A key node discovery method suitable for a multi-industry chain network with a group structure

Abstract

The application provides a key node discovery method suitable for a multiple industrial chain network with a group structure. Firstly, the multiple industrial chain network is modeled into a multi-layer undirected network through graph theory technology, and the enterprise group is modeled into an undirected sub-network; secondly, the calculation formula of group structure modularity and group density is defined; then, the global sub-network is obtained from the node with group colony bridge function, and the node local sub-network is divided according to the node single colony and multi-colony attributes, and the layer influence of the node is obtained; then, the calculation formula of network layer complexity and importance is defined; finally, the influence of all nodes in the multi-layer undirected network is obtained, and the key enterprise in the multiple industrial chain network is discovered. Compared with the traditional key node discovery method, the method comprehensively considers the multiple connection relationship between enterprises and the synergistic effect of the enterprise group, is more in line with the actual scene of the multiple industrial chain network with the enterprise group structure, and can more accurately discover the key enterprise with high influence.

Description

Technical Field

[0001] This invention relates to the field of multi-networked industrial chains, and more specifically to a method for discovering key nodes in multi-networked industrial chains with a group structure. Background Technology

[0002] The industrial chain has evolved from a traditional linear and simple structure into a complex, multi-dimensional network system. This change is reflected in the diversification of relationships between enterprise nodes in the industrial chain network, the variety of cooperation models, and the increasing complexity of various cluster relationships. Against this backdrop, multi-layered industrial chain networks with cluster structures have become the new norm, with complex connections between different industrial chains, and the dependencies and cluster structures of enterprises have become more intricate. Identifying key nodes and key enterprises within the industrial chain network is crucial for further allocating industrial chain resources, protecting key enterprises, and safeguarding the stability of the industrial chain. Simultaneously, the multiplicity of the industrial chain, the multi-dimensionality of the relationship network, and the complexity of the cluster structure add multi-dimensional topological relationships and hidden relational attributes to the assessment of node influence, significantly increasing the difficulty of identifying key enterprises.

[0003] The key node discovery method in a multi-layered supply chain network with a cluster structure refers to assessing the influence of nodes in a multi-layered nested supply chain network by considering their individual attributes, relationships between nodes, cluster structure, and inter-layer network influence. This process identifies key nodes within the network and thus determines the most influential companies in the supply chain. The concept of a cluster is particularly important in multi-layered supply chains. A cluster of companies in a supply chain is a group of companies connected in various ways, such as through supply chains, technological cooperation, strategic alliances, or other business models. This structure not only strengthens synergies between companies but also provides them with resources and competitiveness. Therefore, analyzing the cluster structure and assessing the influence of company clusters within the supply chain can better identify key companies.

[0004] Finding key nodes in networks is a hot topic, and key node identification algorithms have been applied in various fields such as social networks, transportation systems, and virus propagation. However, most existing research focuses on single-layer networks, analyzing the network structure and identifying key nodes from the topology. A few studies have begun to focus on multi-layer undirected networks, considering the differences in topological relationships between different network layers, but they do not consider the individual group attributes of nodes or the impact of these group attributes on nodes. In short, most existing research lacks a comprehensive consideration of the multiple attributes of nodes and the community structure, thus its effectiveness in analyzing complex network systems such as industrial chains, which have complex structures, numerous attributes, and significant group effects, is not ideal. To more accurately find key nodes in industrial chains, this method considers the multiple connections between enterprises and the synergistic effects of enterprise groups, which is more in line with the actual scenario of multi-industry chain networks with enterprise group structures. This invention discloses a method for discovering key nodes in multi-industry chain networks with group structures. Summary of the Invention

[0005] Technical Problem: The purpose of this invention is to propose a method for discovering key nodes in a multi-networked industrial chain network with a cluster structure, applicable to the context of multiple networked industrial chains. This method faces three major challenges: 1) The complexity of the cluster structure lies in the various forms of connections between its members. These connections have a direct or indirect impact on the influence of nodes within the cluster. In an industrial chain, a company may exist in multiple enterprise clusters or only one, meaning the number and structure of clusters to which a node belongs are uncertain; 2) In multiple industrial chains, companies no longer participate in only a single industrial chain but may simultaneously be in multiple industrial chains. This cross-industry chain participation means that a company's influence is not limited to a single industrial chain but also includes its influence throughout the entire multi-industry chain network. Therefore, it is necessary to construct a multi-layered industrial chain network and calculate the influence within and between network layers separately; 3) Due to the complexity of the industrial chain network and the diverse connections between nodes, the influence of factors such as inter-cluster synergy, multiple attributes of enterprises, and connections between inside and outside the chain must be considered simultaneously.

