A method for identifying critical paths and intermediate nodes of implicit water shortage risk transmission based on betweenness centrality algorithm

Abstract

The present invention discloses a method for identifying key paths and intermediate nodes of implicit water shortage risk transmission based on the betweenness centrality algorithm, which relates to the field of water resources management. The method includes obtaining the water shortage probability of each region, and calculating the water shortage risk of each department in each region based on the water resource dependence of each department in each region combined with the water shortage probability of each region; constructing an implicit water shortage risk transfer matrix based on the water shortage risk of each department and a multi-regional input-output model; identifying the key transmission paths of implicit water shortage risk based on structural path analysis and the implicit water shortage risk transfer matrix, and constructing an implicit water shortage risk transmission network; identifying key intermediate nodes in the implicit water shortage risk transmission network based on the betweenness centrality algorithm. The present invention can identify all key transmission paths and intermediate nodes of implicit water shortage risk propagation in the supply chain, thereby enhancing the resilience of the entire trade network in coping with water shortage.

Description

Technical Field

[0001] The present invention relates to the field of water resource management, and particularly to a method for identifying key paths and intermediate nodes of implicit water shortage risk transmission based on betweenness centrality algorithm. Background Art

[0002] With the global climate change and population growth, the problem of water resource shortage has become increasingly serious, which has become a major challenge restricting the sustainable development of social economy. Due to the high correlation of trade networks, regional water shortage will not only cause direct economic losses to water-intensive sectors such as local agriculture and power generation, but also spread risks to other regions through the supply chain, resulting in a chain reaction. This kind of water shortage risk transmitted based on trade links can be defined as implicit water shortage risk. Identifying the key paths and intermediate nodes of implicit water shortage risk transmission is of great significance for enhancing the resilience of trade networks.

[0003] Traditional research has mainly focused on the problem of water resource shortage within geographical boundaries, and paid less attention to the transmission mechanism of implicit water shortage risk across regions. Although some studies have identified the source-sink relationship of implicit water shortage risk transmission, the description of its intermediate transmission paths and key intermediate nodes is still insufficient. In the process of implicit water shortage risk transmission, there are multiple important intermediate nodes playing the role of "bridges", and these intermediate nodes transmit a large amount of implicit water shortage risk in the trade network. Identifying the above key intermediate nodes helps to implement effective intervention before the risk spreads to downstream regions. For this reason, this application introduces the betweenness centrality algorithm based on structure path analysis (SPA) to effectively identify the key transmission paths and important intermediate nodes of implicit water shortage risk in the trade network, providing a scientific basis for formulating risk prevention and control measures. Summary of the Invention

[0004] To solve the above problems, this application proposes a method for identifying key paths and intermediate nodes of implicit water shortage risk transmission based on betweenness centrality algorithm, including the following steps: S1. Obtain the water shortage probability of each region, and calculate the water shortage risk of each department in each region based on the water resource dependence of each department in each region combined with the water shortage probability of each region;

[0005] S2. Construct an implicit water shortage risk transmission matrix based on the water shortage risk of each department and based on the multi-regional input-output model;

[0006] S3. Based on structure path analysis SPA and the implicit water shortage risk transmission matrix, identify the key transmission paths of implicit water shortage risk, and construct an implicit water shortage risk transmission network;

[0007] S4. Identify the key intermediate nodes in the implicit water shortage risk transmission network based on betweenness centrality algorithm Betweenness.

[0008] Preferably, the expression for the water shortage probability of each region is:

[0009]

[0010] In the formula: WSP i represents that the water shortage probability of region i is equal to the expected value of the random variable w i ; the random variable w i follows a lognormal distribution, and its variance σ is the standard deviation and is equal to 1; where WSI i represents the water pressure index of region i, WC i represents the water consumption of region i, Q i represents the available fresh water volume of region i.

[0011] Preferably, the expression for the water resource dependence degree of each department in each region is:

[0012]

[0013] In the formula: WD m,i represents the water resource dependence degree of department m in region i; WC m,i represents the water consumption of department m in region i; WI m,i represents the water intensity of department m in region i, which is equal to the water consumption WC of the department in this region m,i divided by its total output x m,i ; α is the truncation parameter of WD m,i and is set to 0.5.

