Biological invasion cross-border introduction risk network analysis method and system

Abstract

The invention relates to the field of biological invasion cross-border introduction risk analysis, in particular to the field of biological invasion cross-border introduction risk analysis, and particularly relates to a biological invasion cross-border introduction risk network analysis method and system. According to the method, the topological structure, the node importance and the network toughness of the biological intrusion cross-border introduction risk network are comprehensively analyzed, the characteristics of the biological intrusion propagation network are deeply analyzed from different angles, multiple algorithms complement each other and work cooperatively, the characteristics of the biological intrusion propagation network can be comprehensively analyzed from different angles, and the network performance is improved. Therefore, the reliability and the accuracy of the analysis result are improved; the reliability and the accuracy of the analysis result are remarkably improved; a comparative analysis method of target attacks and random attacks is introduced, and a scientific basis is provided for formulation of a precise prevention and control strategy by simulating the network stability after key nodes are removed.

Description

Technical Field

[0001] The present invention relates to the field of cross-border biological invasion risk analysis, and in particular to a network analysis method and system for cross-border biological invasion risk analysis. Background Art

[0002] Biological invasions have become a global problem threatening ecological security, agricultural production, and human health. Cross-border introduction is the first critical stage of biological invasions and the first line of defense for early prevention. If potential risks can be effectively identified and measures taken at this stage, the hazards and prevention and control costs in subsequent stages will be significantly reduced. Traditional static data analysis methods are no longer able to effectively meet the collaborative needs of identifying key risk pathways, demarcating risk areas, and assessing the overall risk characteristics of the network. For example, in terms of identifying key risk pathways, traditional methods often rely on single indicators or static models, making it difficult to capture dynamically changing propagation patterns; the results of risk area demarcation are not accurate enough and lack flexibility. Summary of the Invention

[0003] The purpose of the present invention is to provide a network analysis system for the risk of cross-border introduction of biological invasions.

[0004] Another object of the present invention is to provide a method for analyzing the risk network of cross-border biological invasion.

[0005] The method for analyzing a cross-border biological invasion risk network according to the present invention comprises the following steps:

[0006] S1 Quantitatively assess the importance of risk nodes: using a network centrality assessment algorithm, quantitatively assess the risk levels of the source nodes and destination nodes in the cross-border introduction risk network of invasive species;

[0007] S2 performs group cluster analysis on the risk network of cross-border introduction of invasive species: by clustering the source nodes and the destination nodes based on their respective centrality characteristics, combining the weight values ​​of the links between the source and the destination, and then evaluating the high-risk node clusters;

[0008] S3 Risk Network Vulnerability Analysis: Use vulnerability analysis methods to assess the stability of the cross-border introduction risk network of invasive species under different prevention and control strategies to identify key nodes and paths in the network.

[0009] According to the method for analyzing a cross-border biological invasion risk network of the present invention, in the step of quantitatively evaluating the importance of risk nodes in S1, the network centrality evaluation algorithm includes:

[0010] S1-1: Degree centrality analysis, respectively calculate the out-degree centrality of the incoming source node and the in-degree centrality of the incoming land node. Among them, the incoming source node with high out-degree centrality indicates that the incoming source node will become the main source of transmission in the cross-border spread of biological invasion; and the incoming land node with high in-degree centrality indicates that the incoming land node is susceptible to the impact of biological invasion. The calculation formula of degree centrality is as follows:

[0011]

[0012] Among them, C D (i) is the degree centrality of node i at the incoming source or incoming destination, deg(i) is the degree of node i (the incoming source is the out-degree and the incoming destination is the in-degree), and N is the total number of nodes in the cross-border incoming risk network;

[0013] S1-2: Closeness centrality analysis. For incoming source nodes and incoming destination nodes, higher closeness centrality values ​​indicate that the incoming source nodes and incoming destination nodes propagate faster in the cross-border incoming network and are located in the core area of ​​the cross-border incoming risk network. The calculation formula for closeness centrality is as follows:

[0014]

[0015] Where Cc(i) is the closeness centrality of node i of the incoming source or incoming destination, d(i,j) is the shortest path length from node i to node j, and N is the total number of nodes in the cross-border incoming risk network;