[0006] Technical solution:

[0007] In multi-chain supply chain networks with cluster structures, the increasing complexity of cluster structures and multi-layered heterogeneous networks presents new challenges for key node discovery. Particularly within supply chains, the identification of key enterprises is crucial for collaborative management and optimal resource allocation among firms. The process of finding and evaluating key nodes in multi-layered undirected networks involves extremely complex variables and influencing factors, including but not limited to the diverse relationships between nodes, the roles and positions of nodes in different relational networks, and the contribution of the cluster to the influence of individual nodes. To address this challenge, a method for key node discovery in multi-chain supply chain networks with cluster structures needs to be designed. This method should consider the multiple connections between enterprises and the collaborative effects of enterprise clusters, better reflecting the real-world scenario of multi-chain supply chain networks with enterprise cluster structures, thereby more accurately identifying highly influential key enterprises.

[0008] The modeling of multi-chain industry networks and the analysis of community influence are performed using graph theory techniques. First, the multi-chain industry network with a community structure is represented by a binary tuple MN = (G, C). This multi-layered undirected network includes undirected subnetworks of communities C = {C1, C2, ..., C}. α ,…,C A} and a multi-relation network G = {G1, G2, ..., G} α ,…,G A In the α-th layer network, there exist nodes and relational connections G. α =(V,E) α Next, to analyze and evaluate the local and global influence of nodes with different community attributes in the industry chain network, the industry chain network is divided into local subnetworks and global subnetworks. Considering the impact of different community structures and the number of communities a node belongs to, the local subnetworks in the multiple industry chains are further divided into multi-community node local subnetworks and single-community node local subnetworks. The nodes in the α-th layer are then divided according to the number of communities they belong to. Then, the α-th layer is divided into a set of local subnetworks of multiple community nodes. A set of local subnetworks of a single community node C α With the global subnetwork set GN α CM through group module degree αk With group density CD αk Calculate the influence CI of the k-th firm group in the α-th layer network. αk .

[0009] In the multi-chain industry network, the influence analysis stage within the node layer is performed. Based on the influence of the community, the influence (WEC) of node i at layer α on node i by its own community is calculated. αi And the neighboring nodes ng(i) of node i in the local subnetwork of the multi-community nodes in layer α. αThe influence brought to node i LCS by considering the local influence of the nodes themselves αi Local influence (LCE) with neighboring nodes αi The local influence (LCI) of a node within the network layer is obtained. αi Then, analyze whether the node has global influence and whether it plays a role in connecting clusters within the industry chain. If the node has global influence, calculate the intra-layer global influence (GI) in the sub-network. αi Finally, the intra-layer local influence (LCI) of the nodes is summed. αi GI with global influence within the layer αi The SLI method obtains the intra-layer influence of a node in that network layer. αi .

[0010] The stage of analyzing the inter-layer influence of nodes in a multi-industry chain network. This involves calculating the network layer complexity (LC). α Network layer importance LS α The inter-layer influence of node i in layer α is calculated and represented as LI. α Then, to assess the impact of a node on the entire multi-chain industry, the complexity of the industry chain structure and the diversity of the node's own attributes must be considered, and the influence MI of node i on the multi-chain industry should be calculated. i Finally, the influence of all nodes is ranked from largest to smallest to identify the key nodes in the multi-layered undirected network with a group structure, thereby discovering key enterprises with high influence in the multi-industry chain network.

[0011] Beneficial effects:

[0012] (1) This invention quantifies the impact of communities on nodes in a multi-layer undirected network. It considers the community attributes of nodes in the network layer and quantifies the influence of communities on nodes. Applied to multi-industry chain networks, it assesses and calculates the synergistic effect between enterprises by strengthening enterprise group structures. It also distinguishes between enterprises belonging to multiple enterprise groups and those belonging to only one enterprise group, addressing the problems of complex structures within enterprise groups and diverse relationships between enterprise groups, and quantifying the impact of enterprise groups on enterprises within the industry chain.