[0014] Preferably, the expression for the water shortage risk of each department in each region is:

[0015] WSR m,i = WSP i × WD m,i × x m,i ;

[0016] In the formula: WSR m,i represents the water shortage risk of department m in region i; WSP i represents the water shortage probability of region i; WD m,i represents the water resource dependence degree of department m in region i; x m,i represents the total output of department m in region i.

[0017] Preferably, the expression for the implicit water shortage risk transfer matrix is:

[0018]

[0019] where: U represents a matrix, and the elements represent the implicit water shortage risk amount of the transmission from department m (donor) in region i to department n (recipient) in region j;

[0020] W is a row vector, and each element represents the water shortage risk of each department within each region. The expression is the process of diagonalizing the vector W;

[0021] The matrix (I - B) -1 is usually referred to as the Ghosh inverse matrix, and its elements represent the output of department n in region j caused by the production of a unit product in department m in region i (including direct and indirect). B is the direct output coefficient matrix in the multi-region input-output model, and I is the identity matrix.

[0022] Preferably, based on the structural path analysis SPA and the implicit water shortage risk transfer matrix, the specific content of identifying the key transmission paths of the implicit water shortage risk and constructing the implicit water shortage risk transmission network is as follows:

[0023] After performing a Taylor expansion on the Ghosh inverse matrix, the implicit water shortage risk is decomposed into different production levels:

[0024] G = (I - B) -1 = I + B + B 2 + B 3 + …;

[0025]

[0026] Assume that a specific supply chain path starts from department m in region i, passes through department k (r1, r2, … r k ), and ends at department q in the same region. The implicit water shortage risk amount transmitted by this path can be mathematically expressed as follows:

[0027]

[0028] where: EWSR SPA represents the implicit water shortage risk amount transmitted through this path; P(m, qr1, r2, … r k ) represents the weight of the supply chain path (m → r1 → r2 → … → r k → q);

[0029] W m,i represents the water shortage risk of department m in region i;

[0030] The element is an element in the matrix B;

[0031] By comparing the EWSR of each path SPAThe magnitude of the value, and further determine the key transmission path of the implicit water shortage risk;

[0032] The implicit water shortage risk transmission network consists of supply chain paths.

[0033] Preferably, the specific content of identifying the key intermediate nodes in the implicit water shortage risk transmission network based on the Betweenness centrality algorithm is as follows:

[0034]

[0035] In the formula: b i represents the Betweenness centrality of department i;

[0036] n represents the number of departments in the implicit water shortage risk transmission network;

[0037] t k represents the emergence time of department i between the two ends of the supply chain path (m → r1 → r2 → … → r k → q).

[0038] Define the total weight of the supply chain path passing through department i as b i (l1, l2):

[0039]

[0040] In the formula: l1 represents the number of upstream departments of department i, and l2 represents the number of downstream departments of department i. Both l1 and l2 are integers greater than or equal to 1;

[0041] J i represents a matrix with 1 at the (i, i) element and 0 at other elements;

[0042] e represents a unit column vector e of size n×1, all of whose elements are equal to 1;

[0043] Define T = GB = BG = B + B 2 + B 3 + …, the Betweenness centrality of department i can be written as:

[0044]

[0045] In the formula: the n×n matrix T = GB is composed of the Ghosh inverse matrix G and the direct output coefficient matrix B, and the element t ij represents the direct and indirect output of department j generated by the single output of department i;

[0046] By comparing the Betweenness centrality values b of each regional department iThe size is further used to determine the key intermediate nodes in the implicit water shortage risk transmission network.