[0016] S1-3: Betweenness centrality. In the cross-border introduction risk network of invasive species, the source nodes or the introduction destination nodes with high betweenness centrality are located at transportation hubs, or play a key transit role in the cross-border introduction risk network. By controlling these nodes, the introduction path of biological invasion can be cut off. The calculation formula of betweenness centrality is as follows:

[0017]

[0018] Among them, C B (i) is the betweenness centrality of the incoming source or incoming destination node i, σ st (i) is the number of nodes passing through i in the shortest path from s to t, σ st is the total number of shortest paths from node s to t;

[0019] S1-4: Eigenvector centrality analysis: By calculating the eigenvector centrality, we can identify the incoming source nodes and incoming destination nodes directly associated with the high-risk nodes. The formula is as follows:

[0020]

[0021] Among them, CE (i) is the eigenvector centrality value of the incoming source or incoming location node i in the cross-border incoming risk network. The higher the value, the higher the A ij is the adjacency matrix element of the network. If the weight value of the biological invasion from node i to node j is not equal to 0, then A ij is 1, if it is equal to 0 then A ij is 0, C E (j) is the eigenvector centrality value of node j, and λ is the corresponding eigenvalue of the adjacency matrix;

[0022] S1-5: By comprehensively considering the incoming probability / weight and random jumps, the overall influence of the node is measured. The incoming source node with a high PageRank value is a high-risk incoming source, and the incoming destination node with a high PageRank value faces a high risk of biological invasion. The formula is as follows:

[0023]

[0024] Where PR(i) is the PageRank value of node i at the incoming source or incoming destination, d is the damping factor (usually 0.85), N is the total number of nodes in the cross-border incoming risk network, and L(j) is the total number of nodes connected to node j.

[0025] According to the method for analyzing the cross-border introduction risk network of biological invasions of the present invention, the introduction source nodes and the introduction destination nodes are clustered by the following method:

[0026] S2-1 K-Means clustering: For the incoming source nodes, clustering is performed based on the weight values ​​of the links between the incoming source and the incoming destination. For the incoming destination nodes, clustering is performed based on the weight values ​​of their links with the incoming source. Incoming destination nodes with large weight values ​​of their links with the incoming source are grouped together, and risk nodes with similar characteristics are merged into the same cluster. The formula is as follows:

[0027]

[0028] Where N is the total number of nodes in the cross-border risk network, X i is the characteristic of the i-th risk node, μ i is the feature of the center point of the i-th cluster, x∈C i Indicates whether node x belongs to cluster C i ;

[0029] S2-2 hierarchical clustering: when clustering incoming source nodes, incoming source nodes with similar characteristics to incoming land links are gradually merged; for incoming land nodes, clustering is performed based on the number of invasive species and trade flow characteristics of the incoming land nodes and incoming source links, and incoming land node groups with similar susceptibility are found; when merging clusters, incoming source and incoming land nodes with similar propagation relationships are gradually merged based on these link characteristics. The hierarchical clustering formula is as follows:

[0030]

[0031] Where A and B represent different clusters, i and j represent risk nodes belonging to i and j respectively, d(i, j) represents the distance between risk nodes i and j, and d(A, B) is the minimum distance between clusters A and B, which is used to judge the similarity between clusters, determine the merging order, and reveal the propagation hierarchical relationship of risk nodes.

[0032] S2-3 density-based cluster analysis, in which, when analyzing incoming source nodes, clustering is performed based on the number of invasive species and the characteristic density of trade flows linked to the incoming source nodes and the incoming land, and the incoming source nodes with higher characteristic density are classified into one category. At the same time, abnormal incoming source nodes that deviate from the normal density distribution are identified, representing new sources of invasion risks; for incoming land nodes, clustering is performed based on the number of invasive species and the characteristic density of trade flows linked to the incoming land nodes and the incoming source, and abnormal incoming land nodes are detected, indicating the presence of sudden biological invasion events. Based on density, The incoming source and incoming ground nodes with similar link feature density are clustered into one category. The core parameters of density-based clustering are the neighborhood radius ε and the minimum number of neighbors MinPts, which are used to detect abnormal biological invasion events and sudden areas. The neighborhood radius ε: defines the neighborhood range of the risk node. If the number of neighbor nodes within the ε radius of a risk node meets the minimum requirement, it becomes a core node. The minimum number of neighbors (MinPts) is the threshold for judging whether a risk node is a core node. If the number of neighbors of a risk node in the ε neighborhood is ≥MinPts, the node is a core node, otherwise it is a boundary point or a noise point.

