DebtG: A Graph Model for Debt Relationship

Round 1

Reviewer 1 Report

The paper addresses a critical issue of the nowadays network economy, where entities are highly connected to each other through various types of flows. In this context, focusing on debt between companies - also exacerbated by the Covid-19 pandemic - is a great idea, particularly when authors advance methods that may help in alleviating the debt burden in an economy. Hence, the topic of the paper is interesting and attractive for readers.

However, the paper needs improvements in various areas, which I highlight below:

• The Introduction should be enlarged and enriched by providing more context for the research and discussing more the rationale behind the paper. In particular, I suggest the author(s) provide more details about the debt situation of companies around the world and/or in China, since the case study is related to a Chinese province. Moreover, the profitability of settling platforms should also be addressed in the Introduction and the authors need to explain why this is a critical issue. I also suggest removing the reference to Investopedia right at the beginning of the paper, this is not very academic and other sources for the definition of debt can be found.
• The definitions of debt path, circuit, and tree are interesting, but they just mimic definitions from programming and the word "debt" has been put in front. Building on this, it is not clear to me what the algorithm used by the authors brings i.e., what is new and original about this algorithm that cannot be found in other programming algorithms. The authors need to explain this better.
• In the example of DebtG (Figure 1) the author(s) uses(e) the starting date of the debt to define the arc. I believe the date when the debt is due would be more useful for the settling algorithm to be implemented.
• In the case analysis, the authors need to provide a description of the debt situation between entities, they only mention that "The data contain 7,664 entities and 8,704 debts". In my opinion, this is not enough, a more thorough presentation of the data should be done in order for readers to understand how critical the debt issue is for these entities. This would also help the authors delve into the benefits of their algorithm.
• Also in the case study, it is not at all clear to me how the settling platform increases its profitability after applying the algorithm. This should be explained by the authors.
• Conclusions focus more on what is to be done than on what the research had achieved, so I suggest the authors to revise them extensively. The authors need to address the utility of their work and its applications, as well as the estimated benefits and results.

Author Response

The author would like to thank the editor and all of the reviewers for their helpful and insightful comments. I have improved the quality of the manuscript by carefully taking all the comments into consideration. The modifications in this revised manuscript as well as the responses to the editor’s and reviewers’ comments are described below.

In the revised paper, the modifications are marked up using the “Track Changes” function in MS Word.

The paper addresses a critical issue of the nowadays network economy, where entities are highly connected to each other through various types of flows. In this context, focusing on debt between companies - also exacerbated by the Covid-19 pandemic - is a great idea, particularly when authors advance methods that may help in alleviating the debt burden in an economy. Hence, the topic of the paper is interesting and attractive for readers.

However, the paper needs improvements in various areas, which I highlight below:

1. The Introduction should be enlarged and enriched by providing more context for the research and discussing more the rationale behind the paper. In particular, I suggest the author(s) provide more details about the debt situation of companies around the world and/or in China, since the case study is related to a Chinese province. Moreover, the profitability of settling platforms should also be addressed in the Introduction and the authors need to explain why this is a critical issue. I also suggest removing the reference to Investopedia right at the beginning of the paper, this is not very academic and other sources for the definition of debt can be found.

(1) The debt situation of Chinese enterprises in 2020 is provided, according to People’s Bank of China. Please see lines 31-34 now. “According to PBC (People’s Bank of China), in 2020, the loan balance of Chinese enterprises reached ￥53 trillion, and the debt ratio exceeded 56%, which is 1.09 times of China's GDP in 2020.”

(2) The necessity of third-party platform is introduced in Introduction, as lines 41-45 now. “It relies on a third-party platform to collect and process a large amount of debt information. As debt is one of the business secrets of enterprises, this platform must be highly credible and recognized by all entities. Meanwhile, the platform should be able to make profits when settling debts to maintain its operation. This platform maybe Ministry of Finance [12] or subsidy center [13].”

(3)The reference to Investopedia is removed, and a new reference [1] is used to present the concept of debt, as line 20. In further, the number of all referenced are changed accordingly.

2. The definitions of debt path, circuit, and tree are interesting, but they just mimic definitions from programming and the word "debt" has been put in front. Building on this, it is not clear to me what the algorithm used by the authors brings i.e., what is new and original about this algorithm that cannot be found in other programming algorithms. The authors need to explain this better.

