Modularity-Based Incremental Label Propagation Algorithm for Community Detection

Round 1

Reviewer 1 Report

This is an interesting, original topic and a relevant study. Authors propose improvements to an algorithm that has certain limitations in detection due to the randomness of label assignment.

The overall structure of the paper is good, but some sections could be improved. The author(s) provide a good theoretical framework and the mathematical proposal of the algorithm seems solid, but I miss a flowchart or illustration of how the code works. Before acceptance, some modifications are suggested to be made, which are listed as follows:

1. Community Detection. Can Authors explain it in more depth the “community detection” concept and its applicability? There are certain terms that are not explained in the introduction. For instance, Authors uses 23 times “community detection” terminology, but it is not explained clearly. The use of abbreviations would be appreciated.
2. Other suggestion is that the authors should provide a more consistent literature review. There is a total of 40 references, but there are only 7 research works submitted since 2017.
3. 189 paragraph: There is no point in putting two equal tables except for one column (table 2 and table 3).
4. It is not clear what type of platform authors have used for the implementation. Algorithm phrase is used 48 types.
5. I would recommend using less bright colours in figure 5. Although it is not necessary, some more quality in the images would be nice. Since all the images in figure 5 have the same axes, I think it would be good to unify all the figures into one. In general, all the images lose resolution when they are zoomed in, especially in the text.
6. The abstract indicates that there is a great randomness in the process of updating the label and that it is a problem in the stability of the results. What exactly causes this lack of stability? what applications does the Label Propagation Algorithm have? what is a community detection algorithm used for? what does it mean that it is fast and efficient, should it give results of why it is fast compared to other proposals?
7. Conclusion: Authors do not talk about proposals for future work
8. I also recommend the use of the list of abbreviations at the end of the manuscript.

On the whole, the article is easy to read and can be published with the major amendments previously indicated.

Author Response

Thank you very much for your comments, so that we have further improved the manuscript. In response to your comments, we have added our description of the algorithm and an algorithm flowchart. Below, I will answer your question point by point.

Reviewer#1, Concern#1: Community Detection. Can Authors explain it in more depth the “community detection” concept and its applicability? There are certain terms that are not explained in the introduction. For instance, Authors uses 23 times “community detection” terminology, but it is not explained clearly. The use of abbreviations would be appreciated.

Author response: We are very sorry for our unclear descriptions about community detection. Community structure is one of the most important characteristics of complex networks, allowing us to unearth in-depth network information that may not be obtained from direct observation. Since the community structure of most networks is not obvious, we need to use community detection algorithms to find it.

However, community detection is an ill-defined problem due to the absence of a universal definition of the object for detection, i.e., “community”. As so far multiple definitions of communities have been proposed, and many methods to detect them and performance evaluation techniques have also been presented. The classical view relies on the degree distributions of the nodes to determine communities, which depends on the relation between the internal and external degree of the nodes under consideration. The modern view relies on calculating the probability of edge formation between nodes, i.e., the community should be one in which there is a preferential linking pattern. This definition states that nodes in a community would have a higher probability of linking with each other than with nodes of other communities.

Author action: We revised the introduction and added description on community detection(Line 29-33)

Reviewer#1, Concern#2: Other suggestion is that the authors should provide a more consistent literature review. There is a total of 40 references, but there are only 7 research works submitted since 2017.

Author response: We thank you for carefully reviewing our manuscript.

Author action: We updated our references.

1. Cunchao T. et al. A Unified Framework for Community Detection and Network Representation Learning. IEEE Transactions on Knowledge & Data Engineering 2019, 31, 1051-1065.
2. Nerurkar P.; Chandane M.; Bhirud S. A Comparative Analysis of Community Detection Algorithms on Social Networks. Computational Intelligence: Theories, Applications and Future Directions 2019, 1, 287-298.
3. Zheng, X. et al. Privacy-preserved community discovery in online social networks. Future Generation Computer Systems 2019, 93, 1002-1009.
4. Guishan, W.; Xuezao, R.; Xueying, L. research on Community Center-metric and Community Detection Algorithm for Complex Networks. Proceedings of 2019 International Conference on Applied Mathematics, Modeling, Simulation and Optimization, Gui Lin, China, 21-22/4/2019.

Reviewer#1, Concern#3: 189 paragraph: There is no point in putting two equal tables except for one column (table 2 and table 3).

Author response: Thank you for your advice. We noticed that there is a great similarity between the two tables, so we integrated the two tables into one table, which makes it more concise and clear.

Author action: We replaced the original table 1-2 with a new table. In the new table, there are two experimental groups, i.e., Group A and Group B. And the mu of each group is 0.1-0.5 and the interval is 0.1.

Reviewer#1, Concern#4: It is not clear what type of platform authors have used for the implementation. Algorithm phrase is used 48 types.

Author response: We are sorry for our unclear description about the type of platform. We have added the description of computer configuration, software, operating environment, etc. In our future work, we will pay more attention to the details of this part of the statement.

Author action: We added the description of computer configuration, software, operating environment, etc. (Line 214-216)

Reviewer#1, Concern#5: I would recommend using less bright colours in figure 5. Although it is not necessary, some more quality in the images would be nice. Since all the images in figure 5 have the same axes, I think it would be good to unify all the figures into one. In general, all the images lose resolution when they are zoomed in, especially in the text.