[0033] S2-4 spectral clustering analysis: When clustering incoming source nodes, the connection strength and propagation probability of the incoming source nodes with other nodes, as well as the number of invasive species and trade flow characteristics linked to the incoming destination, are combined to identify groups of incoming source nodes with similar propagation influence in the complex network structure. For incoming destination nodes, the position of the incoming destination node in the network, the degree of connection with different incoming sources, and the number of invasive species and trade flow characteristics linked to the incoming destination nodes are considered to cluster incoming destination nodes with similar network characteristics. When merging clusters, incoming source and incoming destination nodes with similar network characteristics and propagation relationships are clustered based on the entire network structure and link characteristics.

[0034] S2-5 Gaussian mixture model analysis: When clustering source nodes, the source nodes are classified according to the number of invasive species linked to the destination during the cross-border introduction of invasive species and trade flow factors; for destination nodes, the destination nodes are clustered according to characteristics such as the number of invasive species linked to the source and trade flow; if merge clustering is performed, the source and destination nodes are grouped according to the similarity in uncertainty characteristics and link characteristics. The formula is as follows:

[0035]

[0036] Where x is the risk node (source or destination node) in the cross-border risk network, represented by a eigenvector, K is the number of Gaussian distribution components, that is, the risk nodes are divided into K categories, π i The weight of the i-th Gaussian distribution represents the prior probability that the risk node belongs to the i-th category, μ i is the mean vector of the i-th Gaussian distribution.

[0037] According to the method for analyzing the cross-border transmission risk network of biological invasions of the present invention, in the step of S3 risk network vulnerability analysis, the risk network vulnerability is analyzed based on the following strategies:

[0038] S3-1 is a topology-based attack strategy that includes the following algorithms:

[0039] (1) Degree centrality algorithm: The degree of direct interaction of a node in the network is measured by calculating the number of connections between nodes. For an incoming source node, a larger out-degree means that it has a stronger ability to spread biological invasions outward and is an important source of transmission; for an incoming ground node, a larger in-degree means that it receives biological invasions more frequently and is more likely to become an invasion target. The formula is as follows:

[0040]

[0041] Among them, C D (i) is the degree centrality of node i at the incoming source or incoming destination, deg(i) is the degree of node i, where the incoming source is the out-degree and the incoming destination is the in-degree, and N is the total number of nodes in the cross-border incoming risk network.

[0042] (2) The proximity centrality algorithm measures the average shortest path distance from a node to all other nodes in the network, indicating the node's propagation efficiency in the network. Nodes with high proximity centrality are at the core of the risk network for cross-border introduction of invasive species and are more likely to cause rapid spread of biological invasions. By removing the nodes with the highest proximity centrality in turn, their impact on network connectivity is evaluated. The calculation formula for proximity centrality is as follows:

[0043]

[0044] Among them, C C (i) is the closeness centrality of node i of the incoming source or incoming destination, d(i,j) is the shortest path length from node i to node j, N is the total number of nodes in the cross-border incoming risk network,

[0045] (3) Betweenness centrality algorithm measures the frequency of a node on all shortest paths. Nodes with high betweenness centrality are “critical control points” in the network and have a great impact on the cross-border risk network of biological invasions. Removing these nodes can assess their impact on the stability of the cross-border risk network. The formula is:

[0046]

[0047] Among them, C B (i) is the betweenness centrality of the incoming source or incoming destination node i, σst(i) is the number of shortest paths from node s to t that pass through i, and σst is the total number of shortest paths from node s to t.