[0013] (2) This invention introduces the calculation of the influence between network layers in a multi-layer undirected network. In a multi-industry chain network, it avoids the limitation of only considering the single role of an enterprise in the industry chain, and analyzes the influence of multiple relationships in the industry chain on the enterprise. It considers not only the influence of an enterprise in a certain relationship network, but also the influence of an enterprise in cross-industry chain networks.

[0014] (3) This invention improves the accuracy of key node discovery in multi-layer undirected networks. The calculation of node influence in multiple industrial chains is no longer limited to the analysis of node structure, but takes into account multiple aspects such as the various connection relationships between nodes in the industrial chain, multiple attributes, and the synergistic effect of nodes in the community, so as to more accurately discover key nodes in multi-industry chain networks with group structure. Attached Figure Description

[0015] Figure 1 It is a flowchart demonstrating the modeling and subnetwork partitioning of a multi-industry chain network with a group structure.

[0016] Figure 2 It is a flowchart illustrating the calculation of influence within the node layer of a multi-industry chain network with a group structure.

[0017] Figure 3 It is a flowchart illustrating the calculation of inter-node influence in a multi-industry chain network with a group structure.

[0018] Figure 4 This is a schematic diagram of the main principle of the method of the present invention. Detailed Implementation

[0019] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the present invention.

[0020] As shown in the figure, this invention provides a method for discovering key nodes in multi-industry chain networks with group structures. It models the multi-industry chain network as a multi-layer undirected network using graph theory, and the enterprise groups as undirected subnetworks. Nodes in the network are enterprises with community attributes. Secondly, to quantify the influence of enterprise groups, formulas are defined for calculating the modularity and density of the group structure. Next, a global subnetwork is obtained from nodes that act as community bridges, and local subnetworks are divided based on the single-community and multi-community attributes of each node. By analyzing the global subnetwork and local subnetworks, and considering the influence of neighboring nodes, the intra-layer influence of each node is obtained. Then, to measure the inter-layer influence of a node in the industry chain network, formulas are defined for calculating network layer complexity and importance. Finally, the influence of all nodes in the multi-layer undirected network is comprehensively derived from three aspects: the influence of the node's group structure, the node's intra-layer and inter-layer influence, thereby discovering key nodes with significant influence, i.e., key enterprises in the multi-industry chain network.

[0021] The specific implementation process is as follows:

[0022] Step 1: Considering the impact of network hierarchy and community structure on nodes in multiple industry chains, this step analyzes the multiple relationships among enterprises, including collaboration, competition, and cooperation. Graph theory is used to model the multiple industry chain network as a multi-layered undirected network. In the initial stage, a multi-industry chain network model is defined. A multi-industry chain network with a group structure is represented by a binary tuple MN = (G, C); G represents the complex, nested relationship network in the multi-layered undirected network, i.e., the set of different relationship networks among enterprises in the industry chain, G = {G1, G2, ..., G...}. α ,…,G A The relational network of the α-th layer is represented as G. α =(V,E) α ), where α∈{1,2,…,A}, A is the total number of network layers; V represents the nodes in the multi-layer undirected network, that is, the set of enterprise nodes in the multiple industry chains V={V1,V2,…,V i ,…,V B}, where i∈{1,2,…,B}, and B is the total number of nodes in the multi-layer undirected network; E α This represents the connection relationship between nodes in the α-th layer network. The connection matrix between node i and node j in the α-th layer network is represented as follows:

[0023]

[0024] C represents the undirected subnetwork of the community, C = {C1, C2, ..., C}. α ,…,C A In practical terms, this represents a set of enterprise groups within different layers of a network within an industry chain. The set of clusters in the α-th layer network is represented as... Where α∈{1,2,…,A}, K α Let C be the number of communities in the α-th layer network; the k-th community in the α-th layer network is denoted as C. αk =(VC) αk EC αk ), where k∈{1,2,…,K} α};VC αk VC represents the set of nodes in the k-th community of the α-th layer network. αk ={i|k∈γ αi ,i∈{1,…,B}},γ αi Let EC be the set of community numbers for node i in the α-th layer network; αk Let be the connection matrix between nodes in the k-th community of the α-th layer network, denoted as

[0025]

[0026] Step 2: In a multi-chain industry network with a cluster structure, the cluster attributes of nodes differ. In the industry chain, this manifests as a company potentially existing in multiple clusters simultaneously, or only in one. To quantify the impact of clusters on nodes in the network layer, nodes are classified based on whether they belong to multiple clusters at layer α. Let the set of nodes in the multi-community layer α be . in Indicates whether node i is a multi-community node in the α-layer network.