Author response: Thank you for your advice. Although all the images in figure 5 have the same axes, but their scales are different and same gaps are small. If we put them together, it could be difficult to find the difference between different algorithms. So we just changed the color of the images.

Author action: We changed the color of figure 5. We also replaced all the text which are lose resolution and improved the quality of the images.

Reviewer#1, Concern#6: The abstract indicates that there is a great randomness in the process of updating the label and that it is a problem in the stability of the results. What exactly causes this lack of stability? what applications does the Label Propagation Algorithm have? what is a community detection algorithm used for? what does it mean that it is fast and efficient, should it give results of why it is fast compared to other proposals?

Author response: Thank you for your comment. As mentioned in our manuscript, Label Propagation Algorithm (LPA) has a great randomness in the process of updating the label. Because LPA always randomly selects a node to start spreading labels, which makes some nodes that are neither tightly connected nor sparsely allocated to different communities during each update process. It results in great instability of detection results. LPA, as a community detection algorithm, is often used to mine the structural characteristics of a network. It helps us to better understand a network. For example, in a social network, we can quickly discover which people connect densely, that is, belong to the same community. Meanwhile, we can also find out the one which plays a key role in this social network, i.e., the nodes with large degree. The reason why we said that LPA is a fast algorithm is due to its linear time complexity, which is mentioned in our Abstract and Introduction section. Because of the great randomness, the efficiency of LPA is indeed not obvious. For the sake of rigor, we have removed the word “efficient” from the Abstract.

Author action: We revised the part of description of LPA (Line 59-65). And we removed the world “efficient” (Line 10).

Reviewer#1, Concern#7: Conclusion: Authors do not talk about proposals for future work.

Author response: Thank you for your advice. This allows us to find the missing part in the manuscript and help us improved the quality of our work. We have added some proposals for our future work.

Author action: We added the proposals for our future work (Line 293-296).

Reviewer#1, Concern#8: I also recommend the use of the list of abbreviations at the end of the manuscript.

Author response: Thank you for your advice. We agree that the list of abbreviations will help readers read our article more conveniently.

Author action: We added a new section Appendix with the list of abbreviations.

Reviewer 2 Report

I read the manuscript with great interest and I think that is is a very good work that deserve to be published.

Author Response

We are truly grateful for your evaluation of our manuscript, and we have further improved our manuscript, looking forward to bringing a high-quality article to readers.

Reviewer 3 Report

In general the research is well conducted. The work is interesting and innovative.

The authors should emphasize and discuss more in detain on their written:

1. the elements of novelty of their work and when the proposed approach is better than existing approaches
2. the network structures which call for the different methodologies (when using a methodology than another one).
3. the computational approaches: if exists an R package or a Python library they have implemented to use the approach 

An English revision could be reasonable.

Author Response

We appreciate your positive comments on our manuscript, and we will answer your questions point-by-point.

Reviewer#3, Concern#1: The elements of novelty of their work and when the proposed approach is better than existing approaches.

Author response: Thank you for your advice. At present, most LPA improved algorithms are optimized on the basis of random initialization. Although they can improve the performance of the algorithm to a certain extent, they cannot change the problem of randomness. Our proposed algorithm is based on Label Propagation Algorithm (LPA). It uses incremental label propagation strategy which start label propagation from the node which has the largest degree. So it greatly improves the randomness of the original LPA (Line 241-248). Besides, our algorithm uses modularity as an optimization function, so MILPA can also achieve good results which can be seen in Modularity section.

Author action: In order to emphasize the novelty of our work, we revised Introduction and Conclusion and Future Work section. We highlight the disadvantages of original LPA and advantages of our MILPA.

Reviewer#3, Concern#2: The network structures which call for the different methodologies (when using a methodology than another one).

Author response: We are sorry for our unclear descriptions. The structure of the real network may be quite different. For example, some networks are small-world networks, some networks are scale-free networks, some networks are the assortative structure, some networks are the disassortative structure. There is no community detection algorithm that is suitable for all networks. Different community detection algorithms may have different effects on different networks. For specific networks, some algorithms may have good results, and some may not be good. In practical applications, this must be considered. However, the focus of our article is to test the effectiveness of the proposed
algorithm. It needs to be compared with other algorithms on different networks.
Only testing in different networks can find the differences between these
algorithms, so the network structure in our paper is not a major consideration, and our experimental method is the same as many other papers, such as reference 1,2,3 and so on.

1. Murata, T.; Afzal, N. Modularity Optimization as a Training Criterion for Graph Neural Networks. Complex Network 2018, pp, 123-135.
2. Biswas, A.; Biswas, B. Analyzing evolutionary optimization and community detection algorithms using regression line dominance. Information Sciences 2017, 396, 185-201.
3. Newman, M. E. J. Fast algorithm for detecting community structure in networks. Physical Review E 2003, 69, 066133.

Author action: We have revised the manuscript to supplement the description of the real-world network structure (Line 203-210).

Reviewer#3, Concern#3: The computational approaches: if exists an R package or a Python library they have implemented to use the approach. 

Author response: Thank you for your comment. The code of our algorithm is written by ourselves, there is no ready-made R package or Python library. All the experiments were implemented in Pycharm with Python3.6 on a PC with 16GB memory, Intel core i7 processor and Win10 system. We will open our algorithm in the future.

Round 2

Reviewer 1 Report

The paper has been improved by the revisions and the authors have spent a good effort on the manuscript. All my comments have been answered. I believe that the manuscript can be processed for publication in its current form.