Important node identification method and device for multilayer supply chain network, equipment and medium

Abstract

The invention provides an important node identification method and device for a multilayer supply chain network, equipment and a medium, and relates to the technical field of supply chain management. The method comprises the following steps: constructing a directed weighted multilayer complex network, combining a centrality index, identifying nodes of an intermediate layer network, and obtaining a candidate node set M; according to the M, descending sorting is carried out according to the occurrence frequency of the nodes, in combination with a preset proportion, a head segment and a tail segment of nodes of a descending sorting list are intercepted to serve as a first batch of important node sets and an unconsidered node set, and a to-be-determined node candidate set ranking the middle part is obtained; traversing and calculating the influence on the network efficiency after any node is deleted in the to-be-determined node candidate set, and selecting a node combination with the influence ranking conforming to a threshold value to be added into a second batch of important node sets; and searching important nodes of the upper and lower networks to form a third batch of important node set, thereby completing important node identification. According to the method, the characteristics of the multilayer network can be captured, important nodes can be identified, and the accuracy is high.

Description

Technical Field

[0001] The present invention relates to the technical field of supply chain management, and in particular to a method, device, equipment and medium for identifying important nodes in a multi-layer supply chain network. Background Art

[0002] Driven by globalization, technological progress and increasingly sophisticated market division of labor, supply chain networks are becoming more complex and multi-layered. Supply chain networks are not only the main channels for product flow and value transfer, but also the link between producers, suppliers, distributors and end users. However, the complexity of such networks also makes them more vulnerable to external shocks, affecting the sustainable development of enterprises.

[0003] Most of the existing literature is based on single-layer network node identification methods, ignoring the impact of network scale and real network characteristics on node importance identification. With the increasing complexity of supply chain network structure, traditional single-layer network analysis methods can no longer fully capture its dynamic characteristics. However, multi-layer networks contain multiple interconnected layers, representing different stages of production, logistics and distribution, providing a more comprehensive understanding of supply chain behavior and a more comprehensive perspective for studying interactions between network levels, information transmission and risk propagation.

[0004] Despite the increasing importance of multi-layer supply chain networks, the analysis of their node characteristics has not received sufficient attention in existing research. The main reason is that the complexity of the multi-layer network structure increases the difficulty of node characteristic analysis. However, ignoring these characteristics may lead to insufficient identification of supply chain risks and bottlenecks, thus affecting the supply chain management and decision-making of enterprises.

[0005] In view of this, the applicant filed this application after studying the existing technology. Summary of the invention

[0006] The present invention aims to provide a method, device, equipment and medium for identifying important nodes in a multi-layer supply chain network, so as to solve the shortcomings of existing methods such as being unable to identify and provide real information on the characteristics of each node in a multi-layer supply chain network, and being difficult to accurately identify and determine the optimal key node combination.

[0007] In order to solve the above technical problems, the present invention is implemented through the following technical solutions: A method for identifying important nodes in a multi-layer supply chain network, comprising: S1, based on the upstream and downstream hierarchical relationships of the supply chain network, construct a directed weighted multi-layer complex network ; S2, according to the directed weighted multi-layer complex network , centrality index and the preset proportion of important nodes in the middle layer network, identify the structural characteristic nodes of the middle layer network, and obtain the candidate node set M; wherein the centrality index includes: node degree centrality, closeness centrality, betweenness centrality and structural hole index; S3, sorting the candidate node set M in descending order according to the frequency of occurrence of the nodes, and intercepting the first and last segments of the descending sort list as the first batch of important node sets and the set of nodes not to be considered, respectively, according to a preset interception ratio parameter, so as to obtain a candidate set of nodes to be determined in the middle of the ranking; S4, traversing and calculating the impact of deleting a node from the candidate set of nodes to be determined on the network efficiency, and selecting a node combination whose impact ranking meets a preset threshold to add to the second batch of important node sets; S5, obtaining an intermediate layer important node set according to the first batch of important node sets and the second batch of important node sets; then searching in the upper and lower layers of the directed weighted multi-layer complex network for nodes whose node degree centrality values ​​connected to important nodes in the intermediate layer important node set exceed a preset threshold as important nodes of the upper and lower layers of the network, forming a third batch of important node sets; S6, obtaining a complete set of important nodes based on the intermediate layer important node set and the third batch of important node sets, and completing the identification of important nodes in the multi-layer supply chain network.

[0008] Preferably, in constructing a directed weighted multi-layer complex network hour: First, according to the upstream and downstream hierarchical relationship of the supply chain network, the data of the intermediate layer network is determined; wherein the supply chain network includes the manufacturing supply chain network; Then, based on the supplier and customer data of the middle layer, the upstream and downstream network layers are built respectively to determine the network Upstream enterprise nodes and downstream enterprise nodes and their network layers; According to the preset time period, the network The cooperation frequency of each pair of nodes and the proportion of the average annual cooperation transaction amount in the network are calculated. The weight of the edge to measure the closeness of the connection between enterprises; Determine the network based on the direction of supply chain logistics The direction of the middle edge completes the directed weighted multi-layer complex network 's construction.

[0009] Preferably, the candidate node set M is sorted by calculating the node degree centrality, closeness centrality, betweenness centrality and structural hole index of each node respectively, and sorting them according to the index values; according to the preset ratio , select the corresponding proportion of nodes as candidate nodes, and get the node degree centrality set , closeness centrality set , betweenness centrality set With structural hole collection , thus obtaining the candidate node set M; The calculation formula of the node degree centrality is: ; in, represents the node degree centrality of node i; N is the network The total number of nodes; Indicates the direct relationship between node i and node j; The calculation formula of the closeness centrality is: ; in, represents the closeness centrality of node i; represents the shortest path between node i and node j; The calculation formula of the betweenness centrality is: ; in, Representation Node Betweenness centrality of ; Indicates the number of shortest paths; Indicates passing through node The number of shortest paths; The structural hole index measures the degree of constraint when a node forms a structural hole through the constraint coefficient. The calculation formula is: ; ; ; in, is the set of neighbor nodes of node i; It represents the proportion of energy that node i puts into maintaining the relationship with its neighbor node j, that is, the node connection strength. The more neighbor nodes node i has, The smaller; , are the node connection strengths between nodes i and j and their common neighbor q, respectively; Represents the edge between nodes i and j; constraint coefficient The smaller it is, the more neighbor nodes the node to be evaluated has.