[0027]

[0028] if |γ αi |>1, otherwise|γ αi |=1; Let the set of nodes of a single community at layer α be ?

[0029] Step 3: In a multi-chain industry network with a cluster structure, to analyze and evaluate the local and global influence of nodes with community attributes, the industry network is divided into local subnetworks and global subnetworks. Considering the impact of community structure and the number of communities a node belongs to, the local subnetworks are further divided into two types: multi-community node local subnetworks and single-community node local subnetworks. In the multi-chain industry network, the β-th multi-community node local subnetwork of the α-th layer network consists of triples. It is represented as , where β∈{1,2,…,P} α}, The set of community numbers for the local subnetwork of the β-th multi-community node in the α-th layer network. P α The total number of multi-group subnetworks in the α-th layer network. Let the set of nodes of the local subnetwork of the β-th multi-community node in the α-th layer network be represented. This represents the connection matrix between nodes in the local subnetwork of the β-th multi-community node in the α-th layer network.

[0030]

[0031] The k-th local subnetwork of the α-th layer network is represented as the undirected subnetwork C of the community. αk =(VC) αk EC αk In a multi-industry chain network, the global subnetwork GN of the α-layer network... α =(VGN)α EGN α VGN α The set of nodes representing the global subnetwork of the α-th layer network. in Let ng(i) be the set of community numbers of the neighboring nodes of node i in the α-th layer network. α Let ng(i) be the set of neighboring nodes of node i in the α-th layer of the network. In the industry chain network, ng(i) is represented by the set of direct upstream and downstream neighboring enterprises of enterprise i in the α-th layer of the network. α ={j|E αij =1,j≠i}, meaning that as long as a node in the α-th layer network has a neighbor node whose community number is inconsistent with its own, it is a node in the global sub-network of that layer; EGN α This represents the connection matrix between nodes in the global subnetwork of the α-th layer network, and its elements are...

[0032]

[0033] Step 4: Calculate the influence of enterprise clusters. In a multi-industry chain network with a cluster structure, different clusters have different impacts on nodes. In order to quantify the influence of clusters, the formulas for calculating the cluster structure modularity and cluster density are defined in the undirected subnetwork of the cluster. The specific process is as follows.

[0034] 4.1 Calculate the group modularity. Group modularity considers the number of nodes in a cluster, that is, the number of enterprises in an enterprise cluster. It is obtained by the ratio of the number of nodes in the k-th cluster at layer α to the total number of nodes in the network, expressed as:

[0035]

[0036] Among them, CM αk |VC represents the group modularity of the k-th enterprise group in layer α. αk | represents the number of nodes in the k-th community of the α-th layer, and B represents the total number of nodes in the network.

[0037] 4.2 Calculate the cluster density. The cluster density considers the connectivity between firms within a cluster. It is calculated by dividing the number of edges in the k-th cluster at layer α by the maximum number of edges in all clusters, expressed as:

[0038]

[0039] Among them, CD αk |EC represents the group density of the k-th firm group in layer α, αk | represents the number of edges in the k-th community of the α-th layer, max{|EC αk|} represents the maximum number of edges in all communities of the α-th layer network, k∈{1,…,K} α}

[0040] 4.3 The influence of a firm group is calculated by multiplying the group modularity and group density of the k-th firm group at layer α, and is expressed as follows:

[0041] CI αk =CM αk *CD αk

[0042] Among them, CI αk This represents the influence of the k-th enterprise group in the α-layer network.

[0043] Step 5: Calculate the intra-layer influence of nodes in a multi-chain industry network. In a multi-chain industry with a group structure, the intra-layer influence of a node includes its local influence as well as its global influence on the current network layer as a bridge node.

[0044] 5.1 The influence of a node's own community on node i in the α-layer network is calculated by summing the influences of all communities to which the node belongs, and is expressed as:

[0045]

[0046] Among them, WEC αi Let α be the influence that the community to which node i belongs at layer α exerts on node i.

