Critical path and intermediate node identification method for implied water shortage risk transmission based on intermediary centrality algorithm

Abstract

The invention discloses a key path and intermediate node identification method for implied water shortage risk transmission based on an intermediary centrality algorithm, and relates to the field of water resource management. The water shortage risk of each department in each area is calculated based on the water resource dependency of each department in each area and in combination with the water shortage probability of each area; constructing a hidden water shortage risk transfer matrix according to the water shortage risk of each department and based on a multi-region input-output model; based on the structural path analysis and the hidden water shortage risk transfer matrix, identifying a key transmission path of the hidden water shortage risk, and constructing a hidden water shortage risk transmission network; the key intermediate nodes in the implicit water shortage risk transmission network are identified based on an intermediary centrality algorithm, and all key transmission paths and intermediate nodes of implicit water shortage risk transmission in a supply chain can be identified, so that the toughness of the whole trade network in coping with water resource shortage is improved.

Description

Technical Field

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

[0002] With global climate change and population growth, water shortage is becoming increasingly serious and 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 lead to direct economic losses in local water-intensive sectors such as agriculture and power generation, but may also spread risks to other regions through the supply chain, causing chain reactions. This 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 to improving the resilience of trade networks.

[0003] Traditional research is mainly limited to water shortage issues within geographical boundaries, and less attention is paid to the transmission mechanism of implicit water shortage risks across regions. Although some studies have identified the source-sink relationship of implicit water shortage risk transmission, the characterization 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 that play the role of "bridges". These intermediate nodes transmit a large number of implicit water shortage risks in the trade network. Identifying the above key intermediate nodes will help to implement effective intervention before the risk spreads to downstream areas. To this end, this application introduces a betweenness centrality algorithm (Betweenness) based on structural path analysis (SPA) to effectively identify the key transmission paths and important intermediate nodes of implicit water shortage risks in the trade network, and provide 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 the key path and intermediate nodes of implicit water shortage risk transmission based on the betweenness centrality algorithm, including the following steps: S1, obtaining the water shortage probability of each region, obtaining 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 transfer matrix based on the water shortage risks of each sector and the multi-regional input-output model;

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

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

[0008] Preferably, the expression of water shortage probability in each area is:

[0009]

[0010] 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.

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

[0012]

[0013] 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.

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

[0015] WSR m,i =WSP i ×WD m,i × m,i ;

[0016] 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.

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

[0018]

[0019] Where: U represents a matrix, whose elements It represents the implicit water shortage risk amount transmitted from sector m (donor) in region i to recipient n in region j;

[0020] 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;

[0021] Matrix (IB) -1 Often called the Ghosh inverse matrix, its elements It represents the cumulative (both direct and indirect) output of department n in region j caused by the 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.

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

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

[0024] G=(IB) -1 =I+B+B 2 +B 3 +…;

[0025]

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

[0027]

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

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

[0030] element is an element in matrix B;

[0031] By comparing the EWSR of each path SPAThe value is then used to determine the key transmission path of the hidden 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 algorithm is:

[0034]

[0035] Where: b i represents the betweenness centrality of department i;

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

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

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

[0039]

[0040] 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;

[0041] J i represents a matrix where the element (i,i) is 1 and the other elements are zero;

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

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

[0044]

[0045] Where: n×n matrix T=GB is composed of Ghosh inverse matrix G and direct output coefficient matrix B. The element t in the matrix ij represents the direct and indirect output of sector j generated by the single output of sector i;

[0046] By comparing the betweenness centrality values ​​b of each regional department iThe size of the water shortage risk can be determined by analyzing the key intermediate nodes in the implicit water shortage risk transmission network.

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

[0048] 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;

[0049] 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;

[0050] Path identification unit: Based on structural path analysis SPA 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;

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

[0052] Preferably, an electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of a method for identifying a critical path and intermediate nodes for transmitting implicit water shortage risks based on an betweenness centrality algorithm are implemented.

[0053] At the same time, in order 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, and when the computer program is executed by a processor, the steps of the method for identifying critical paths and intermediate nodes for implicit water shortage risk transmission based on an betweenness centrality algorithm are implemented.

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

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

[0057] The technical method of the present invention is further described in detail below through the drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a step diagram of a method for identifying a critical path and intermediate nodes for implicit water shortage risk transmission based on a betweenness centrality algorithm of the present invention;

[0059] Figure 2 It is a unit diagram of the key path and intermediate node identification system of the implicit water shortage risk transmission of the betweenness centrality algorithm of the present invention. DETAILED DESCRIPTION

[0060] The technical method of the present invention is further described below by means of the accompanying drawings and embodiments. It should be noted that unless otherwise specifically stated, the relative arrangement of the components and steps, numerical expressions and numerical values ​​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 in nature and is in no way intended to limit the present application, its application, or uses.

[0062] Technologies, systems, and devices known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, systems, and devices should be considered part of the specification.