[0010] Preferably, the first set of important nodes Number of The calculation formula is: ; in, A parameter representing the interception ratio of the first set of important nodes; Indicates the number of candidate node sets.

[0011] The node set is not considered Number of The calculation formula is: ; in, represents the interception ratio parameter of the node set not considered; Indicates the number of candidate node sets.

[0012] Preferably, when calculating the network efficiency When , the cascading failure model is used to calculate the impact of important node failure on network robustness, specifically: According to the centrality index, setting the initial load of the cascading failure model node; The maximum capacity of the calculation node is: ; in, Representation Node Maximum capacity; is the spare capacity factor, which is used to measure the processing capacity of the node when it exceeds the initial load; Representation Node Initial load of Assuming that node i fails, if the load exceeds the maximum capacity of the node, a load redistribution process is performed and the failed node Assign to any of its adjacent nodes The load is: ; in, For adjacent nodes Load increment; For adjacent nodes The load distribution weight of For Node The importance of is the node degree centrality index; is the set of neighbor nodes of node i; For Node Real-time load; Then the cascade failure propagation is carried out, and at the preset time step Internal, faulty node The adjacent nodes of Real-time load for: ; in, For adjacent nodes exist Real-time load at the time; For adjacent nodes exist Real-time load at the time; Due to the load redistribution process, the load of the neighboring nodes of the failed node changes. , then node j fails, and a new round of load redistribution process is carried out until a node that meets the node capacity limit is allocated; if , then no new round of load redistribution process is performed, and the propagation process ends; Calculate the network efficiency based on the shortest path length between any two valid nodes in the network : ; ; in, represents the shortest path between nodes i and j, that is, the minimum overload function value; Represents the current valid node set; express The node pair consisting of nodes i and j in the set; Represents a node pair The shortest path length of the network The total number of nodes.

[0013] Preferably, when deleting a node from the candidate set of nodes to be determined, a random attack strategy is used to select the node to be deleted, and then Python programming is used to generate a random sequence to attack the network node.

[0014] Preferably, when deleting a node combination from the candidate set of nodes to be determined, a deliberate attack strategy is adopted to select the nodes to be deleted, that is, the nodes are removed in sequence according to the ranking results of the importance of the nodes.

[0015] The present invention also provides an important node identification device for a multi-layer supply chain network, comprising: Multi-layer supply chain network construction unit, used to construct a directed weighted multi-layer complex network based on the upstream and downstream hierarchical relationships of the supply chain network ; A candidate node set calculation unit is used to calculate the candidate node set according to the directed weighted multi-layer complex network , centrality index and the preset proportion of important nodes in the middle layer network, identify the structural characteristic nodes of the middle layer network, and obtain the candidate node set M; wherein the centrality index includes: node degree centrality, closeness centrality, betweenness centrality and structural hole index; The first batch of important node units is used to sort the candidate node set M in descending order according to the frequency of occurrence of the nodes, and according to a preset interception ratio parameter, intercept the first and last segments of the descending sort list as the first batch of important node sets and the node set not to be considered, respectively, so as to obtain a candidate set of nodes to be determined in the middle of the ranking; The second batch of important node units are used to traverse and calculate the impact of deleting a node from the candidate node set to be determined on the network efficiency, and select node combinations whose impact rankings meet a preset threshold to add to the second batch of important node sets; The third batch of important node units is used to obtain an intermediate layer important node set according to the first batch of important node sets and the second batch of important node sets; then, in the upper and lower layers of the directed weighted multi-layer complex network, search for nodes whose node degree centrality values ​​connected to important nodes in the intermediate layer important node set exceed a preset threshold value as important nodes of the upper and lower layers of the network, forming a third batch of important node sets; The complete important node unit is used to obtain a complete important node set based on the intermediate layer important node set and the third batch of important node sets, so as to complete the important node identification of the multi-layer supply chain network.

[0016] The present invention also provides an important node identification device for a multi-layer supply chain network, including a processor and a memory, wherein the memory stores a computer program, and the computer program can be executed by the processor to implement an important node identification method for a multi-layer supply chain network as described above.

[0017] The present invention also provides a computer-readable storage medium, on which computer-readable instructions are stored. When the computer-readable instructions are executed by a processor of a device where the computer-readable storage medium is located, a method for identifying important nodes in a multi-layer supply chain network as described above is implemented.

[0018] In summary, compared with the prior art, the present invention has the following beneficial effects: The present invention combines four centrality indicators to determine the candidate node set of the middle level, and then combines the influence of node appearance frequency and network efficiency to select the middle-layer important node set through multiple important node screening; then, based on the middle-layer important node set, search for the important nodes of the upper and lower layer networks that meet the preset requirements and are connected to the middle-layer important nodes, so as to realize the identification of important nodes in the multi-layer supply chain network.

[0019] The method of the present invention is applied to a real multi-layer supply chain network model, such as a multi-layer manufacturing supply chain network, to better capture the characteristics of the network and identify important nodes in the multi-layer supply chain network; the identified key supply chain nodes are characterized by high accuracy, and have superior performance in community characteristics, attribute characteristics and ESG performance analysis, and nodes with serious inconsistencies between actual environmental protection behaviors and commitments (referred to as deviations from commitments) are eliminated, thereby optimizing the supply chain management strategy in the enterprise management process, improving the overall resilience and adaptability of the supply chain network, reducing management risks, and maintaining the sustainability and robust development of the supply chain network. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0021] Figure 1 A schematic diagram of a method for identifying important nodes in a multi-layer supply chain network provided in Example 1.

[0022] Figure 2 A flowchart of a method for identifying important nodes in a multi-layer supply chain network provided in Example 1.

[0023] Figure 3 This is a diagram showing changes in network efficiency and the ratio of the largest connected subgraph during random attacks and deliberate attacks provided in Example 1.

[0024] Figure 4 This is the Gephi visualization result diagram provided for Example 2.

[0025] Figure 5 The upstream and downstream concentration distribution of important nodes in the middle layer provided in Example 2.

[0026] Figure 6 This is a network concentration distribution diagram of important nodes in the middle layer provided in Example 2.

[0027] Figure 7 A schematic diagram of an important node identification device for a multi-layer supply chain network provided in Example 3.

[0028] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the invention claimed for protection, but merely represents the selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0030] Embodiment 1 Embodiment 1 of the present invention provides a method for identifying important nodes in a multi-layer supply chain network, which can be implemented by an important node identification device for a multi-layer supply chain network (hereinafter referred to as the important node identification device), and in particular, executed by one or more processors in the important node identification device.

