Exploring Graph and Digraph Persistence

Round 1

Reviewer 1 Report

Exploring graph and digraph persistence

 

Mattia G. Bergomi, Massimo Ferri

The authors propose a computational method to generate compact representations of large networks according to graph-theoretical features or custom properties defined on the networks’ vertices.

According to the reviewer, the authors significantly expand their knowledge in the field of the weighted graphs and digraphs.

With respect to other researchers, they leverage a generalization of topological persistence adapted to work on weighted graphs and digraphs. In this framework, they widen the notion of monotone feature on (di)graphs—i.e., feature respecting inclusion—and thus, well suited to generate filtrations and persistence diagrams.

The reviewer propose take into account this methodology to analysis of any physical system (electrical, mechanical etc.)

The authors made a thorough analysis of the presented results.

The authors made the detailed literature survey - 42 items containing new knowledge.

The reviewer has no objections to the figures. One can interpret the results. They are also legible.

In the reviewer’s opinion, the research idea is interesting, and the manuscript is very well structured. The paper can be published in this form.

Author Response

We thank the Reviewer for the expressions of interest. We definitely want to move on to applications; even more, we wish that other researchers apply our technique.

Reviewer 2 Report

I had the opportunity to read "Exploring graph and digraph persistence" manuscript submitted as an original research article to "Algorithms" journal. 

The manuscript is aimed to:

- provide strategies to compute rank-based persistence on directed or undirected weighted graphs

- provide an algorithmic approach to encode features as persistence diagrams carrying compact information

The manuscript is valuable and deserves publication.

Some issues must be addressed:

- in the first part of the manuscript the general impression is of lack of specificity; the authors should add some sentences to increase the specificity, some examples to clarify the topic and its issues;

- some typo errors requires attention: "This is done, e.g., in [26], where a connection between Laplacian, persistence, and network circuit graphs is drawn. [27] does persistence on discrete curvature for the evaluation of graph generative models." (please revise)

"graphs and directed graphs", "graphs and digraphs" appears often together; it should be find a way in which the terminology should be simplified (to graphs for instance) and where for directed graphs the statements do not applies, then should be given a specific statement.

In " In particular, we introduce the concept of simple features in section 4, and single-vertex features in section 5." probably single-vertex was supposed to be in italic too. Regarding to the italic style - whenever the authors used italic style is in my perception that it is about an important concept related to the topic. I would like to ask the authors to revise everywhere italic style appears to be sure that the italicized concept is properly defined and/or referenced.

Most of the paper is math-style based (and page 4 is representative to this, see the list: "Definition 4. [9, Def. 5]", "Definition 5. [9, Def. 6, Prop. 1]", "Definition 7. [9, Def. 8]", "Definition 9. [9, Def. 8]", "Definition 10. [9, Def. 9]", "Definition 11. [9, Def. 10]", "Definition 12. [9, Def. 11]", "Proposition 13. [9, Prop. 2]", "Definition 14. [9, Def. 13]"). However, the journal to which it was submitted is "Algorithms" and in this regard the manuscript style is very poor: it is only one algorithm mentioned, in only one section, which is not even given in the paper. Furthermore, for the associated software (Pyton implementation I'M GUESSING BECAUSE THE AUTHORS FORGET TO MENTION THE CODED LANGUAGE) is given as a link to a library. The authors should do better. 

In my opinion more literature must be added, in the introductory section and in the discussion section - by the way, discussion of the results is missing. The authors can consider to include discussions about the use of the graph persistence in other scientific fields, such as physics, chemistry and biology.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors improved their manuscript in all parts. Still are some shortcomings, for instance notations (ex.: "in-edges" and "out-edges" in text - lines 347-348 in "6.3 Results" and "in_edges" and "out_edges" in the only one - which is nonnumbered - equation in between line 348 and 349.

Overall, the manuscript can be accepted for publication while some of these shortcomings can be patched at production stage.