[0048] (4) PageRank algorithm: The incoming source or incoming destination node with a high PageRank value is the key risk node. The formula is:

[0049]

[0050] Where PR(i) is the PageRank value of the incoming source or incoming destination node i, d is the damping factor, N is the total number of nodes in the cross-border incoming risk network, L(j) is the total number of nodes connected to node j,

[0051] (5) The eigenvector centrality algorithm not only considers the number of direct connections, but also gives higher weights to nodes connected to important nodes, identifying key incoming sources or incoming nodes that connect to multiple important transmission sources. Removing these nodes can observe the overall risk characteristics of the risk network. The formula is:

[0052]

[0053] Among them, C E (i) is the eigenvector centrality value of the incoming source or incoming location node i in the cross-border incoming risk network. The higher the value, the higher the risk importance of the node in the cross-border incoming risk network. ij is the adjacency matrix element of the network. If the weight value of the biological invasion from node i to node j is not equal to 0, then A ij is 1, if it is equal to 0 then A ij is 0, C E (j) is the eigenvector centrality value of node j, λ is the eigenvalue corresponding to the adjacency matrix,

[0054] (6) Clustering coefficient algorithm measures the degree of connectivity between node neighbors. Nodes with high clustering coefficients are located in local high-density areas. By removing these nodes, we can observe the changes in the local structure of the risk network. The formula is as follows:

[0055]

[0056] Among them, e i : the actual number of edges between node i’s neighbors; k i : degree of node i,

[0057] (7) K-Core analysis is used to identify the core source or entry point nodes of the cross-border biological invasion risk network. By removing the nodes with the highest K-Core, the changes in risk characteristics after the important nodes of the network are observed.

[0058] K c =max{k|G k is a k-core subgraph of G};

[0059] S3-2 is based on a random attack strategy. By randomly selecting incoming source or incoming destination nodes in the network and removing them, it simulates the impact of random emergencies in the natural environment on network stability. By comparing the damage degree of random removal and targeted attack, it analyzes the vulnerability of the cross-border incoming risk network to random events.

[0060] S3-3 is based on the edge removal attack strategy, including:

[0061] (1) Remove the edge with the largest weight: Remove the edge with the largest weight and analyze the impact of the high propagation channel of biological invasion on the overall network.

[0062] (2) Randomly remove edges: Randomly remove paths in the network to simulate changes in network connectivity under uncertain environments and observe changes in the network under different removal strategies

[0063] The analysis system of the cross-border biological invasion risk network according to the present invention includes a centrality analysis module, a cluster analysis module, and a vulnerability analysis module, wherein:

[0064] The centrality analysis module is used to quantitatively assess the importance of risk nodes and quantitatively assess the risk levels of the source nodes and the destination nodes in the cross-border introduction risk network of invasive species through a network centrality assessment algorithm;

[0065] The cluster analysis module performs group cluster analysis on the cross-border introduction risk network of invasive species, and evaluates high-risk node clusters by clustering the introduction source nodes and the introduction destination nodes based on their respective centrality characteristics and combining the weight values ​​of the introduction source and introduction destination links;

[0066] The vulnerability analysis module is used to analyze the vulnerability of risk networks: assess the stability of the risk network of cross-border introduction of invasive species under different prevention and control strategies, and identify key nodes and paths in the network.

[0067] Beneficial technical effects

[0068] The technical solution of this invention achieves full automation from data import to output by comprehensively analyzing the topological structure, node importance, and network resilience of the risk network for cross-border biological invasions. First, the system converts the input edge list data into a network graph model and uses multiple centrality indicators to identify key transmission nodes. Second, cluster analysis is used to divide similar transmission areas. Finally, combined with resilience analysis, the stability of the risk network after prevention and control measures are implemented at different key nodes is evaluated, generating detailed analysis reports and high-quality visualization charts.

[0069] According to the technical solution of the present invention, the characteristics of the biological invasion propagation network are deeply analyzed from different angles. Multiple algorithms complement each other and work together, which can comprehensively analyze the characteristics of the biological invasion propagation network from different angles, thereby improving the reliability and accuracy of the analysis results. The reliability and accuracy of the analysis results are significantly improved; a comparative analysis method of targeted attacks and random attacks is introduced, and the network stability after the removal of key nodes is simulated, providing a scientific basis for the formulation of precise prevention and control strategies. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 A flowchart showing the network analysis method for the cross-border introduction risk of biological invasions proposed in this application;

[0071] Figure 2 Shows the system structure of the cross-border biological invasion risk network analysis system applied in this application. DETAILED DESCRIPTION

[0072] the term:

[0073] In the present invention, the term "node" means: in the cross-border introduction risk network of biological invasions, it represents the source or introduction site of the cross-border introduction of invasive species, including the introduction source node and the introduction site node, which can be represented by the country / region name (such as United States / New York; China / Xiamen) or a custom code (such as 1, 2).