[0031] In this embodiment, the important node identification device may be an electronic device equipped with a processor, the processor having a computer program of the important node identification method of the multi-layer supply chain network and the computer program can be executed, such as a computer, a smart phone, a smart tablet, a workstation, etc., which is not limited here.

[0032] Since multi-layer supply chain networks are composed of multiple interconnected layers, which may represent different product lines, market regions or logistics channels, in-depth analysis of the interactions between these layers not only helps to better understand the nature of supply chain operations, but also provides a scientific basis for identifying key nodes, thereby optimizing supply chain management strategies and improving the overall resilience and adaptability of the network.

[0033] While a single network provides valuable insights into the dynamics of supply chains, other hierarchical relationships in the supply chain, such as the relationship between suppliers and manufacturers or the relationship between manufacturers and distributors, have been largely ignored. Multi-layer supply chain networks involve multiple paths and connections, and disruptions in any layer may have cascading effects throughout the network, causing severe delays and increased costs in the overall supply chain network. Therefore, it is crucial to study the identification of important nodes in multi-layer supply chain networks.

[0034] Using real data to build a real supply chain network model can better capture the characteristics of the network. At the same time, the problem of identifying important nodes in the supply chain network is the basis for studying risk propagation, information diffusion and stability. Therefore, the network construction model is realized, and the relevant analysis methods proposed in combination with the real characteristics of the network will be more in line with the actual situation and have reasonable practical significance.

[0035] Identifying important nodes in a supply chain network usually involves four steps: The first step is to give an initial undirected graph ,in represents a node set, represents the edge set, represents the weight of the edge, Indicates the network layer where the node is located.

[0036] Given a set of all levels of a supply chain network : ..., ..., ; in, Represents a level, i is The i-th layer, n is the total number of levels in the supply chain network, and each level of the supply chain network is composed of enterprise nodes with consistent functions.

[0037] For example, in a three-tier manufacturing supply chain network, Indicates the supplier level, represents the manufacturer level, Indicates the retailer tier.

[0038] In the second step, each level can be defined as a collection of companies with similar functions, namely: ,... ,.., ; in, express The jth node in is the total number of nodes in this layer.

[0039] The third step is to design a suitable multi-layer network important node identification algorithm based on network characteristics to identify important nodes. Generally, a single indicator algorithm is used for identification. The expression of the identified important nodes is: ,.., ,..., , ,..., ,..., ,..., ; ; in, ,.., Indicates the important nodes identified; express The layer; , Indicates the total number of nodes in the corresponding network layer.

[0040] The fourth step is to detect the impact of important nodes on network robustness based on the cascading failure model. The network operation efficiency is used as the main measurement indicator, which can quantify the degree of paralysis of the entire network after the cascading failure occurs. Network efficiency is an important indicator to measure the efficiency of information transmission between nodes in the network. It is usually evaluated by calculating the shortest path length between all pairs of nodes in the network. The higher the network efficiency, the more efficient the information transmission in the network. The expression is: ; ; in, represents the shortest path between nodes i and j, that is, the minimum overload function value. Overload and failure will cause the connectivity of the network to deteriorate. Therefore, the minimum overload function can reflect the efficiency of information transmission between nodes; It represents the average efficiency of the entire network.

[0041] Represents the current valid node set; express The node pair consisting of nodes i and j in the set; Represents a node pair The shortest path length; N is the network The total number of nodes.

[0042] If there is no path between nodes i and j (i.e., they are disconnected), then we usually set =∞ (or a very large number).

[0043] When calculating the shortest path, you can use the Floyd-Warshall algorithm or other shortest path algorithms (such as the Dijkstra algorithm or the Bellman-Ford algorithm) to calculate the shortest path lengths between all node pairs and generate a shortest path matrix D, where 。 In the embodiment of the present invention, two types of indicators based on global network information and local information are considered, and an important node identification algorithm (FMSM) integrating multi-scale indicators is proposed. This method takes advantage of the four indicators of node degree centrality, closeness centrality, betweenness centrality, and structural hole index to effectively select more important nodes in the identification process, avoiding the defect that a single algorithm is not applicable in some scenarios.

[0044] like Figure 1-Figure 2 As shown, a method for identifying important nodes in a multi-layer supply chain network includes steps S1 to S6.

[0045] S1, based on the upstream and downstream hierarchical relationships of the supply chain network, construct a directed weighted multi-layer complex network .

[0046] Furthermore, in constructing a directed weighted multi-layer complex network hour: First, according to the upstream and downstream hierarchical relationships of the supply chain network, determine the data of the middle-layer network; for example, according to the supply chain network of the manufacturing industry, suppliers, manufacturers, distributors or retailers, determine the data of the middle-layer network, that is, the manufacturer's data; Then, based on the supplier and customer data of the middle layer, the upstream and downstream network layers are built respectively to determine the network Upstream enterprise nodes and downstream enterprise nodes and their network layers; According to the preset time period, the network The cooperation frequency of each pair of nodes and the proportion of the average annual cooperation transaction amount in the network are calculated. The weight of the edge to measure the closeness of the connection between enterprises; Determine the network based on the direction of supply chain logistics The direction of the middle edge completes the directed weighted multi-layer complex network 's construction.

[0047] Of course, other methods can also be used to build the network as needed , there is no limitation here. For example, when calculating edge weights, only transaction amount data can be used, or other indicators can be combined for weighted calculation.

[0048] S2, according to the directed weighted multi-layer complex network , centrality index and the preset proportion of important nodes in the middle layer network , identify the structural feature nodes of the middle layer network and obtain the candidate node set M; wherein the centrality indicators include: node degree centrality, closeness centrality, betweenness centrality and structural hole indicators.

