Community Detection Problem Based on Polarization Measures: An Application to Twitter: The COVID-19 Case in Spain

Round 1

Reviewer 1 Report

The paper titled “Community Detection Problem Based on Polarization Measures. An application to Twitter: the COVID-19 case in Spain” by I. Gutiérrez, J. A. Guevara, D. Gomez, J. Castro, and R. Espínola, presents a way for taking into account the Polarization of nodes in the community detection problem. The polarization fuzzy measure is defined. It is a model to represent the capacity of a set of elements to argue. An algorithm for finding groups whose elements are not polarized is also proposed. A real case is considered. It is a network obtained from Twitter concerning the political position against the Spanish government taken by influencers. 

The paper is structured correctly. The introduction and the preliminaries seem comprehensive. 

The results are properly discussed, and the conclusions are evident. 

In some points, English should be improved. For instance:

Line 225: “…each of these the poles…”

Line 232: “… was define…”

Author Response

Thanks for your comments. Please, see in the attached file our answer.

All the best, 

The authors

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper has been well prepared, and can be accepted after the following minor revisions:

1.      Table 5: The border line below the last row is missing.

2.      Please make Figure 8 clearer.

3.      Please remove the lines around Figures 8-11.

Author Response

Thanks for your comments. Please, see in the attached file our answer.

All the best, 

The authors

Author Response File: Author Response.pdf

Reviewer 3 Report

The work is devoted to the study of community detection problems based on polarization measures with the application and to the development of an approach to their solution based on additional information. The additional information is fuzzy and is modeled by a fuzzy measure that represents the possibility of polarization, i.e. division of society into two different groups that are opposite in political views. Fuzzy in work is the capacity of the elements causing the conflict. For formalization, processing of additional fuzzy information and the use of a fuzzy graph, a fuzzy measure, the methods of fuzzy set theories are used, which ensure the adequacy, realistic solution.An effective algorithm for searching for groups of society is proposed, the elements of which are not polarized. Examples are given that explain the idea of solving the problems under study, a real case from the social network Twitter is described, setting out the political position of the opposition of the Spanish government in the context of the crisis associated with COVID-19. A parametric approach to the problem of community detection based on polarization measures and a weighted average is proposed and described. The problem of detecting communities is considered on the basis of fuzzy criteria, incl. information about relationships between people, based on this knowledge of the corresponding positions on any longitudinal axis. To solve this problem, the idea developed in the additional Louvain algorithm is used. It is proposed to consider combinations of two components of a non-polarization extended fuzzy graph as a basis for calculating the modularity variation to take into account additional information. To create a method for finding communities in a non-polarization extended fuzzy graph, it is proposed to sum the non-polarization fuzzy measure into the adjacency matrix of a weighted graph. The pseudocode of the Polarization Louvain algorithm is given, which implements this method.In general, the work is interesting and is based on the use of a promising approach to solving the problems under study, it can be applied in solving some issues of the present time and is recommended for publication.

At the same time, some comments should be highlighted that can improve the structure and quality of work.

1.  The structure of the work could be reduced to a more standard structure, where the results are clearly distinguished, highlighting their results from others and discussing the results obtained and their novelty, originality.
2.   In section 2- Preliminaries, there are many well-known definitions and explanations that take up a lot of volume. This part of the work could be combined with the Introduction, and only the most basic points proposed in the work could be cited, and it is enough to organize links to known definitions.
3. In the text of the work, the degrees of belonging of all individuals to the poles X_A and X_B are designated by the membership functions, respectively ηX_A , ηX_B  ,  i.e. membership functions are denoted by non-standard designations (usually denoted by  μ_A(x), μ_B(x) ), and what structure (analytical expression) these membership functions have and how they are constructed are not given. These are important points in the practical application of fuzzy set methods (fuzzy mathematics).
4.  In section 5-Results, it is desirable to show which application, for example, the Fuzzy Logic Toolbox application of the MatLab system, or others, the construction of the membership function and fuzzy modeling processes are implemented. And also it is not clear how the fuzzy graphs are constructed in this section, for example, in Figures 10, 11.
5. In sections 5-Results and 6-Discussions, their own results are insufficiently substantiated compared with similar results from other studies. It seems to us in these sections it is better to substantiate the novelty and originality of our results obtained in this paper.

To that end, I would recommend to the authors to make the above-suggested corrections prior to be accepted in the Journal.

Author Response

Thank you for your comments. Please, see in the attached file our answer.

All the best, 

The authors

Author Response File: Author Response.pdf