[0074] The term "link characteristics" means: the attribute characteristics used to describe the incoming risk path between the incoming source node and the incoming destination node, specifically including the link weight value, such as the risk intensity value quantified based on indicators such as trade flow and the number of entry quarantine interceptions, which is used to assess the risk level of the transmission relationship between the incoming source and the incoming destination nodes.

[0075] The term "centrality characteristics" means: indicator characteristics calculated by the network centrality evaluation algorithm, which are used to measure the importance and influence of incoming source nodes and incoming destination nodes in the risk network, including degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, PageRank value, etc., reflecting the risk importance of nodes in the incoming risk network from different dimensions, such as incoming source capability, susceptibility to intrusion, propagation efficiency, transit role, overall influence, etc.

[0076] The term "edge with high incoming degree" refers to a propagation path with high incoming degree.

[0077] like Figure 1 and Figure 2 As shown, the method for analyzing the cross-border introduction risk network of biological invasion according to the present invention includes the following steps:

[0078] S1 quantitatively evaluates the importance of risk nodes. Through the network centrality evaluation algorithm, the risk level of the source node and the entry point node in the cross-border introduction risk network of invasive species is quantitatively evaluated.

[0079] S2 performs a cluster analysis on the risk network of cross-border introduction of invasive species. Using five clustering algorithms, including K-Means, hierarchical clustering, DBSCAN, spectral clustering, and Gaussian mixture model (GMM), the authors cluster the source and destination nodes based on their respective centrality characteristics, and combine the weights of the links between the source and destination to assess the clustering of high-risk nodes.

[0080] S3 risk network vulnerability analysis uses vulnerability analysis methods to evaluate the stability of the cross-border introduction risk network of invasive species under different prevention and control strategies, identify key nodes and paths in the network, and comprehensively evaluate the two types of risk nodes: introduction sources and introduction areas, to derive the overall risk characteristics of the cross-border introduction risk network of invasive species.

[0081] In the step of S1: quantitatively evaluating the importance of risk nodes, the algorithm for evaluating the network centrality includes the following centrality analysis:

[0082] S1-1: Degree centrality analysis, calculate the out-degree centrality of the incoming source node and the in-degree centrality of the incoming destination node respectively. Among them, the incoming source node with high out-degree centrality indicates that it will become the main source of transmission in the cross-border spread of biological invasion; while the incoming destination node with high in-degree centrality indicates that it is susceptible to the impact of biological invasion. The calculation formula of degree centrality is as follows:

[0083]

[0084] Among them, C D(i) is the degree centrality of node i at the incoming source or incoming destination, deg(i) is the degree of node i (the incoming source is the out-degree and the incoming destination is the in-degree), and N is the total number of nodes in the cross-border incoming risk network.

[0085] S1-2: Closeness centrality analysis. For incoming source nodes and incoming destination nodes, higher closeness centrality values ​​indicate faster propagation in the cross-border incoming network. These nodes are usually located in the core area of ​​the cross-border incoming risk network. Such incoming source nodes can spread invasive organisms to other areas more quickly, while such incoming destination nodes are susceptible to biological invasions from multiple sources. The calculation formula for closeness centrality is as follows:

[0086]

[0087] Where Cc(i) is the closeness centrality of node i at the incoming source or incoming destination, d(i,j) is the shortest path length from node i to node j, and N is the total number of nodes in the cross-border incoming risk network.