[0047] A key path and intermediate node identification system for implicit water shortage risk transmission based on the betweenness centrality algorithm, comprising:

[0048] A data acquisition unit: acquiring the water shortage probability of each region, and acquiring the water shortage risk of each department in each region calculated by combining the water resource dependence degree of each department in each region with the water shortage probability of each region;

[0049] A matrix calculation unit: calculating an implicit water shortage risk transfer matrix based on the water shortage risk of each department and based on a multi-region input-output model;

[0050] A path identification unit: identifying the key transmission path of the implicit water shortage risk and constructing an implicit water shortage risk transmission network based on the structural path analysis SPA and the implicit water shortage risk transfer matrix;

[0051] An intermediate node identification unit: identifying the key intermediate nodes in the implicit water shortage risk transmission network based on the betweenness centrality algorithm Betweenness.

[0052] Preferably, an electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the method for identifying the key path and intermediate nodes of the implicit water shortage risk transmission based on the betweenness centrality algorithm are implemented.

[0053] Meanwhile, to solve the above technical problems, the present invention also provides a storage medium.

[0054] Preferably, a computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the steps of the method for identifying the key path and intermediate nodes of the implicit water shortage risk transmission based on the betweenness centrality algorithm are implemented.

[0055] In summary, for the method for identifying the key path and intermediate nodes of the implicit water shortage risk transmission based on the betweenness centrality algorithm of the present invention, compared with the traditional technology, the present invention introduces a monetized index of the water shortage risk and calculates an implicit water shortage risk transfer matrix in combination with an input-output model. The key supply chain path of the implicit water shortage risk transmission is identified through the structural path analysis SPA, and an implicit water shortage risk transmission network is constructed.

[0056] Finally, based on the Betweenness centrality algorithm, the key intermediate nodes in the implicit water shortage risk transmission network were identified. By identifying the key supply chain paths and intermediate nodes for implicit water shortage risk transmission, not only can supply chain disruptions caused by water shortages be effectively avoided, but it also helps prevent the spread of implicit water shortage risks from a certain node to the outside, thereby enhancing the stability of the supply chain and the resilience of the trade network.

[0057] The technical method of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Brief Description of the Drawings

[0058] Figure 1 It is a flowchart of the method for identifying the key path and intermediate nodes of implicit water shortage risk transmission based on the Betweenness centrality algorithm of the present invention;

[0059] Figure 2 It is a unit diagram of the system for identifying the key path and intermediate nodes of implicit water shortage risk transmission of the Betweenness centrality algorithm of the present invention. Detailed Embodiments

[0060] The technical method of the present invention will be further described below with reference to the accompanying drawings and embodiments. It should be noted that: unless otherwise specifically stated, the relative arrangements, numerical expressions, and numerical values of the components and steps described in these embodiments do not limit the scope of the present application.

[0061] The following description of at least one exemplary embodiment is merely illustrative and in no way limits the present application and its application or use.

[0062] Known technologies, systems, and devices for those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, the technologies, systems, and devices should be regarded as part of the specification.

[0063] In all the examples shown and discussed here, any specific value should be construed as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments may have different values.

[0064] Unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meaning understood by those of ordinary skill in the field to which the present invention belongs.

[0065] The present invention shows significant advantages compared to the prior art in water shortage risk assessment and management. In the invention, in addition to direct economic losses in water-intensive sectors such as local agriculture and power generation, water shortage risks may also spread the risks to other regions through the supply chain, generating implicit water shortage risks transmitted based on trade links.

[0066] By comprehensively identifying all key supply chain paths and intermediate nodes in the transmission process of implicit water shortage risks, the present invention can help prevent supply chain disruptions caused by water shortages and the spread of implicit water shortage risks at a certain node to the outside, thereby avoiding the generation of systemic risks. This measure not only addresses important challenges in current water resource management but also provides a practical solution for enhancing the stability of the supply chain and the resilience of the trade network.

[0067] Example 1

[0068] As Figure 1 shown, the present invention provides a method for identifying key paths and intermediate nodes of implicit water shortage risk transmission based on the betweenness centrality algorithm, including the following steps:

[0069] S1. Obtain the water shortage probability of each region, and calculate the water shortage risk of each department in each region based on the water resource dependence of each department in each region combined with the water shortage probability of each region;

[0070] Preferably, the expression for the water shortage probability of each region is:

[0071]

[0072] In the formula: WSP i represents that the water shortage probability of region i is equal to the expected value of the random variable w i ; the random variable w i follows a lognormal distribution, and its variance σ is the standard deviation, equal to 1; where WSI i represents the water stress index of region i, WC i represents the water consumption of region i, and Q i represents the available fresh water volume of region i.

