equation 2, with some examples.
In the paragraph after equation 3, the authors mention the extreme cases of the hierarchical level. What are these extremes?
In equation 4, please explain the meaning of h.
In equation 5, what is h? Also, it is not clear how the networks are constructed according to the model. Please, explain better and provide some examples (maybe some plots).
In Figure 1, how was the network generated and with which hyperparameters?
In figure 2, which is the value of the coupling strength K? Why did the authors consider 20% of the nodes? How does this percentage influence the results?
In equation 9, what is n?
In figure 11, is it possible to include other networks? For example, a cortical network and a social one, since these networks are associated with information spreading.
There is a typo in the caption of figure 12.

Source

    © 2022 the Reviewer.

Content of review 2, reviewed on July 22, 2023

The authors improved the paper, and the current version is ready for publication. This is an important paper for understanding dynamical process in directed networks.

Source

    © 2023 the Reviewer.

References

    Niall, R., Peter, T., Samuel, J. 2023. Influence and influenceability: global directionality in directed complex networks. Royal Society Open Science.

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