[0088] S1-3: Betweenness centrality. In the cross-border introduction risk network of invasive species, source nodes or destination nodes with high betweenness centrality often serve as transmission bridges (bridgeheads). These nodes may be located at transportation hubs or play a key transit role in the cross-border introduction risk network. By controlling these nodes, the introduction path of biological invasion can be effectively cut off. The calculation formula for betweenness centrality is as follows:

[0089]

[0090] Among them, C B (i) is the betweenness centrality of the incoming source or incoming destination node i, σ st (i) is the number of nodes passing through i in the shortest path from s to t, σ st is the total number of shortest paths from node s to t.

[0091] S1-4: Eigenvector centrality analysis. When identifying incoming source nodes and incoming destination nodes, this indicator can mine those nodes that are directly associated with high-risk nodes. These nodes play a core role in the cross-border introduction of biological invasions. Eigenvector centrality not only considers the number of connections, but also gives higher weights to nodes connected to important nodes. The formula is as follows:

[0092]

[0093] Among them, C E (i) is the eigenvector centrality value of the incoming source or incoming location node i in the cross-border incoming risk network. The higher the value, the higher the A ijis the adjacency matrix element of the network. If the weight value of the biological invasion from node i to node j is not equal to 0, then A ij is 1, if it is equal to 0 then A ij is 0, C E (j) is the eigenvector centrality value of node j, and λ is the corresponding eigenvalue of the adjacency matrix.

[0094] S1-5: By comprehensively considering the incoming probability / weight and random jumps, the overall influence of the node is measured. The incoming source node with a high PageRank value is a high-risk incoming source, and the incoming destination node with a high PageRank value faces a high risk of biological invasion. The formula is as follows:

[0095]

[0096] Where PR(i) is the PageRank value of node i at the incoming source or incoming destination, d is the damping factor (usually 0.85), N is the total number of nodes in the cross-border incoming risk network, and L(j) is the total number of nodes connected to node j.

[0097] By comprehensively analyzing the result values ​​of the risk nodes (incoming source nodes and incoming destination nodes) obtained by these five algorithms, the risk level ranking of the incoming source nodes and incoming destination nodes is determined according to five different dimensions. According to the ranking results, high-risk transmission paths can be identified, that is, those transmission / incoming paths with both high incoming source out-degree and high incoming destination in-degree. At the same time, it can also provide decision-making basis for the cross-border introduction risk management of invasive species, including the incoming source areas that need to be monitored, the incoming destination areas that need to strengthen prevention and control, and the key incoming risk paths.

[0098] According to the analysis method of the cross-border introduction risk network of biological invasions of the present invention, in the step S2 of performing group cluster analysis on the cross-border introduction risk network of invasive species, five clustering algorithms, namely K-Means, hierarchical clustering, DBSCAN, spectral clustering and Gaussian mixture model (GMM), are used to cluster the incoming source and incoming destination nodes based on their respective centrality characteristics, and the weight values ​​of the incoming source and incoming destination links are combined to evaluate the high-risk node clustering. When processing the data, the structured data in the cross-border introduction risk network of invasive species is used as input, and the incoming source nodes and incoming destination nodes are clustered using the five clustering algorithms, wherein,

[0099] S2-1 K-Means clustering: For the incoming source nodes, clustering is performed based on the weighted values ​​of the links between the incoming source and the incoming destination (such as invasive species output, trade volume, etc.). For example, incoming source nodes with high trade volume, high invasive species output, and large weighted links to the incoming destination are grouped together, indicating that these incoming source nodes are at high risk. For incoming destination nodes, clustering is performed based on the weighted values ​​of their links to the incoming source (including trade volume, invasive species introduction, etc.). Incoming destination nodes with large weighted links to the incoming source are grouped together, indicating that these incoming destinations are at high risk of biological invasion. Taking into account the characteristics of the incoming source and incoming destination nodes and their links, risk nodes with similar characteristics are merged into the same cluster. The formula is as follows:

[0100]

[0101] Where N is the total number of nodes in the cross-border risk network, X i is the characteristic of the i-th risk node,

[0102] μ i is the feature x∈C of the center point (cluster center) of the i-th cluster i Indicates whether node x belongs to cluster C i .