[0073] Preferably, the expression for the water resource dependence of each department in each region is:

[0074]

[0075] In the formula: WD m,i represents the water resource dependence of department m in region i; WC m,i represents the water consumption of department m in region i; WI m,i represents the water intensity of department m in region i, which is equal to the water consumption WC m,i of the department in the region divided by its total output x m,i ; α is the truncation parameter of WD m,i , set to 0.5.

[0076] Preferably, the expression for the water shortage risk of each department in each region is:

[0077] WSR m,i = WSP i × WD m,i × x m,i ;

[0078] Where: WSR m,i represents the water shortage risk of department m in region i; WSP i represents the water shortage probability of region i; WD m,i represents the water resource dependence degree of department m in region i; x m,i represents the total output of department m in region i.

[0079] S2. Construct an implicit water shortage risk transfer matrix based on the water shortage risks of each department and the multi-regional input-output model;

[0080] Preferably, the expression of the implicit water shortage risk transfer matrix is:

[0081]

[0082] Where: U represents a matrix, and its element represents the amount of implicit water shortage risk transferred from department m (donor) in region i to department n (recipient) in region j;

[0083] W is a row vector, and each element represents the water shortage risk of each department in each region. The expression is the process of diagonalizing the vector W;

[0084] The matrix (I - B) -1 is usually called the Ghosh inverse matrix, and its element represents the output volume of department n in region j caused by department m in region i for producing a unit product (including direct and indirect), B is the direct output coefficient matrix in the multi-regional input-output model, and I is the identity matrix.

[0085] S3. Based on the structural path analysis SPA and the implicit water shortage risk transfer matrix, identify the key transfer paths of the implicit water shortage risk and construct an implicit water shortage risk transfer network;

[0086] Preferably, based on the structural path analysis SPA and the implicit water shortage risk transfer matrix, the specific content of identifying the key transfer paths of the implicit water shortage risk and constructing an implicit water shortage risk transfer network is:

[0087] After performing a Taylor expansion on the Ghosh inverse matrix, decompose the implicit water shortage risk into different production levels:

[0088] G = (I - B) -1 = I + B + B 2 + B3 +…;

[0089]

[0090] Suppose a specific supply chain path starts from department m in region i, passes through department k (r1, r2, … r k ), and ends at department q in the same region. The amount of implicit water shortage risk transmitted by this path can be mathematically expressed as follows:

[0091]

[0092] In the formula: EWSR SPA represents the amount of implicit water shortage risk transmitted through this path; P(m, qr1, r2, … r k ) represents the weight of the supply chain path (m → r1 → r2 → … → r k → q);

[0093] W m,i represents the water shortage risk of department m in region i;

[0094] Element is an element in matrix B;

[0095] By comparing the magnitudes of the EWSR SPA values of each path, the critical transmission path of the implicit water shortage risk is determined;

[0096] The implicit water shortage risk transmission network is composed of supply chain paths.

[0097] S4. Identify the critical intermediate nodes in the implicit water shortage risk transmission network based on the Betweenness centrality algorithm.

[0098] Preferably, the specific content of identifying the critical intermediate nodes in the implicit water shortage risk transmission network based on the Betweenness centrality algorithm is as follows:

[0099]

[0100] In the formula: b i represents the Betweenness centrality of department i;

[0101] n represents the number of departments in the implicit water shortage risk transmission network;

[0102] t k represents the occurrence time of department i between the two ends of the supply chain path (m → r1 → r2 → … → r k → q).

[0103] Define the total weight of the supply chain paths passing through department i as bi (l1, l2):

[0104]

[0105] Where: l1 represents the number of upstream departments of department i, and l2 represents the number of downstream departments of department i. Both l1 and l2 are integers greater than or equal to 1;

[0106] J i represents a matrix that is 1 at the (i, i) element and 0 at other elements;

[0107] e represents a unit column vector e of size n×1, all of whose elements are equal to 1.