[0063] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not limiting. Therefore, other examples of the exemplary embodiments may have different values.

[0064] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0065] The present invention shows significant advantages over the prior art in water shortage risk assessment and management. In the invention, water shortage risk not only causes direct economic losses to local water-intensive sectors such as agriculture and power generation, but also may spread the risk to other regions through the supply chain, generating implicit water shortage risks based on trade links.

[0066] By comprehensively identifying all key supply chain paths and intermediate nodes where implicit water shortage risks are transmitted, the present invention can help prevent supply chain disruptions caused by water shortages, as well as 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 improving the stability of the supply chain and the resilience of the trade network.

[0067] Example 1

[0068] like Figure 1 The present invention provides a method for identifying a critical path and intermediate nodes for implicit water shortage risk transmission based on a betweenness centrality algorithm, comprising the following steps:

[0069] 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;

[0070] Preferably, the expression of water shortage probability in each area is:

[0071]

[0072] 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.

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

[0074]

[0075] 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.

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

[0077] WSR m,i =WSP i ×WD m,i × m,i ;

[0078] 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.

[0079] 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;

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

[0081]

[0082] Where: U represents a matrix, whose elements It represents the implicit water shortage risk amount transmitted from sector m (donor) in region i to sector n (receiver) in region j;

[0083] 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;

[0084] Matrix (IB) -1 Often called the Ghosh inverse matrix, its elements It represents the cumulative (both direct and indirect) output of department n in region j caused by the 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.

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

[0086] Preferably, based on the structural path analysis SPA and the implicit water shortage risk transmission matrix, the key transmission paths of the implicit water shortage risk are identified, and the specific contents of constructing the implicit water shortage risk transmission network are as follows:

[0087] After Taylor expansion of the Ghosh inverse matrix, the implicit water shortage risk is decomposed into different production levels:

[0088] G=(IB) -1 =I+B+B 2 +B3 +…;

[0089]

[0090] Assume that a specific supply chain path starts from department m in region i and passes through departments k (r1, r2, ... k ), and ends in sector q within the region. The implicit water shortage risk transmitted by this path can be mathematically expressed as follows:

[0091]

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

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

[0094] element is an element in matrix B;

[0095] 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;

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

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

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

[0099]

[0100] Where: b i represents the betweenness centrality of department i;

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

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

[0103] Define the total weight of the supply chain path 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 where the element (i,i) is 1 and the other elements are zero;

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

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

[0109]

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

[0111] 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.

[0112] Example 2

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

[0114] 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;

[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 structural path analysis SPA 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;

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

[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 ​​in brackets in the above results are relative values, not the actual amount of economic loss. These relative values ​​reflect the relative amount of potential economic losses. By comparing the sizes of these values, the key supply chain paths and intermediate nodes where water shortage risks are transmitted can be identified.

[0128] The above results reveal that local water shortage risks can cause potential indirect economic losses to external regional sectors through trade networks, and identify the key supply chain paths and intermediate nodes for the transmission of implicit water shortage risks, laying the foundation for a systematic and comprehensive assessment of the impact of water shortage risks on the economy. This analysis provides data support for the formulation of more effective response strategies, thereby enhancing the resilience of the entire trade network in dealing with implicit water shortage risks. The significance of identifying key intermediate nodes is that it can help us intervene in risk transmission in a timely manner, thereby preventing potential serious consequences.

[0129] Specifically, for the regional departments on the key supply chain paths of implicit water shortage risk transmission, each regional department should take active measures to reduce the impact of risks: first, adjust trade strategies and optimize industrial structure to reduce dependence on specific suppliers. Second, establish inter-regional cooperation mechanisms to enhance the ability to cope with implicit water shortage risks through resource and technology sharing. Finally, strengthen the monitoring and evaluation system to identify potential risks in a timely manner and formulate corresponding emergency plans to ensure that risks can be responded to quickly and effectively when they occur. 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 stable supply when demand fluctuates. Second, promote enterprises to diversify their 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 key supply chain intermediate nodes, use information sharing platforms and technical means to improve the ability to respond to water shortage events, and 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 rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical method of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical method to 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.

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 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.

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 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.

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: 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.

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 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 Often called the Ghosh inverse matrix, its 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.

6. According to claim 5, 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 sector q within the region. The implicit water shortage risk transmitted by this path can be mathematically expressed as follows: Where: EWSR SPA represents the implicit water shortage risk transmitted through this path; P(m,qr1,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.

7. According to claim 6, a method for identifying critical paths and intermediate nodes of implicit water shortage risk transmission based on betweenness centrality algorithm, 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 occurrence time of sector 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, and l2 represents the number of downstream departments of department i. 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 can be written as: Where: n×n matrix T=GB is composed of Ghosh inverse matrix G and direct output coefficient matrix B. The element 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.

8. 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; 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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