[0103] S2-2 hierarchical clustering uses similarity calculation (minimum distance) to determine the merged risk nodes, including the incoming source (from) and incoming destination (to) nodes. When clustering the incoming source nodes, the number of invasive species and trade flows linked to the incoming destination are considered. The incoming source nodes with similar characteristics in these aspects are gradually merged to reveal the characteristics of the incoming sources in different transmission levels. For the incoming destination nodes, clustering is performed based on the number of invasive species and trade flows linked to the incoming source to find groups of incoming destination nodes with similar susceptibility. When merging clusters, based on these link characteristics, the incoming source and incoming destination nodes with similar transmission relationships are gradually merged. Hierarchical clustering: Similar clusters are gradually merged from the bottom up until a complete hierarchical structure is formed. The formula is as follows:

[0104]

[0105] Among them, A and B represent different clusters, i and j represent risk nodes belonging to i and j respectively, d(i, j) represents the distance between risk nodes i and j (such as the similarity distance calculated based on the weight of the number of invasive species), and d(A, B) is the minimum distance between clusters A and B, which is used to judge the similarity between clusters, determine the merging order, and reveal the propagation hierarchical relationship of risk nodes.

[0106] S2-3 uses density-based clustering analysis. When analyzing incoming source nodes, clustering is performed based on the number of invasive species and the characteristic density of trade flows linked to the incoming source. Incoming source nodes with high characteristic density are grouped together, and anomalous incoming source nodes that deviate from the normal density distribution are identified, representing new invasion risk sources. For incoming source nodes, clustering is performed based on the number of invasive species and the characteristic density of trade flows linked to the incoming source. Anomalous incoming source nodes are detected, indicating the presence of sudden biological invasion events. Finally, based on density, incoming source and incoming source nodes with similar characteristic density of links are grouped together. Density-based clustering can detect clusters of arbitrary shapes and identify outliers. Its core parameters are the neighborhood radius ε and the minimum number of neighbors, MinPts. It is used to detect anomalous biological invasion events and sudden outbreak areas. ε (neighborhood radius) defines the neighborhood range of a risk node. A risk node becomes a core node if the minimum number of neighboring nodes within the ε radius meets the requirement. MinPts (minimum number of neighbors) is the threshold for determining whether a risk node is a core node. If the number of neighbors of a risk node in the ε neighborhood is ≥ MinPts, then the node is a core node, otherwise it may be a boundary point or a noise point (abnormal intrusion event).

[0107] S2-4 spectral clustering analysis comprehensively considers the connection relationship between the incoming source nodes and the incoming destination nodes in the network, as well as the number of invasive species and trade flow characteristics related to the links. When clustering the incoming source nodes, the connection strength, propagation probability, and the number of invasive species and trade flows linked to the incoming destination are combined to find the incoming source node group with similar propagation influence in the complex network structure. For the incoming destination nodes, considering their position in the network, the degree of connection with different incoming sources, and the number of invasive species and trade flows linked, the incoming destination nodes with similar network characteristics are clustered together. When merging clusters, based on the entire network structure and link characteristics, the incoming source and incoming destination nodes with similar network characteristics and propagation relationships are clustered. Clustering is performed using the eigenvectors of the graph Laplacian matrix. First, the Laplacian matrix is ​​calculated, and then the first K eigenvectors are extracted for K-Means clustering. Used for biological invasion networks with weights and complex topologies. W (adjacency matrix): If there is an association between two risk nodes i and j in the cross-border incoming risk network (such as the biological invasion incoming path, the weight value is not equal to 0), then W i,j is the value of the corresponding weight. If there is no association, W i,j is 0. D (degree matrix),

[0108] D ii =∑ j W ij, represents the sum of the connection weights of risk node i. L = DW, which is used to characterize the network topology. The hidden features of risk nodes are extracted through their feature vectors and then combined with K-Means clustering.

[0109] S2-5 Gaussian mixture model (GMM) analysis: When clustering source nodes, the uncertainty of the cross-border introduction of invasive species, as well as the number of invasive species linked to the introduction site and trade flow factors are considered. GMM will classify the source nodes based on these characteristics. For the introduction site nodes, due to the uncertainty of the introduction of biological invasions, the introduction site nodes are reasonably clustered based on the number of invasive species linked to the introduction source and trade flow. If merge clustering is performed, the similarity of the introduction source and introduction site nodes in uncertainty characteristics and link characteristics is considered to group them. The formula is as follows:

[0110]

[0111] Where x is the risk node (source or destination node) in the cross-border risk network, represented by a feature vector (such as invasion frequency, propagation capability, etc.), K is the number of preset Gaussian distribution components, that is, the risk nodes are planned to be divided into K categories, π i The weight of the i-th Gaussian distribution represents the prior probability that the risk node belongs to the i-th category, μ i is the mean vector of the i-th Gaussian distribution, which describes the core features of the corresponding risk node.