[0049] Furthermore, the candidate node set M is sorted by calculating the node degree centrality, closeness centrality, betweenness centrality and structural hole index of each node respectively, and sorting them according to the index values; according to the preset ratio , select the nodes corresponding to the index value as candidate nodes, and obtain the node degree centrality set , closeness centrality set , betweenness centrality set With structural hole collection , thus obtaining the candidate node set M; The node degree centrality is an indicator that measures the number of direct connections of a node in the network. That is, the larger the degree of a node, the more important the node is in the network. The degree of a node refers to the number of edges directly connected to the node. The calculation formula is: ; in, represents the node degree centrality of node i; N is the network The total number of nodes; Indicates the direct relationship between node i and node j; The closeness centrality, or adjacency centrality, is an indicator that measures the proximity of a node to other nodes in the network. The higher the adjacency centrality of a node, the shorter the average shortest path to other nodes in the network, that is, the more central the node is in the network. The calculation formula is: ; in, represents the closeness centrality of node i; represents the shortest path between node i and node j; The betweenness centrality is an indicator that measures whether a node serves as a bridge for the shortest paths between other nodes in the network. The higher the betweenness centrality of a node, the more critical it is in the network, because more shortest paths pass through the node. The calculation formula is: ; in, Representation Node Betweenness centrality of ; Indicates the number of shortest paths; Indicates passing through node The number of shortest paths; The structural hole indicator (Structural Hole) refers to the gap or blank between two nodes that are not directly connected in the network. When a third node can bridge this gap, this node has the advantage of a structural hole. By filling this "bridging" role, the node gains control over information and resources and the uniqueness of information. The structural hole theory believes that the more structural holes a node occupies, the stronger its ability to control information, the more resources it can obtain, and the more competitive advantages it has. The position and influence of a node in a structural hole can be quantitatively evaluated by calculating indicators such as the effective size, efficiency, and constraint of the node.

[0050] In this embodiment, a constraint coefficient is defined to measure the degree of constraint when a node forms a structural hole. The constraint coefficient can reflect the connection density between a node and its neighboring nodes. If the constraint coefficient of a node is smaller, it means that the neighborhood connection density is lower and it is easier to form a structural hole. The calculation formula is: ; ; ; in, is the set of neighbor nodes of node i; It represents the proportion of energy that node i puts into maintaining the relationship with its neighbor node j, that is, the node connection strength. The more neighbor nodes node i has, The smaller; , are the node connection strengths between nodes i and j and their common neighbor q, respectively; Represents the edge between nodes i and j; constraint coefficient The smaller it is, the more neighbor nodes the node to be evaluated has, and the degree of closure between neighbor nodes is not high, which is more conducive to expanding the influence range of the node, indicating that this node has a wide influence in the network and is very important.

[0051] According to the node degree centrality set , closeness centrality set , betweenness centrality set With structural hole collection , get the candidate node set M: M= + + + .

[0052] S3, according to the candidate node set M, the nodes are sorted in descending order according to their frequencies of occurrence. According to the preset interception ratio parameter, the first and last segments of the descending sorted list are intercepted as the first batch of important node sets and the set of nodes not to be considered, respectively, so as to obtain the candidate set of nodes to be determined in the middle part of the ranking.

[0053] Let the intercept ratio parameter be and , then the first batch of important node sets is the top-ranked node set in the candidate node set M, and its number The calculation formula is: ; in, A parameter representing the interception ratio of the first set of important nodes; represents the number of the candidate node set; The node set is not considered is the node set with the lowest ranking in the candidate node set M, and its number The calculation formula is: ; in, Indicates the interception ratio parameter of the node set not considered.

[0054] Then, the candidate set of nodes to be determined in the middle of the ranking is

[0055] S4, traverse and calculate the impact on network efficiency after deleting a node from the candidate node set to be determined, and select a node combination with an impact ranking that meets a preset threshold to add to the second batch of important node sets ; Specifically, in the candidate set of nodes to be determined In the process, the influence of each node combination failure on network efficiency is calculated by traversing and calculating. According to the influence on network efficiency, the node combination whose influence ranking meets the preset threshold (set as needed, such as ranking first or ranking top 5, which is not limited here) is selected to screen out the second batch of important node sets. Then, the important nodes in the middle layer are .

[0056] When a node in a multi-layer supply chain network encounters an emergency and fails, it often triggers a chain reaction, affecting the operation of the entire supply chain. When a node fails, the nodes that have a cooperative relationship with it are affected and need to urgently find a replacement node, which increases the pressure on the replacement node or even collapses it, thus affecting the nodes in the relevant range and causing them to fail one after another. This effect continues to expand and eventually paralyzes the entire network.

[0057] When calculating the network efficiency, a cascading failure model is used to calculate the impact of failure of important nodes on the network. The cascading failure design process is specifically as follows: The first step is to set the initial load of the node of the cascading failure model according to the centrality index; The second step is to calculate the maximum capacity of the node. The formula is: ; in, Representation Node Maximum capacity; is the spare capacity factor, which is used to measure the processing capacity of the node when it exceeds the initial load; Representation Node Initial load of The third step is load redistribution. Assuming that node i fails, if the load exceeds the maximum capacity of the node, the load redistribution process is carried out and the failed node Assign to any of its adjacent nodes The load is: ; in, For adjacent nodes Load increment; For adjacent nodes The load distribution weight of For Node The importance of is the node degree centrality index; is the set of neighbor nodes of node i; For Node Real-time load; The fourth step is to carry out cascading failure propagation at a preset time step. Internal, faulty node The adjacent nodes of Real-time load for: ; in, For adjacent nodes exist Real-time load at the time; For adjacent nodes exist Real-time load.

[0058] Due to the load redistribution process, the load of the neighboring nodes of the failed node changes. , then node j fails, and a new round of load redistribution process is carried out until a node that meets the node capacity limit is allocated; if , then no new round of load redistribution process is performed, and the propagation process ends; Then, the network efficiency is calculated based on the shortest path length between any two valid nodes in the network. . The calculation method of has been described above and will not be repeated here.

[0059] Preferably, when deleting a node from the candidate set of nodes to be determined, a random attack or deliberate attack strategy is used to select the node to be deleted, and then the supply chain network is attacked. When the random attack strategy is selected, Python programming is used to generate a random sequence to attack the network nodes.

[0060] When the deliberate attack strategy is selected, the nodes are removed in sequence according to the ranking results of the importance of the nodes.

[0061] S5, obtaining an intermediate layer important node set according to the first batch of important node sets and the second batch of important node sets Then, in the upper and lower networks of the directed weighted multi-layer complex network, nodes whose node degree centrality values ​​connected to the important nodes in the middle layer important node set exceed a preset threshold are searched as important nodes of the upper and lower network to form the third batch of important node set g.

[0062] Specifically, the set of important nodes in the middle layer .

[0063] The preset threshold here can select nodes with larger degree values ​​according to actual conditions, thereby selecting the number of important nodes in the upper and lower network layers to form the third batch of important node set g.

