The coritivity, h(G), of a connected graph G, is defined by h(G) = max{ω(G-S)-|S|: S∈C(G)}, where ω(G) denotes the number of components of a graph G, C(G) denotes the collection of cut-sets of G. In this paper, the...The coritivity, h(G), of a connected graph G, is defined by h(G) = max{ω(G-S)-|S|: S∈C(G)}, where ω(G) denotes the number of components of a graph G, C(G) denotes the collection of cut-sets of G. In this paper, the notion of complementary coritivity is proposed, and the relations between coritivity and its complement are studied, for example, two bounds, Nordaus-Gaddum problems and some foundational properties etc.展开更多
Joint loan guarantee contracts and mutual guarantee contracts among SMEs form the basis of SME guarantee networks. The expansion of these networks increases the fragility of a financial system as a result of the regio...Joint loan guarantee contracts and mutual guarantee contracts among SMEs form the basis of SME guarantee networks. The expansion of these networks increases the fragility of a financial system as a result of the regional and industrial risk contagion embedded within them. By providing a theoretical framework of a loan guarantee network, a method is proposed for calculating the amount of risk spillover caused by loan guarantees taking the perspective of the entire network. In addition,the route of risk contagion in guarantee networks is analyzed, revealing that when default risk shocks occur, risk contagion travels along the nodes not once but for several rounds and that the risk control of one firm cannot prevent these systemic risks. Therefore, a risk control scheme is designed based on the location and importance of firms in the network. Using data from a real guarantee network,we demonstrate that identifying the node locations of firms' in the guarantee network(including the coritivity and closeness of the firm) can help in understanding risk contagion mechanisms and preventing systemic credit risk before a crisis occurs.展开更多
基金Research supported by the National Natural Science Foundation of China
文摘The coritivity, h(G), of a connected graph G, is defined by h(G) = max{ω(G-S)-|S|: S∈C(G)}, where ω(G) denotes the number of components of a graph G, C(G) denotes the collection of cut-sets of G. In this paper, the notion of complementary coritivity is proposed, and the relations between coritivity and its complement are studied, for example, two bounds, Nordaus-Gaddum problems and some foundational properties etc.
基金supported by the National Nature Science Foundation of China under Grant Nos.71172186,71472148,71572144 and 71502138
文摘Joint loan guarantee contracts and mutual guarantee contracts among SMEs form the basis of SME guarantee networks. The expansion of these networks increases the fragility of a financial system as a result of the regional and industrial risk contagion embedded within them. By providing a theoretical framework of a loan guarantee network, a method is proposed for calculating the amount of risk spillover caused by loan guarantees taking the perspective of the entire network. In addition,the route of risk contagion in guarantee networks is analyzed, revealing that when default risk shocks occur, risk contagion travels along the nodes not once but for several rounds and that the risk control of one firm cannot prevent these systemic risks. Therefore, a risk control scheme is designed based on the location and importance of firms in the network. Using data from a real guarantee network,we demonstrate that identifying the node locations of firms' in the guarantee network(including the coritivity and closeness of the firm) can help in understanding risk contagion mechanisms and preventing systemic credit risk before a crisis occurs.