[0047] 5.2 Calculate the intra-layer local influence of a node in a multi-layer undirected network. The intra-layer local influence considers the local influence of the node itself and the local influence of its neighboring nodes. The specific process is as follows.

[0048] 5.2.1 Calculate the importance of a node's local structure within a layer. The importance of local structure considers both the node's connectivity within its local subnetwork and the influence of its community. It is calculated by summing the ratio of the number of edges of node i in its local subnetwork at layer α to the total number of edges in that subnetwork, and then adding this ratio to the influence of the node's own community within that local subnetwork. This is expressed as:

[0049]

[0050] in, Let be the number of edges directly connected to node i in the local subnetwork of the multi-community node at layer α. Let |EC be the total number of edges in the sub-local network of the multi-community node where node i is located at layer α. αk| represents the number of edges directly connected to node i in the local subnetwork of the single community at layer α, |EC α | represents the total number of edges in the local subnetwork of the single community node of node i at layer α.

[0051] 5.2.2 The Influence of Neighbor Nodes in the Local Subnetwork of a Multi-Community Node. The importance of a node's direct neighbors directly affects the node's overall importance. When assessing a node's importance, its direct neighbors must be evaluated alongside its own structure. This influence is derived from the magnitude of the community's influence on the neighbors of node i in its local subnetwork at layer α. In a multi-industry chain network, a node's direct neighbors represent the upstream and downstream enterprises of the enterprise, denoted as...

[0052]

[0053] in, Let i be the direct neighbor of node i in the local subnetwork of the multi-community at layer α. The influence it brings to node i.

[0054] 5.2.3 The intra-layer local influence of a node in the network layer is calculated by multiplying the node's own local influence within the layer by the local influence of its neighboring nodes, and is expressed as:

[0055] LCI αi =LCS αi *LCE αi

[0056] Among them, LCI αi Let LCS be the local influence of node i within the α-th layer. αi For the local structural importance of node i in layer α, LCE αi Let node i be affected by its direct neighbor nodes at level α.

[0057] 5.3 Calculating the Intra-Layer Global Influence of Nodes. In multi-layer undirected networks, nodes not only have local influence but also a global effect on the entire network layer, connecting different communities. To calculate global influence, we first identify nodes with global effects and then evaluate their global influence. This is achieved by calculating the ratio of the number of edges of node i in its global sub-network at layer α to the total number of edges in that sub-network, summing this ratio with the influence of the node's own community within that sub-network, and then multiplying this sum with the global influence of the node's neighbors in the global network. This is expressed as:

[0058]

[0059] Among them, |EGN αi | represents the number of edges directly connected to node i in the global subnetwork at level α, |EGN α | represents the total number of edges in the global subnetwork of layer α. Let i be the direct neighbor of node i in the global subnetwork at level α. The influence that node brings to node i

[0060] 5.4 Calculating the Intra-Layer Influence of Nodes: In a multi-chain industry with a group structure, the intra-layer local influence and intra-layer global influence of a node jointly determine the node's intra-layer influence at that layer. This is calculated by summing the intra-layer local influence and global influence of the node. The intra-layer influence of node i at layer α is expressed as:

[0061] SLI αi =(LCS) αi *LCE αi )+GI αi =LCI αi +GI αi

[0062] Among them, SLI αi LCI represents the intra-layer influence of node i in layer α. αi GI represents the local influence of node i within layer α. αi This represents the global influence of a node within the α-th layer.

[0063] Step 6: Calculate the inter-layer influence of nodes in a multi-layer undirected network. In a multi-chain industry with a group structure, the influence of nodes needs to be fully considered when evaluating the characteristics of the multi-layer network structure. The influence of a node in a multi-chain industry includes intra-layer influence and inter-layer influence. To measure the inter-layer influence of nodes in the industry chain network, formulas for calculating network layer complexity and importance are defined.

[0064] 6.1 The complexity of a network layer is calculated by taking the average of the squared degrees of the network layer and the square of the average degree, expressed as:

[0065]

[0066] Among them, LC α For the network layer complexity of the α-th layer, D α Let α be the degree of the α-th network layer. <D α 2 > represents the mean of the squared degrees of the α-th network layer. <D α > 2 denoted as the square of the mean degree of the α-th network layer.