(1) I present the difference between the related definitions, as lines 183-189. “The debt path and debt circuit are respectively the extension of path and cycle in graph theory, where the “extension” means all arcs between two neighboring vertices should be included in debt path and debt circuit. The debt tree is different from directed tree in graph theory. In graph theory, a directed tree is a directed graph which would be connected and acyclic if the directions on the arcs were ignored. In DebtG, the debt tree is connected but cyclic if the directions on the arcs were ignored. For example, the debt tree in Figure 4 has a cycle {1,2,3,4} so it is not a directed tree in graph theory.”

(2) I present the new idea of Algorithm 1 in lines 230-233. “The differences between Algorithm 1 and traditional cycle detection algorithms include: (1) Algorithm 1 removes the vertices whose out- or in-degree is 0 in first, while existing algorithms don’t; (2) Algorithm 1 clears a debt circuit once it is detected, while existing algorithms try to detect all cycles and choose the best one to clear.”

(3) Due to the debt tree is a new concept, so Algorithm 2 is new and original.

3.In the example of DebtG (Figure 1) the author(s) uses(e) the starting date of the debt to define the arc. I believe the date when the debt is due would be more useful for the settling algorithm to be implemented.

Yes, debt due date is more important than debt arising date. Now, I emphasis debt due date in many places, such as lines 103 and 155. Because the space of Figure 1 is very limited, it cannot contain many attributes. I point out that the dates of Figure 1 can have two possible meanings: debt arising date or debt due date (line 159).

4.In the case analysis, the authors need to provide a description of the debt situation between entities, they only mention that "The data contain 7,664 entities and 8,704 debts". In my opinion, this is not enough, a more thorough presentation of the data should be done in order for readers to understand how critical the debt issue is for these entities. This would also help the authors delve into the benefits of their algorithm.

The debt data used in the paper is obtained from YouRong Information Technology Co., Ltd. YouRong only provided me the ID of creditor, ID of debtor, and the amount of debt, because it is worried about divulging customers’ privacies. Therefore, I cannot understand how critical the debt issue is for these entities as well. I am so sorry.

The total amount of debt is ￥1.61 billion (line 311), and Algorithm 1 can settle ￥13.35 million debts (line 315). The settled debt amount of Algorithm 2 cannot be calculated because I don’t know the candidate path heads and tree roots, so I don’t know how many debt trees and debt paths are obtained by YouRong Co. Ltd.

5.Also in the case study, it is not at all clear to me how the settling platform increases its profitability after applying the algorithm. This should be explained by the authors.

I explain the reason in lines 282-286 now. “Due to Algorithm 1 improves the efficiency of clearing debt circuit, the platform can detect and settle more debt circuits than existing methods. This paper puts forward the concepts and settling methods of debt tree and debt path for the first time. These two new structures enhance the ability and scope of the platform to settle debt problems, so the platform can benefit from them.”

6.Conclusions focus more on what is to be done than on what the research had achieved, so I suggest the authors to revise them extensively. The authors need to address the utility of their work and its applications, as well as the estimated benefits and results.

Now, lines 356-361 provide the potential benefits. “On one hand, the profit analysis proves that this platform can be profitable, which will be a potential emerging industry. On the other hand, the settlement of a large number of debts is conducive to the healthy, rapid and sustainable development of the economy.”

Moreover, lines 362-366 provide a factual application in YouRong Co. Ltd. “Based on tens of thousands of debt information collected from more than 1,000 enterprises, YouRong solved more than 2,000 debts of them, with a total amount of debt more than ￥100 million and a profit of more than ￥1 million.”

Thanks again for your helpful and insightful comments!

Author Response File: Author Response.docx

Reviewer 2 Report

Paper deals with important tasks. The author is built a graph model DebtG of debt relationship between massive entities. It can be used in various domains. Two algorithms are developed to deal with large-scale graphs. The practical results are presented too.

Paper has great scientific and practical value.

It has a logical structure, all necessary sections are presented in the manuscript. 

The following suggestions are given:

1. Introduction section should be extended It would be great to add the numerical results to the main contribution part.
2. It would be good to extend the limitation of the current methods in the Related works section. The author mentioned existing gaps, but it is not understandable why these gaps can not be solved.
3. Table 1 should be explained in more detail.
4. Conclusion section should be extended using numerical results obtained in the paper. It would be great to analyze the possibility to use Algorithm 1 and algorithm 2 in parallel mode. How does it decrease the time complexity?

