DebtG: A Graph Model for Debt Relationship

Abstract

Debt is common in daily transactions, but it may bring great harm to individuals, enterprises, and society and even lead to a debt crisis. This paper proposes a weighted directed multi-arc graph model DebtG of debts among a large number of entities, including individuals, enterprises, banks, and governments, etc. Both vertices and arcs of DebtG have attributes. In further, it defines three basic debt structures: debt path, debt tree, and debt circuit, and it presents algorithms to detect them and basic methods to solve debt clearing problems using these structures. Because the data collection and computation need a third-party platform, this paper also presents the profit analysis of the platform. It carries out a case analysis using the real-life data of enterprises in Huangdao Zone. Finally, it points out four key problems that should be addressed in the future.

Finding Debt Cycles: QUBO Formulations for the Maximum Weighted Cycle Problem Solved Using Quantum Annealing

“…The former finds a cycle with length of exactly c log(|V|) for any constant c, while the latter is of length log(|V|) log(log(|V|)) , provided those exist. Björklund et al [26], however, showed that there does not exist a polynomial time approximation within an approximation ratio of |V| 1− for any unless P = N P. Cui [4] aimed at finding all cycles in a directed graph with the use of classical computing but failed.…”

“…For the last and biggest instance, we use the debt data (Retrieved from https://figshare.com/articles/dataset/data_txt/14547432/1. (accessed on 10 June 2023)) collected in Huangdao Zone, Shandong Province, China [4]. This graph, as depicted in Figure 3, was decreased in size by deleting all vertices, with an inbound or outbound degree equal to zero and all the corresponding in-/out-arcs.…”

“…The weight of the arc, with the debtor being the source and the creditor the sink, stands for the amount of debt the debtor owes the respective creditor. Such a graph, DebtG, was introduced by Huanquing Cui [4], and this paper will make use of it. With this definition, it is possible that one debtor has multiple debts to the same creditor, but each debt has different properties, such as a different due date, a different interest rate, etc.…”