[0067] 6.2 Calculate the importance of network layers and evaluate the connections between nodes in the network layers. The specific process is as follows:

[0068] 6.2.1 Establishing a convergence network in a multi-industry chain network

[0069] The aggregated network represents all non-repeating connections between nodes in the industry chain. That is, regardless of the relationship between companies, every two nodes are connected in the aggregated network. The aggregated network is represented as CN. total =(V, ECN) total ECN total The connection matrix between nodes in an aggregation network represents the connection relationships between nodes.

[0070]

[0071] 6.2.2 Calculate the importance of a network layer. This is done by analyzing the overall connectivity of the network layer and dividing the number of edges in that layer by the number of edges in the aggregated multi-industry chain network. The importance is expressed as:

[0072]

[0073] Among them, LS α Let |E| represent the importance of the α-th layer of the network. α | represents the number of edges connecting nodes on the α-th layer network, |ECN total | represents the total number of edges in the aggregated network.

[0074] 6.3 The inter-layer influence in a multilayer undirected network is calculated by multiplying the network's complexity and importance, and is expressed as follows:

[0075] LI α =LC α *LS α

[0076] Among them, LI α For the interlayer influence of the α-th layer, LC α For the complexity of the α-th layer of the network, LS α α represents the importance of the network layer.

[0077] Step 7: Calculate the overall influence ranking of nodes in a multi-industry chain network and identify key nodes. In a multi-industry chain network with a group structure, considering the influence of a node on the entire multi-layer undirected network requires not only considering the node's own attributes and differences in network layer structure, but also the different roles and characteristics of the node in different network layers. That is, evaluating the influence of a company in a multi-industry chain requires considering the multiple connections between companies and the synergistic effects of the company group. The influence of node i in the multi-industry chain is calculated by multiplying the node's intra-layer influence and inter-layer influence in each layer, and then summing the results across all network layers. This is expressed as:

[0078]

[0079] Among them, MI i SLI enhances the influence of node i across multiple industry chains. αi Let LI represent the intra-layer influence of node i in layer α. α Let i be the interlayer influence of node i in layer α.

[0080] Finally, the influence of all nodes is ranked from largest to smallest, and the key nodes in the multi-layer undirected network are identified based on the magnitude of influence, thereby identifying the key enterprises in the multi-industry chain network.

Claims

1. A method for discovering key nodes in a multi-chain industry chain network with a group structure, characterized in that, This study uses graph theory to model a multi-layer undirected network of supply chains, with enterprise clusters modeled as undirected subnetworks. Nodes in the network represent enterprises with cluster attributes. Secondly, to quantify the influence of enterprise clusters, formulas are defined for calculating cluster modularity and cluster density. Next, a global subnetwork is obtained from nodes acting as cluster bridges, and local subnetworks are defined based on whether a node is in a single or multiple cluster. By analyzing the global and local subnetworks and considering the influence of neighboring nodes, the intra-layer influence of each node is obtained. Then, to measure the inter-layer influence of nodes in the supply chain network, formulas are defined for calculating network layer complexity and importance. Finally, the influence of all nodes in the multi-layer undirected network is comprehensively calculated from three aspects: the influence of the node's cluster structure, its intra-layer and inter-layer influence, and the influence of all nodes is ranked from largest to smallest. Based on the magnitude of influence, key nodes in the multi-layer undirected network are identified, thus revealing the key enterprises in the multi-layer supply chain network.

2. The method for discovering key nodes in a multi-chain industry chain network with a group structure according to claim 1, characterized in that: Graph theory is used to model the multi-chain supply chain network as a multi-layer undirected network. The multi-chain supply chain network with a group structure is represented by binary tuples. express; This represents a complex, multi-layered, undirected network of relationships, specifically a collection of different relationship networks among firms in an industry chain. , No. Hierarchical relational network representation is ,in , This represents the total number of network layers. This represents the set of nodes in a multi-layered undirected network, specifically the set of enterprise nodes across multiple industry chains. ,in , The total number of nodes in a multi-layer undirected network; Indicates the first The connection relationships between nodes in a layered network, the first layer Nodes in a layered network With nodes The connection matrix between them is represented as Representing undirected subnetworks of communities In practical terms, it refers to a collection of enterprise groups within different relationship network layers of the industrial chain; the first The community set in the layer network is represented as ,in , For the first Number of communities in a layered network; The first layer of the network Each community is represented as ,in ; Indicates the first The first layer of the network The set of nodes in a community , For nodes In the The set of community IDs in a layered network; For the first The first layer of the network The connection matrix between nodes in a community is represented as follows: .