[0108] Define T = GB = BG = B + B 2 +B 3 +…, the betweenness centrality of department i can be written as:

[0109]

[0110] Where: the n×n matrix T = GB is composed of the Ghosh inverse matrix G and the direct output coefficient matrix B, and the element t in the matrix ij represents the direct and indirect output of department j generated by the single output of department i;

[0111] By comparing the betweenness centrality values b i of each regional department, the key intermediate nodes in the implicit water shortage risk transmission network are determined.

[0112] Example 2

[0113] As Figure 2 shown, a key path and intermediate node identification system for implicit water shortage risk transmission based on the betweenness centrality algorithm includes:

[0114] Data acquisition unit: Obtain the water shortage probability of each region, and obtain the water shortage risk of each department in each region by combining the water resource dependence of each department in each region with the water shortage probability of each region;

[0115] Matrix calculation unit: Calculate the implicit water shortage risk transfer matrix based on the water shortage risk of each department and the multi-regional input-output model;

[0116] Path identification unit: Based on the structural path analysis SPA and the implicit water shortage risk transfer matrix, identify the key transmission paths of the implicit water shortage risk and construct the implicit water shortage risk transmission network;

[0117] Intermediate node identification unit: Based on the betweenness centrality algorithm Betweenness, identify the key intermediate nodes in the implicit water shortage risk transmission network.

[0118] Example 3

[0119] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the method for identifying the critical path and intermediate nodes of implicit water shortage risk transmission based on the betweenness centrality algorithm are implemented.

[0120] Example 4

[0121] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the method for identifying a critical path and intermediate nodes for transmitting an implicit water shortage risk.

[0122] Example 5

[0123] Based on the input-output table data of 2017, each province and city contains 42 industrial sectors, and the data is up to date as of 2017. The key path and intermediate node identification method of implicit water shortage risk transmission described in Example 1 is used to identify the key path and intermediate nodes of implicit water shortage risk transmission according to the algorithms and formulas specified in each step. The results are as follows:

[0124] The five regional sectors with the greatest risk of water shortage are: Hebei - agriculture, forestry, animal husbandry and fishery services (101.6 billion yuan), Jiangsu - textile industry (97.8 billion yuan), Shaanxi - non-metallic mineral and other mineral mining and dressing industries (71.2 billion yuan), Shanghai - chemical industry (70.9 billion yuan), and Beijing - food manufacturing industry (59.7 billion yuan).

[0125] The key supply chain paths for the transmission of implicit water shortage risks: Shanghai-Chemical Industry → Zhejiang-General Equipment Manufacturing Industry (2.1 billion yuan), Jiangsu-Chemical Industry → Shandong-Food Manufacturing Industry (1.8 billion yuan), Henan-Agriculture, Forestry, Animal Husbandry and Fishery Services → Guangdong-General Equipment Manufacturing Industry (1.6 billion yuan), Anhui-Metal Products, Machinery and Equipment Repair Services → Guangdong-Information Transmission, Software and Information Technology Services (1.5 billion yuan), Beijing-Papermaking, Printing, Educational and Sports Goods Manufacturing Industry → Liaoning-Waste and Scrap (1.1 billion yuan).

[0126] The key intermediate nodes for the transmission of implicit water shortage risks: Shanghai-chemical industry (99.7 billion yuan), Hebei-food manufacturing industry (91.5 billion yuan), Guangdong-communication equipment, computer and other electronic equipment manufacturing industry (86.4 billion yuan), Shaanxi-metal products industry (80.9 billion yuan), Zhejiang-general equipment manufacturing industry (75.5 billion yuan).

[0127] The water shortage risk values within brackets in the above results are relative values, rather than actual amounts of economic losses. These relative values reflect the relative magnitudes of potential economic losses. By comparing the magnitudes of these values, the key supply chain paths and intermediate nodes for the transmission of implicit water shortage risks can be identified.