Author Response

The author would like to thank the editor and all of the reviewers for their helpful and insightful comments. I have improved the quality of the manuscript by carefully taking all the comments into consideration. The modifications in this revised manuscript as well as the responses to the editor’s and reviewers’ comments are described below.

In the revised paper, the modifications are marked up using the “Track Changes” function in MS Word.

Paper deals with important tasks. The author is built a graph model DebtG of debt relationship between massive entities. It can be used in various domains. Two algorithms are developed to deal with large-scale graphs. The practical results are presented too.

Paper has great scientific and practical value.

It has a logical structure, all necessary sections are presented in the manuscript.

The following suggestions are given:

1.Introduction section should be extended It would be great to add the numerical results to the main contribution part.

I am so sorry that I cannot understand “numerical results to the main contribution part”. The main contribution is to present (1) One graph model of debt relationship; (2) Three debt structures; and (3) Two algorithms.

If the “numerical results” refer to the profitability of DebtG, it is mentioned in lines 356-361, Section 5 now. “On one hand, the profit analysis proves that this platform can be profitable, which will be a potential emerging industry. On the other hand, the settlement of a large number of debts is conducive to the healthy, rapid and sustainable development of the economy.”

DebtG has been applied in a company, as said in lines 362-366. “Now, the proposed algorithms have been applied by YouRong Information Technology Co., Ltd, located in Qingdao, China. Based on tens of thousands of debt information collected from more than 1,000 enterprises, YouRong solved more than 2,000 debts of them, with a total amount of debt more than ￥100 million and a profit of more than ￥1 million.”

2.It would be good to extend the limitation of the current methods in the Related works section. The author mentioned existing gaps, but it is not understandable why these gaps can not be solved.

I extend the limitations of the current methods, as lines 102-135, which are:

• The entities involved in debt relationships have many attributes that affect debt clearing. For example, the due date of debt is more important than the amount of debt in determining the order of debt settlement. However, the current models only focus on the debt amount in order to clear the largest amount of debt.
• There is often more than one debt between a pair of entities, and these debts also have different attributes. An entity may prefer to settle earlier debts with higher discounts, or vice versa. But the current models only contain at most one debt between a pair of entities.
• It may be impossible to solve debt clearing problem by constructing cycles with the help of Ministry of Finance (see [12]) or subsidy center (see [13]). When a series of entities form a debt path (see Section 3), refs. [12-13] add the third-party platform to the path to construct a cycle, and the platform pays the first debtor to clear the debts. However, the last creditor has no obligation to pay platform because it does not owe the platform.

3.Table 1 should be explained in more detail.

I explained Table 1 in detail now, as lines 314-321. “These debt circuits can clear￥13.35 million debts. Table 1 presents the details of these 40 debt circuits. In Table 1, the “sequence of vertices” is the IDs of entities involved in a debt circuit, and the “settle amount” is the settle amount of corresponding debe circuit. For example, the second-row means  is a debt circuit, and its settle amount it￥33,000. We can see that some debt circuits share common arcs. For example, the debt circuits of the second to sixth rows share a common arc .”

4.Conclusion section should be extended using numerical results obtained in the paper. It would be great to analyze the possibility to use Algorithm 1 and algorithm 2 in parallel mode. How does it decrease the time complexity?

• I present the numerical results of application of DebtG in YouRong Co. Ltd., as lines 262-366.
• I am so sorry that I don’t analyze the possibility to use two algorithms in parallel mode. I think it is very difficult to parallelize the two algorithms directly, and it needs a new paper to discuss the parallel algorithms. A possible approach is to use some distributed graph computing engine, such as Pregel, GraphX, etc. It may be beyond the scope of this article.

Thanks again for your helpful and insightful comments!

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

I am pleased to see that the authors have used my comments and suggestions and improved their paper. I suggest that next time they do research, to begin with understanding the underlying data and further apply the research methods.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

There is no comment to authors

Reviewer 2 Report

It would be beneficial for the discussion a clear definition of the term 'debt problem', and what the author means when he uses this term. There is any reference in the literature? What does it mean to solve the debt problem? Which is the solution we are looking for?