3. The method for discovering key nodes in a multi-chain industry chain network with a group structure according to claim 2, characterized in that: In the aforementioned multi-industry chain network with a cluster structure, the nodes have different community attributes. In the industry chain, this manifests as a company potentially existing in multiple enterprise clusters simultaneously, or possibly existing in only one. To quantify the impact of the community on the nodes in the network layer, based on the node's position in the [missing information - likely a specific node group or cluster]... Classification based on whether the layer belongs to multiple communities , Indicates the first The multi-community node set of the layer is ,in Represents a node In the Are there multiple cluster nodes in the layered network? if , ,otherwise ; Indicates the first The set of nodes in a single community of a layer is .

4. The method for discovering key nodes in a multi-chain industry chain network with a group structure according to claim 3, characterized in that: In the aforementioned multi-industry chain network with a cluster structure, to analyze and evaluate the local and global influence of nodes with community attributes within the industry chain network, the industry chain network is divided into local subnetworks and global subnetworks. Considering the impact of community structure and the number of communities to which a node belongs on the node, the local subnetwork is further divided into two types: multi-community node local subnetworks and single-community node local subnetworks. In the multi-industry chain network, the first... The first layer of the network A local subnetwork of multiple community nodes consists of triples It means that, among them , For the first The first layer of the network The set of community IDs for a local subnetwork of multiple community nodes , For the first Total number of multi-group subnets in layered networks ; Indicates the first The first layer of the network A set of nodes in a local subnetwork of multiple communities. ; Indicates the first The first layer of the network Connection matrix between nodes in a multi-community local subnetwork No. The first layer of the network A local subnetwork of a community is represented as a community network. ; In a multi-chain industry network, the first The global subnetwork of a layer network is represented as: , Indicates the first The set of nodes in the global subnetwork of a layered network ,in For nodes In the The set of community IDs of neighboring nodes in a layered network. For nodes In the Neighbor nodes in a layered network are represented as enterprises in an industry chain network. In the Set of direct upstream and downstream neighboring enterprises in a layered network That is, as long as the first A node in a layered network has neighboring nodes whose community numbers are inconsistent with its own; this node is the first one in that layered network. Nodes in the global sub-network of the layer; Indicates the first The connection matrix between nodes in the global subnetwork of the layer network, whose elements 。 5. The method for discovering key nodes in a multi-chain industry chain network with a group structure according to claim 4, characterized in that: In the aforementioned multi-industry chain network with a group structure, to quantify the different influences of different communities on nodes, formulas for calculating the group structure modularity and group density are defined in the undirected subnetwork of the communities; the influence of enterprise groups in the industry chain is determined through the first... The first layer The group modularity and group density of each enterprise group are multiplied together to obtain the result. To indicate, among which Representing the first The first layer of the network The influence of a group of companies; Representing the first The first layer The group modularity of a cluster of enterprises considers the number of nodes in the cluster, that is, the number of enterprises in the cluster. This is determined by the number of nodes in the cluster. The first layer The ratio of the number of nodes in a community to the total number of nodes in the network is expressed as: ,in For the first The first layer The number of nodes in a community; Representing the first The first layer The group density of a cluster of firms, which considers the connectivity relationships among firms in the cluster, is calculated using the first... The first layer The number of edges in a community is calculated by dividing the maximum number of edges in all communities, and is expressed as: ,in Representing the first The first layer The number of edges in a community Representing the first The maximum number of edges in all communities of a layered network.