[0064] S6, based on the intermediate layer important node set Together with the third batch of important node sets g, a complete set of important nodes is obtained, completing the identification of important nodes in the multi-layer supply chain network.

[0065] Specifically, the complete set of important nodes is When identifying important nodes, three parameters can be adjusted according to actual needs: , , , thereby controlling the number of complete important node sets output at the end. , , .

[0066] In another preferred embodiment, the algorithm of the present invention (FMSM) is compared with other four algorithms in terms of the impact of failure of the identified important nodes on network efficiency. See Table 1, which shows the superiority of the FMSM algorithm from both vertical and horizontal comparisons.

[0067] This experiment compares the quality of important nodes by referring to the change in network efficiency after deleting important nodes. , set to 0.05, 0.1, and 0.2 respectively. As can be seen from the table, compared with the four important node identification methods of node degree centrality, adjacency centrality, betweenness centrality, and structural holes, the FMSM algorithm has a greater impact on network efficiency, which proves the effectiveness of the FMSM algorithm.

[0068] Table 1. Comparison of improved algorithms under different important node ratios

[0069] To identify the proportion of important nodes in the middle layer; the numbers in brackets represent the number of important nodes in the middle layer.

[0070] At the same time, two attack strategies, random attack and deliberate attack, are used to attack the supply chain network to study its anti-destruction ability. The random attack is to randomly delete the node numbers, and then use Python programming to generate a random sequence attack to delete the network node combination; the deliberate attack is to remove the nodes in sequence according to the ranking results of the node importance index. Among them, the backup capacity coefficient in the cascading failure model is set to 0.2.

[0071] like Figure 3 The figure shows the changes in network efficiency (Figure (a)) and the proportion of the largest connected subgraph (Figure (b)) when the supply chain network faces random attacks (random, brown line in the figure) and intentional attacks (constraint, purple line in the figure) under cascading failure. The horizontal axis represents the proportion of attacked nodes, and the vertical axis represents the proportion of reduced network efficiency (the negative sign indicates that the network efficiency is decreasing). The FMSM algorithm (blue line in the figure) and the important nodes identified by node degree centrality (degree, orange line in the figure) and betweenness centrality (betweenness, red line in the figure) respectively show better performance, while closeness centrality (closeness, green line in the figure) performs poorly.

[0072] from Figure 3It can be seen that when the network faces random attacks (random) under cascading failure conditions, the network efficiency and the proportion of the network's largest connected subgraph decrease slowly due to the sparsity of the network, indicating that random failures within a small range have little impact on the overall operation of the network. When the attack method is changed to intentional attack (constraint), it can be found that as the scale of node failures gradually increases, the changes in network efficiency and the largest connected subgraph gradually decrease. Among them, no matter how the attack ratio changes, the impact of the algorithm FMSM always remains at the position with the greatest impact. When the proportion of attack nodes reaches 50%, the efficiency of the entire network is reduced to almost 0 and is about to collapse.

[0073] Therefore, the test of the cascading failure model further shows that the FMSM algorithm has certain advantages in identifying important nodes. At the same time, the network will show completely different degrees of collapse and states when it is attacked randomly and intentionally. This phenomenon also proves that the identification of important nodes is of great significance to the management and control of network risks.

[0074] In summary, compared with the prior art, the present invention has the following beneficial effects: The present invention proposes an important node identification algorithm that integrates multi-scale indicators for multi-layer supply chain networks, and through characteristic analysis of important nodes in the middle layer, reveals the central role of important nodes in the supply chain network and their importance in network risk prevention and control and information dissemination.

[0075] The algorithm of the present invention is applied to real data to build a real supply chain network model, which can better capture the characteristics of the network, identify important nodes, optimize the supply chain management strategy, improve the overall resilience and adaptability of the network, and maintain the sustainability and robustness of the supply chain network.

[0076] Embodiment 2 The second embodiment selects A-share listed companies that have survived for a long time from 2012 to 2022 as the middle-layer nodes of the network, and uses the supply chain data of the middle-layer nodes to build a multi-layer supply chain network. Considering the availability of data and the robustness of the research results, the original samples are processed as follows: (1) Screening of listed manufacturing companies; (2) Considering that companies that deviate from their commitments are easily eliminated by the market and affect the robustness of the supply chain, we counted the deviations from commitments of all listed companies based on the ESG data of China Securities and Bloomberg ESG, and matched the companies whose deviations from commitments were below the median among the listed manufacturing companies; (3) Companies listed before 2012 were excluded to ensure the robustness of the statistical results; (4) Samples marked as *ST and ST enterprises and samples with missing customer and supplier information were eliminated; (5) Calculate the weight of the link based on the cooperation frequency and average annual cooperation transaction volume of supply chain enterprises from 2012 to 2022.

[0077] Finally, a total of 4,562 research samples were obtained, including 177 listed manufacturing companies in the middle layer, 2,276 supplier samples and 2,109 customer samples. Among them, the supply chain data of listed companies came from the China Stock Market & Accounting Research Database (CSMAR), and the corporate ESG data came from the Chinese Research Data Services (CNRDS).

[0078] Corporate ESG (Environmental, Social and Governance) data is created by commercial and non-profit organizations to assess whether a company's environmental commitments, social responsibilities, and business models are consistent with sustainable development goals.

[0079] When constructing the network, this embodiment first determines the data of the middle layer network, and then builds the upstream and downstream network layers based on the supplier and customer data of the middle layer. The upstream enterprise nodes and downstream enterprise nodes of the network and their network layers are determined according to the supply chain relationship of the listed companies. In addition, the weight of the edge is calculated according to the frequency of cooperation between each pair of nodes and the average annual proportion of cooperative transactions in the time period to measure the closeness of the connection between enterprises. Based on the direction of supply chain logistics, the direction of the edge of the network node is determined, and the frequency of cooperation between node enterprises is added as the weight of the edge, thereby constructing a three-layer supply chain network with 4562 nodes and 4831 directed weighted edges.

[0080] The network density value of a directed graph ranges from 0 to 1, where 0 means there is no connection in the network and 1 means every pair of nodes in the network is connected. The higher the network density, the denser the network and the more connections between nodes; conversely, the lower the density, the sparser the network and the fewer connections between nodes. The network density value is represented by the ratio of the number of existing directed edges (E) to the number of possible directed edges V*(V-1), that is: ; Among them, V represents the number of nodes.