When the author at line 32 says "Inspired by the above networks, ...", probably a good reference here would be Network Science and the study of Complex Networks.

* Newman, Mark. Networks. Oxford university press, 2018.

### Section 2. Related Works

In the Related Work section the discussion of directly related works is missing, and should be improved. The section is mainly devoted to discuss works that are loosely related to the study. 
As an example I report below a reference that seems strictly related to the study proposed by the author. It would be interesting to highlight which are the novelty introduced by the author respect to the reference below.  

* Gazda, Vladimír, Denis Horváth, and Marcel Rešovský. "An application of graph theory in the process of mutual debt compensation." Acta Polytechnica Hungarica 12.3 (2015): 7-24

Moreover, which are the relations of the present study with the so called debts’ clearing problem? How network flow problems are related to the study proposed by the author?

* Păatcaş, Csaba, and Attila Bartha. "Evolutionary solving of the debts’ clearing problem." Acta Universitatis Sapientiae, Informatica 11.2 (2019): 142-158.

### Section 3. DebtG Model and Its Application

In the definition of the graph it is not clear the meaning of 'equivalent users'. Are they two different real entities? Why their debts are common debts? There is a case study that needs such formalization? 
In the graph 'equivalent users' are connected by an undirected edge and for the analysis they are treated as a single node. This suggest that we can use a single node inside the graph and get rid of undirected edges, a label can possibly keep the semantic of the relation between the two entities.

In definition 3 v_1 and v_m are called path head and path end respectively. It is not clear why v_1 should always have 0 in-degree e v_m 0 out-degree. This statement is true only if the debt path is evaluated on its own, outside the graph, i.e. all the connections with nodes not in the path are removed.

Algorithms 1/2: 
- While discussing the algorithm the author references lines number, but they are not reported in the text. 
- The discussion is often reduced to commenting what the code is doing, but the why is often missing, e.g. why are we removing some vertices?
- The author states that '... cycle detection algorithms can be found in many places ... '. It is possible to have any references. It is possible to know on what kind of procedure such algorithms are based and if their results can be beneficial for the algorithm proposed by the author himself?

In discussion of the example starting from line 218 user 5 is missing and in the text it is user 4 that pays 6 and not user 5.

### Section 4. Profit and Case Analysis

In section Profit Analysis the analysis doesn't take into account the possibility that a user u_i can transfer only a portion of what it received because the amount is not enough to cover an entire debt it has with a user u_i+1. 

The Figures and Tables used in the section Case Analysis do not add any value to the discussion and could be probably removed.
The section itself is a report of an application of the algorithms proposed, but doesn't provide any result on the solution of the debt problem. For example how much debt the procedure was able to clear solving the cycles detected in the graph? How the sorting of the vertices impact such value? Can you suggest a possible criterion to choose candidates in the example?
The author states that Algorithm 1 looks for a debt circuit at a time because the procedure was too expensive computationally. It is this the reason behind the design of the algorithm?

### Minor remarks:

* Line 118: If <v_i,v_j> in E, then <v_i,v_j> not in E --> the indices of second edge should be switched. 

Reviewer 3 Report

The topic is interesting, as I believe identifying new tools for modelling real-life processes and phenomena is always a good idea. Nevertheless, the paper needs improvements to make it publishable, which I list below: 

Introduction: I find it quite weak, as it just uses the text in the Abstract and does not provide important information on the relevance of the research, the need for it, and the novelty it brings to the field. As it is now, the Introduction just mentions there is a debt problem - where, who is affected, how much? - and they propose a methodology that visualizes this. Moreover, although they mention that the debt issue is relevant for all - individuals, companies, governments - the authors further say they only refer to enterprises. Well, this needs a justification.

Related works: Needs significant improvement. First, I suggest the authors to start with the debt issue, and then move to the presentation of other works in using graphs. Further, the part on debt needs to be majorly improved, because now it is not able to provide the readers with a good image of the size of debt globally and regionally, its distribution across various types of economic agents, purposes of debt, and so on.

DebtG Model and its application: I find the authors do not sufficiently explain the model and is use for debt detection. 

Profit and case analysis: The authors need to explain more the data for the case, its objectives, and, more importantly, the results.

Conclusions: No implications of the results are presented.

Overall, I find the paper lacks in showing how their results can be used and by whom. Just saying that they help solving the debt issue is almost nothing.