6. The method for discovering key nodes in a multi-chain industry chain network with a group structure according to claim 5, characterized in that: In the aforementioned multi-industry chain network with a group structure, the intra-layer influence of nodes is divided into local influence and global influence on the current network layer as bridge nodes; among which nodes In the The local influence within a layer considers both the local influence of a node itself and the local influence of its neighboring nodes. express; For nodes In the The importance of a layer's local structure considers both the connectivity of nodes within their local subnetworks and the influence of the community on each node. For nodes In the The direct neighbor nodes of the layer bring the nodes Influence; Node In the first Importance of the local structure of a layer Through compute nodes In the first The ratio of the number of edges in the local subnetwork of a layer to the total number of edges in that subnetwork, summed with the influence of the community to which each node in that local subnetwork belongs, is expressed as: For nodes In the first The layer is located in the local sub-network of multiple community nodes and the nodes The number of directly connected edges. For nodes In the first The total number of edges in the multi-group local network of the layer. For nodes In the first The layer is located in the local subnetwork of a single community and its nodes The number of directly connected edges. For nodes No. The total number of edges in the local subnetwork of the single community where the layer is located; where For nodes In the The community of nodes in a local subnetwork provides them with [benefits / resources]. The influence of a group is derived by summing the influence of all its member groups, and is expressed as: Through compute nodes In the The influence of the community on neighboring nodes in the local subnetwork of a layer is determined by the number of neighboring nodes. In a multi-industry chain network, the direct neighbors of a node are the direct upstream and downstream enterprises of the enterprise. For nodes In the Neighboring nodes in the local subnetwork of the layer Bring to the node Influence, expressed as .

7. The method for discovering key nodes in a multi-chain industry chain network with a group structure according to claim 6, characterized in that: In the multi-industry chain network with a group structure, nodes In the first The global influence of a layer considers both the node's own global influence within the layer and the global influence of its neighboring nodes. The impact, through calculation of enterprises In the first The global influence of a layer is calculated by summing the ratio of the number of edges in its global subnetwork to the total number of edges in that subnetwork, and then adding the influence from the cluster to which each node belongs within that subnetwork. This is then multiplied by the global influence from neighboring nodes in the global network. This is expressed as... in, For nodes In the first In the global sub-network of the layer and the nodes The number of directly connected edges. For the first The total number of edges in the global subnetwork of the layer. For nodes In the first direct neighbors of the layer global subnet Bring to the node Its influence.

8. The method for discovering key nodes in a multi-chain industry network with a group structure according to claim 7, characterized in that: In the aforementioned multi-layered industrial chain network with a group structure, the local influence and global influence within a node's layer jointly determine the node's influence within that layer of the network. This influence is calculated by summing the local and global influences. In the first The intra-layer influence of a layer is represented as = .

9. The method for discovering key nodes in a multi-chain industry chain network with a group structure according to claim 8, characterized in that: In the aforementioned multi-layered industrial chain with a group structure, the evaluation of node influence fully considers the multi-attribute and multi-nested characteristics of the multi-network structure. Influence within the multi-layered industrial chain includes both intra-layer and inter-layer influence. To measure the inter-layer influence of a node in the industrial chain network, formulas for calculating network layer complexity and importance are defined. In the first The inter-layer influence of a layer is represented as ;in Representing the first The complexity of a network layer is derived by calculating the average of the squared degrees of the network layer and the square of the average degree, expressed as: , For the first Degree of a layer in a network For the first The mean of the squared degrees of the layers in a multilayer network. For the first The square of the mean degree of each layer in the network; where Representing the first The importance of a network layer takes into account the overall connectivity of the network layer. It is calculated by dividing the number of edges in the network layer by the number of edges in the aggregated multi-industry chain network, and is expressed as follows: = , For the first The number of edges connecting nodes on a layered network. Let be the total number of edges in the aggregated network. The aggregated network represents all non-repeating connections between nodes in the industry chain; that is, regardless of the relationship between companies in the industry chain, every two nodes are connected in the aggregated network. The aggregated network is represented as: , This represents the connection relationships between nodes in an aggregation network. With nodes The connection matrix between them is represented as 。 10. The method for discovering key nodes in a multi-chain industry network with a group structure according to claim 9, characterized in that: In the aforementioned multi-industry chain network with a group structure, considering the impact of nodes on the entire multi-layer undirected network requires not only taking into account the node's own attributes and differences in network layer structure, but also the different roles and characteristics of nodes in different network layers. That is, assessing the influence of enterprises in a multi-industry chain requires considering the multiple connections between enterprises and the synergistic effects of the enterprise group; nodes The influence of a node across multiple industry chains is calculated by multiplying its intra-layer influence and inter-layer influence in each layer, and then summing the results across all network layers. This is represented as... ,in Represents a node In the first Intra-layer influence Represents a node In the first Inter-layer influence.

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