[0081] The graph density of the multi-layer supply chain network in this study is calculated to be 0.000232, indicating that the network in this study is relatively sparse. This means that there are very few direct connections between supply chain nodes in the network, and there may be a large number of indirect connections. Network sparseness may lead to difficulties in information transmission, resource flow, and other aspects, as well as an impact on the overall operation of the supply chain network. For managers of supply chain networks, it is necessary to further strengthen the connection between network nodes and optimize the network structure to improve information transmission efficiency, resource coordination capabilities, and overall operational efficiency.

[0082] Furthermore, through Gephi visualization, we can get Figure 4 From the network diagram shown, it can be seen that the weight of the nodes in the diagram is measured by the node degree, that is, the larger the node degree value, the larger the shape of the node; the edge color is determined according to the source node of the edge, that is, if the supplier node is connected to the middle core layer node, the edge color between the two is consistent with the supplier node.

[0083] Among the upstream and downstream nodes of manufacturing enterprises, the number of nodes of upstream suppliers and downstream customers is almost the same, while nodes with larger node degrees are mainly distributed in the middle-layer network. The upstream and downstream links of enterprises in the supply chain have relatively balanced importance and scale, reflecting the relative balance of the supply and sales links of enterprises in the supply chain, as well as the close cooperation between enterprises and suppliers and customers. There are some nodes with high importance and connectivity in the middle layer, which are nodes that play key roles in the middle links such as logistics, warehousing, and distribution. These nodes have more connections in the network, play the role of bridges and ties, promote the smooth operation of the supply chain, and are crucial to the tasks of information transmission, resource coordination, and collaboration.

[0084] Then identify the entities that play key roles in the supply chain network, such as suppliers, manufacturers, distributors or retailers. These key nodes usually have a decisive impact on the overall performance of the supply chain.

[0085] Taking into account the sparsity and "hourglass-shaped" characteristics of the multi-layer supply chain network, the method of "extending from the middle layer clustering to the upper and lower layers" is adopted to identify the important nodes of the middle layer network, thereby determining the scope of the important nodes of the upper and lower layers and completing the important node identification task. In such a network feature, identifying the middle layer nodes can greatly reduce the complexity and has a high accuracy. Therefore, this embodiment divides the important node identification task into two main steps: the first step is to identify the important nodes in the middle layer of the network; the second step is to identify the important nodes in the upstream and downstream network layers.

[0086] According to the algorithm of the present invention, important nodes in the middle layer are identified. Since the nodes in the middle layer of the supply chain network are all listed companies, they have rich characteristics, including basic attribute characteristics, supply chain attribute characteristics and ESG performance characteristics.

[0087] Sort the nodes in descending order of importance. Collect statistics on the network layer and basic characteristics of the nodes. The important nodes identified this time are all from the electrical machinery and equipment manufacturing industry category of the second-layer network. In addition, the important nodes in the supply chain network are all distributed in the middle layer, and the "bridge" role played by the nodes in the middle layer is in line with the characteristic structure of the multi-layer supply chain network. From the perspective of the industry distribution of enterprises, manufacturing and technology enterprises dominate the key node enterprises, covering a wide range of fields from traditional manufacturing to high-tech. In addition, core node enterprises in the fields of energy, chemical industry and medicine play a core role in raw material supply and product research and development in the supply chain network. The middle layer nodes contain rich supply chain information. Figure 5 As shown, this embodiment analyzes the attribute characteristics of important nodes from eight supply chain concentration indicators, including the average annual sales of the enterprise's largest customer (per_firstcus), the average annual purchase amount of the largest supplier (per_firstsup), the average annual customer concentration (per_cen_cus), the average annual supplier concentration (per_cen_sup), the average annual total operating income (per_gross), the average annual supply chain concentration (per_cen_sc), the average annual customer concentration Herfindahl index (per_cus_her_index), and the average annual supplier concentration Herfindahl index (per_sup_her_index).

[0088] Figure 5 In the figure, the horizontal axis represents the important nodes in the middle layer, the vertical axis represents the indicator range of all nodes in the middle layer in the data, and the red dotted line represents the average value of the indicator of the total nodes in the middle layer. The results in the figure show that the important nodes in the middle layer have a relatively balanced performance in various indicators. The nodes below the average value are mainly around the average value, while the nodes above the average value may have outstanding performance in this indicator.

[0089] Relatively speaking, important nodes perform better in terms of the average annual sales of the largest customer (per_firstcus), the average annual purchase amount of the largest supplier (per_firstsup), and the average annual customer concentration (per_cen_cus), indicating that important nodes control the main sources of large customers and suppliers in the supply chain. In particular, the good performance of the average annual customer concentration reflects that important nodes have a strong ability to maintain important large customers. However, the performance of the average annual supplier concentration is poor, indicating that only a small number of important nodes attach importance to maintaining relationships with key suppliers, and a large number of important nodes may not attach importance to controlling major suppliers, indicating that the supplier body in the supply chain is large, competition is fierce, and it is easy to face customer loss problems.

[0090] Figure 6 It shows the performance of four indicators: annual average operating revenue (per_gross), annual average supply chain concentration (per_cen_sc), annual average customer concentration Herfindahl index (per_cus_her_index) and annual average supplier concentration Herfindahl index (per_sup_her_index) of enterprises at important nodes in the middle layer.

[0091] It can be seen that the important nodes in the middle layer perform better in the two indicators of average annual supply chain concentration and average annual customer concentration Herfindahl index, and perform poorly in the two indicators of average annual total operating income and average annual supplier concentration Herfindahl index. This situation reflects that important nodes attach great importance to the supply chain entities that affect important operating income and expenditure, especially customers. Relatively speaking, important nodes may not perform well in total operating income, indicating that important nodes are more medium-sized enterprises. Such enterprises play an important "connecting" role in the network, which once again proves the "bridge" status of important nodes in the network. The poor performance of the Herfindahl index of the average annual supplier concentration also echoes the poor performance of important nodes in supplier concentration mentioned above.

[0092] As can be seen from Table 2, the ESG performance of manufacturing enterprises in the supply chain network is generally good, and enterprises pay more attention to the performance of the two dimensions of social performance (Soc._score) and corporate governance (Gov._score).

[0093] Table 2. ESG performance statistics of middle-tier nodes

[0094] ESG_score represents ESG score; Env._score represents environmental score; Soc._score represents social responsibility score; Gov._score represents corporate governance score.