[0128] The above results reveal that local water shortage risks can cause potential indirect economic losses to external regional departments through the trade network, and clarify the key supply chain paths and intermediate nodes for the transmission of implicit water shortage risks, laying a foundation for systematically and comprehensively evaluating the impact of water shortage risks on the economy. This analysis provides data support for formulating more effective response strategies, thereby enhancing the resilience of the entire trade network in the face of implicit water shortage risks. The significance of identifying the key intermediate nodes lies in helping us intervene in risk propagation in a timely manner, so as to prevent potential serious consequences.

[0129] Specifically, for the regional departments on the key supply chain paths for the transmission of implicit water shortage risks, each regional department should take proactive measures to reduce the risk impact: First, adjust trade strategies and optimize the industrial structure to reduce dependence on specific suppliers. Second, establish inter-regional cooperation mechanisms to enhance the ability to respond to implicit water shortage risks through resource and technology sharing. Finally, strengthen the monitoring and evaluation system to promptly identify potential risks and formulate corresponding emergency plans to ensure a rapid and effective response in the event of a risk. For the key intermediate nodes in the implicit water shortage risk transmission network, each regional department can take the following measures: First, improve the utilization efficiency and management level of water resources to ensure a stable supply during demand fluctuations. Second, promote the diversification of enterprise supply sources to reduce dependence on any single upstream regional department or input, thereby enhancing the resilience of the system. In addition, strengthen cooperation with the key intermediate nodes of the supply chain, utilize information sharing platforms and technical means to improve the response ability to water shortage events, so as to achieve more efficient risk management.

[0130] Finally, it should be noted that the above embodiments are only used to illustrate the technical method of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical method of the present invention or make equivalent replacements, and these modifications or equivalent replacements cannot make the modified technical method deviate from the spirit and scope of the technical method of the present invention.

Claims

1. A method for identifying the key paths and intermediate nodes of implicit water shortage risk transmission based on betweenness centrality algorithm, characterized in that: The following steps are involved: S1. Obtain the probability of water shortage in each region, and calculate the water shortage risk of each department in each region based on the water resource dependence of each department in each region and the water shortage probability of each region; S2. Construct an implicit water shortage risk transfer matrix based on the water shortage risks of each sector and the multi-regional input-output model; S3. Based on structural path analysis and implicit water shortage risk transmission matrix, identify the key transmission paths of implicit water shortage risk and construct the implicit water shortage risk transmission network; S4, Identify key intermediate nodes in the implicit water shortage risk transmission network based on the betweenness centrality algorithm; The expression of water shortage probability in each region is: Where: WSP i The probability of water shortage in region i is equal to the random variable w i The expected value of the random variable w i It follows a log-normal distribution with a variance of σ is the standard deviation, which is equal to 1; Among them WSI i represents the water stress index of region i, WC i represents the water consumption of area i, Q i represents the amount of fresh water available in region i; The expression of water resource dependence of each department in each region is: Where: WD m,i represents the water resource dependence of department m in region i; WC m,i represents the water consumption of department m in region i; WI m,i represents the water intensity of department m in region i, which is equal to the water consumption WC of the department in the region m,i Divide by its total output x m,i ; α is WD m,i The cutoff parameter is set to 0.

5.

2. According to the method of claim 1, the key path and intermediate node identification method of implicit water shortage risk transmission based on betweenness centrality algorithm is characterized in that: The expression of water shortage risk in each sector in each region is: WSR m,i =WSP i ×WD m,i ×x m,i ; Where: WSR m,i represents the water shortage risk of sector m in region i; WSP i represents the probability of water shortage in region i; WD m,i represents the water resource dependence of department m in region i; x m,i represents the total output of sector m in region i.

3. According to claim 2, a method for identifying critical paths and intermediate nodes of implicit water shortage risk transmission based on betweenness centrality algorithm is characterized in that: The expression of the implicit water shortage risk transfer matrix is: Where: U represents a matrix, whose elements It represents the implicit water shortage risk transmitted from department m in region i to department n in region j; W is a row vector, each element of which represents the water shortage risk of each sector in each region. It refers to the process of diagonalizing vector W; Matrix (IB) -1 It is called the inverse Ghosh matrix, whose elements It represents the output of department n in region j caused by the cumulative production of unit products in department m in region i, B is the direct output coefficient matrix in the multi-region input-output model, and I is the unit matrix.