[0095] In summary, this embodiment establishes a multi-layer supply chain network model based on the supply chain data of listed manufacturing companies from 2012 to 2022. In order to further understand the internal structure of the supply chain network, this embodiment proposes an important node identification algorithm (FMSM) that integrates multi-scale indicators through feature analysis of the multi-layer network. Through the feature analysis of important nodes in the middle layer, the central role of important nodes in the supply chain network and their importance in network risk prevention and control and information dissemination are revealed.

[0096] Embodiment 3 like Figure 7 As shown, the third embodiment of the present invention further provides an important node identification device for a multi-layer supply chain network, comprising: Multi-layer supply chain network construction unit, used to construct a directed weighted multi-layer complex network based on the upstream and downstream hierarchical relationships of the supply chain network ; A candidate node set calculation unit is used to calculate the candidate node set according to the directed weighted multi-layer complex network , centrality index and the preset proportion of important nodes in the middle layer network, identify the structural characteristic nodes of the middle layer network, and obtain the candidate node set M; wherein the centrality index includes: node degree centrality, closeness centrality, betweenness centrality and structural hole index; The first batch of important node units is used to sort the candidate node set M in descending order according to the frequency of occurrence of the nodes, and according to a preset interception ratio parameter, intercept the first and last segments of the descending sort list as the first batch of important node sets and the node set not to be considered, respectively, so as to obtain a candidate set of nodes to be determined in the middle of the ranking; The second batch of important node units are used to traverse and calculate the impact of deleting a node from the candidate node set to be determined on the network efficiency, and select node combinations whose impact rankings meet a preset threshold to add to the second batch of important node sets; The third batch of important node units is used to obtain an intermediate layer important node set according to the first batch of important node sets and the second batch of important node sets; then, in the upper and lower layers of the directed weighted multi-layer complex network, search for nodes whose node degree centrality values ​​connected to important nodes in the intermediate layer important node set exceed a preset threshold value as important nodes of the upper and lower layers of the network, forming a third batch of important node sets; The complete important node unit is used to obtain a complete important node set based on the intermediate layer important node set and the third batch of important node sets, so as to complete the important node identification of the multi-layer supply chain network.

[0097] Embodiment 4 The fourth embodiment of the present invention also provides an important node identification device for a multi-layer supply chain network, which includes a memory and a processor, wherein the memory stores a computer program, and the computer program can be executed by the processor to implement the important node identification method for the multi-layer supply chain network as described above.

[0098] Embodiment 5 The fifth embodiment of the present invention also provides a computer-readable storage medium, on which computer-readable instructions are stored. When the computer-readable instructions are executed by a processor of a device where the computer-readable storage medium is located, the important node identification method of the multi-layer supply chain network as described above is implemented.

[0099] In several embodiments provided in the embodiments of the present invention, it should be understood that the disclosed apparatus and method can also be implemented in other ways. The apparatus and method embodiments described above are merely schematic. For example, the flowcharts in the accompanying drawings show the possible architecture, functions and operations of the apparatus, method and computer program product according to multiple embodiments of the present invention. In this regard, each box in the flowchart or block diagram can represent a module, a program segment or a part of a code, and the module, program segment or a part of the code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs a specified function or action, or can be implemented with a combination of dedicated hardware and computer instructions.

[0100] In addition, the functional modules in the various embodiments of the present invention may be integrated together to form an independent part, or each module may exist independently, or two or more modules may be integrated to form an independent part.

[0101] If the function is implemented in the form of a software function module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art or the part of the technical solution can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions to enable a computer device (which can be a personal computer, electronic device, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program code. It should be noted that in this article, the term "include", "include" or any other variant thereof is intended to cover non-exclusive inclusion, so that the process, method, article or device including a series of elements includes not only those elements, but also includes other elements that are not explicitly listed, or also includes elements inherent to such process, method, article or device. Without more constraints, an element defined by the phrase "comprising a..." does not exclude the existence of other identical elements in the process, method, article or apparatus comprising the element.

[0102] The terms used in the embodiments of the present invention are only for the purpose of describing specific embodiments, and are not intended to limit the present invention. The singular forms "a", "said" and "the" used in the embodiments of the present invention and the appended claims are also intended to include plural forms, unless the context clearly indicates other meanings.

[0103] It should be understood that the term "and / or" used in this article is only a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0104] The word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to determining" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)", depending on the context.

[0105] The "first\second" mentioned in the embodiments is only to distinguish similar objects, and does not represent a specific order for the objects. It is understandable that the "first\second" can be interchanged with the specific order or sequence where permitted. It should be understood that the objects distinguished by "first\second" can be interchanged where appropriate, so that the embodiments described herein can be implemented in an order other than those illustrated or described herein.

[0106] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for identifying important nodes in a multi-layer supply chain network, characterized in that: include: S1, based on the upstream and downstream hierarchical relationships of the supply chain network, construct a directed weighted multi-layer complex network ; S2, according to the directed weighted multi-layer complex network , centrality index and the preset proportion of important nodes in the middle layer network, identify the structural characteristic nodes of the middle layer network, and obtain the candidate node set M; wherein the centrality index includes: node degree centrality, closeness centrality, betweenness centrality and structural hole index; S3, sorting the candidate node set M in descending order according to the frequency of occurrence of the nodes, and intercepting the first and last segments of the descending sort list as the first batch of important node sets and the set of nodes not to be considered, respectively, according to a preset interception ratio parameter, so as to obtain a candidate set of nodes to be determined in the middle of the ranking; S4, traversing and calculating the impact on network efficiency after deleting any node from the candidate set of nodes to be determined, and selecting a node combination whose impact ranking meets a preset threshold to add to the second batch of important node sets; S5, obtaining an intermediate layer important node set according to the first batch of important node sets and the second batch of important node sets; then searching in the upper and lower layers of the directed weighted multi-layer complex network for nodes whose node degree centrality values ​​connected to important nodes in the intermediate layer important node set exceed a preset threshold as important nodes of the upper and lower layers of the network, forming a third batch of important node sets; S6, obtaining a complete set of important nodes based on the intermediate layer important node set and the third batch of important node sets, and completing the identification of important nodes in the multi-layer supply chain network.

2. The method for identifying important nodes in a multi-layer supply chain network according to claim 1, characterized in that , in constructing directed weighted multi-layer complex networks hour: First, according to the upstream and downstream hierarchical relationship of the supply chain network, the data of the intermediate layer network is determined; wherein the supply chain network includes the manufacturing supply chain network; Then, based on the supplier and customer data of the middle layer, the upstream and downstream network layers are built respectively to determine the network Upstream enterprise nodes and downstream enterprise nodes and their network layers; According to the preset time period, the network The cooperation frequency of each pair of nodes and the proportion of the average annual cooperation transaction amount in the network are calculated. The weight of the edge to measure the closeness of the connection between enterprises; Determine the network based on the direction of supply chain logistics The direction of the middle edge completes the directed weighted multi-layer complex network 's construction.

3. The method for identifying important nodes in a multi-layer supply chain network according to claim 1 is characterized in that ,The candidate node set M is sorted by calculating the node degree centrality, closeness centrality, betweenness centrality and structural hole index of each node respectively; According to the preset ratio , select the corresponding proportion of nodes as candidate nodes, and get the node degree centrality set , closeness centrality set , betweenness centrality set With structural hole collection , thus obtaining the candidate node set M; The calculation formula of the node degree centrality is: ； in, represents the node degree centrality of node i; N is the network The total number of nodes; Indicates the direct relationship between node i and node j; The calculation formula of the closeness centrality is: ； in, represents the closeness centrality of node i; represents the shortest path between node i and node j; The calculation formula of the betweenness centrality is: ； in, Representation Node Betweenness centrality of ; Indicates the number of shortest paths; Indicates passing through node The number of shortest paths; The structural hole index measures the degree of constraint when a node forms a structural hole through the constraint coefficient. The calculation formula is: ； ； ； in, is the set of neighbor nodes of node i; It represents the proportion of energy that node i puts into maintaining the relationship with its neighbor node j, that is, the node connection strength. The more neighbor nodes node i has, The smaller; , are the node connection strengths between nodes i and j and their common neighbor q, respectively; Represents the edge between nodes i and j; constraint coefficient The smaller it is, the more neighbor nodes the node to be evaluated has.

4. The method for identifying important nodes in a multi-layer supply chain network according to claim 1, characterized in that , the first set of important nodes Number of The calculation formula is: ； in, A parameter representing the interception ratio of the first set of important nodes; represents the number of the candidate node set; The node set is not considered Number of The calculation formula is: ； in, represents the interception ratio parameter of the node set not considered; Indicates the number of candidate nodes.

5. The method for identifying important nodes in a multi-layer supply chain network according to claim 1, characterized in that , in calculating the network efficiency When , the cascading failure model is used to calculate the impact of important node failure on network robustness, specifically: According to the centrality index, setting the initial load of the cascading failure model node; The maximum capacity of the calculation node is: ； in, Representation Node Maximum capacity; is the spare capacity factor, which is used to measure the processing capacity of the node when it exceeds the initial load; Representation Node Initial load of Assuming that node i fails, if the load exceeds the maximum capacity of the node, a load redistribution process is performed and the failed node Assign to any of its adjacent nodes The load is: ； in, For adjacent nodes Load increment; For adjacent nodes The load distribution weight of For Node The importance of is the node degree centrality index; is the set of neighbor nodes of node i; For Node Real-time load; Then the cascade failure propagation is carried out, and at the preset time step Internal, faulty node The adjacent nodes of Real-time load for: ； in, For adjacent nodes exist Real-time load at the time; For adjacent nodes exist Real-time load at the time; Due to the load redistribution process, the load of the neighboring nodes of the failed node changes. , then node j fails, and a new round of load redistribution process is carried out until a node that meets the node capacity limit is allocated; if , then no new round of load redistribution process is performed, and the propagation process ends; Calculate the network efficiency based on the shortest path length between any two valid nodes in the network : ； ； in, represents the shortest path between nodes i and j, that is, the minimum overload function value; Represents the current valid node set; express The node pair consisting of nodes i and j in the set; Represents a node pair The shortest path length of the network The total number of nodes.

6. The method for identifying important nodes in a multi-layer supply chain network according to claim 5, characterized in that ,When deleting a node from the candidate set of nodes to be determined, a random attack ,strategy is adopted to select the node to be deleted, and then a random ,sequence is generated to attack the network nodes using Python ,programming.

7. The method for identifying important nodes in a multi-layer supply chain network according to claim 5, characterized in that ,When deleting a node from the candidate set of nodes to be determined, a ,deliberate attack strategy is adopted to select the node to be deleted and ,attack the supply chain network, that is, the nodes are removed in order ,according to the ranking results of the importance of the nodes.

8. A device for identifying important nodes in a multi-layer supply chain network, characterized in that: include: Multi-layer supply chain network construction unit, used to construct a directed weighted multi-layer complex network based on the upstream and downstream hierarchical relationships of the supply chain network ; A candidate node set calculation unit is used to calculate the candidate node set according to the directed weighted multi-layer complex network , centrality index and the preset proportion of important nodes in the middle layer network, identify the structural characteristic nodes of the middle layer network, and obtain the candidate node set M; wherein the centrality index includes: node degree centrality, closeness centrality, betweenness centrality and structural hole index; The first batch of important node units is used to sort the candidate node set M in descending order according to the frequency of occurrence of the nodes, and according to a preset interception ratio parameter, intercept the first and last segments of the descending sort list as the first batch of important node sets and the node set not to be considered, respectively, so as to obtain a candidate set of nodes to be determined in the middle of the ranking; The second batch of important node units are used to traverse and calculate the impact on network efficiency after deleting any node from the candidate node set to be determined, and select node combinations whose impact rankings meet a preset threshold to add to the second batch of important node sets; The third batch of important node units is used to obtain an intermediate layer important node set according to the first batch of important node sets and the second batch of important node sets; then, in the upper and lower layers of the directed weighted multi-layer complex network, search for nodes whose node degree centrality values ​​connected to important nodes in the intermediate layer important node set exceed a preset threshold value as important nodes of the upper and lower layers of the network, forming a third batch of important node sets; The complete important node unit is used to obtain a complete important node set based on the intermediate layer important node set and the third batch of important node sets, so as to complete the important node identification of the multi-layer supply chain network.

9. An important node identification device for a multi-layer supply chain network, characterized in that: It includes a processor and a memory, wherein the memory stores a computer program, and the computer program can be executed by the processor to implement a method for identifying important nodes in a multi-layer supply chain network as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-readable instructions, which, when executed by a processor of a device where the computer-readable storage medium is located, implement a method for identifying important nodes in a multi-layer supply chain network as described in any one of claims 1 to 7.

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