4. According to claim 3, a method for identifying critical paths and intermediate nodes of implicit water shortage risk transmission based on betweenness centrality algorithm is characterized in that: Based on structural path analysis and implicit water shortage risk transmission matrix, the key transmission paths of implicit water shortage risk are identified and the specific contents of implicit water shortage risk transmission network are constructed as follows: After Taylor expansion of the Ghosh inverse matrix, the implicit water shortage risk is decomposed into different production levels: G=(I-B) -1 =I+B+B 2 +B 3 +…; A specific supply chain path starts from department m in region i and passes through departments k (r1, r2, ... r k ), and ends in the q sector within the region. The implicit water shortage risk transmitted by this path is mathematically expressed as follows: Where: EWSR SPA represents the implicit water shortage risk transmitted through this path; P(m,q|r1,r2,…r k ) represents the supply chain path (m→r1→r2→…→r k →q) weight; W m,i represents the water shortage risk of sector m in region i; element is an element in matrix B; By comparing the EWSR of each path SPA The value is then used to determine the key transmission path of the hidden water shortage risk; The implicit water shortage risk transmission network consists of supply chain paths.

5. According to claim 4, a method for identifying critical paths and intermediate nodes of implicit water shortage risk transmission based on betweenness centrality algorithm is characterized in that: The specific content of identifying the key intermediate nodes in the implicit water shortage risk transmission network based on the betweenness centrality algorithm is as follows: Where: b i represents the betweenness centrality of department i; n represents the number of sectors in the implicit water shortage risk transmission network; t k represents the supply chain path (m→r1→r2→…→r k →q) the appearance time of department i between the two ends; Define the total weight of the supply chain path through department i as b i (l1,l2): Where: l1 represents the number of upstream departments of department i, l2 represents the number of downstream departments of department i, and both l1 and l2 are integers greater than or equal to 1; J i represents a matrix where the element (i,i) is 1 and the other elements are zero; e represents a unit column vector e of size n×1, all elements of which are equal to 1; Definition: T = GB = BG = B + B 2 +B 3 +…, the betweenness centrality of department i is written as: Where: The n×n matrix T=GB consists of the Ghosh inverse matrix G and the direct output coefficient matrix B. The elements t in the matrix ij represents the direct and indirect output of sector j generated by the single output of sector i; By comparing the betweenness centrality values ​​b of each regional department i The size of the water shortage risk can be determined by analyzing the key intermediate nodes in the implicit water shortage risk transmission network.

6. A critical path and intermediate node identification system for implicit water shortage risk transmission based on betweenness centrality algorithm, characterized in that: include: Data acquisition unit: obtain the probability of water shortage in each region, obtain the water shortage risk of each department in each region based on the water resource dependence of each department in each region and the water shortage probability of each region; The expression of water shortage probability in each region is: Where: WSP i The probability of water shortage in region i is equal to the random variable w i The expected value of the random variable w i It follows a log-normal distribution with a variance of σ is the standard deviation, which is equal to 1; Among them WSI i represents the water stress index of region i, WC i represents the water consumption of area i, Q i represents the amount of fresh water available in region i; The expression of water resource dependence of each department in each region is: Where: WD m,i represents the water resource dependence of department m in region i; WC m,i represents the water consumption of department m in region i; WI m,i represents the water intensity of department m in region i, which is equal to the water consumption WC of the department in the region m,i Divide by its total output x m,i ; α is WD m,i The cutoff parameter is set to 0.5; Matrix calculation unit: Calculate the implicit water shortage risk transfer matrix based on the water shortage risk of each department and the multi-regional input-output model; Path identification unit: Based on structural path analysis and implicit water shortage risk transmission matrix, identify the key transmission paths of implicit water shortage risks and build an implicit water shortage risk transmission network; Intermediate node identification unit: Identify key intermediate nodes in the implicit water shortage risk transmission network based on the betweenness centrality algorithm.

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