[0112] Ultimately, the clustering results from these five algorithms are combined with weights such as the number of invasive species and trade flows linking the source and destination to assess high-risk node clusters. For source node clusters, if nodes within a cluster have high trade volumes, high invasive species outputs, and high weights for connections to multiple high-risk destination nodes, then this cluster is considered a high-risk source cluster. For destination node clusters, if nodes within a cluster have high weights for connections to multiple high-risk source nodes (e.g., high trade volumes, high numbers of invasive species introduced), then this cluster is considered a high-risk destination cluster. In the merged clustering results, if a cluster includes both high-risk source nodes and closely connected high-risk destination nodes, and if the links between these nodes have generally high weights for invasive species numbers and trade flows, then this cluster as a whole is considered high-risk. Based on these assessment results, high-risk areas can be delineated, key prevention and control areas can be identified, and more precise prevention and control strategies can be formulated.

[0113] According to the present invention's method for analyzing a cross-border biological invasion risk network, step S3 primarily targets the cross-border invasive species risk network, applying vulnerability analysis to assess its stability under different prevention and control strategies. This approach identifies key nodes and pathways within the network, comprehensively evaluates both the source (from) and destination (to) risk nodes, and ultimately derives the overall risk profile of the cross-border invasive species risk network. This module supports three attack strategies, each with different specific algorithms.

[0114] S3-1 is a topology-based attack strategy that includes the following algorithms:

[0115] (1) Degree centrality algorithm: measures the degree of direct interaction of a node in the network by calculating the number of connections. For an incoming source node, a larger out-degree means that it has a stronger ability to spread biological invasions outward and is an important source of transmission; for an incoming ground node, a larger in-degree means that it receives biological invasions more frequently and is more likely to become an invasion target. Degree centrality is used to measure the number of connections of a node, indicating the degree of direct interaction of the node in the network. The formula is as follows:

[0116]

[0117] Among them, C D (i) is the degree centrality of node i at the incoming source or incoming destination, deg(i) is the degree of node i (the incoming source is the out-degree and the incoming destination is the in-degree), and N is the total number of nodes in the cross-border incoming risk network.

[0118] (2) The proximity centrality algorithm measures the average shortest path distance from a node to all other nodes in the network, indicating the node's propagation efficiency in the network. That is, nodes with high proximity centrality are at the core of the risk network for cross-border introduction of invasive species, and are more likely to cause the rapid spread of biological invasions. By removing the nodes with the highest proximity centrality in turn, their impact on network connectivity can be evaluated.

[0119]

[0120] Among them, C C (i) is the closeness centrality of node i to the incoming source or incoming destination, d(i,j) is the shortest path length from node i to node j, and N is the total number of nodes in the cross-border incoming risk network.

[0121] (3) The betweenness centrality algorithm measures the frequency of a node's appearance on all shortest paths, indicating its role as a "bridge" in the cross-border spread of biological invasions. Nodes with high betweenness centrality are "critical control points" in the network and have a greater impact on the cross-border transmission risk network of biological invasions. Removing these nodes can assess their impact on the stability of the cross-border transmission risk network.

[0122]

[0123] Among them, C B (i) is the betweenness centrality of the incoming source or incoming destination node i, σ st (i) is the number of nodes passing through i in the shortest path from s to t, σ st is the total number of shortest paths from node s to t.

[0124] (4) PageRank algorithm, considering the propagation probability and random jump mechanism, the incoming source or incoming destination nodes with high PageRank values ​​are key risk nodes. Removing these nodes can evaluate their impact on the network structure:

[0125]

[0126] Where PR(i) is the PageRank value of node i at the incoming source or incoming destination, d is the damping factor (usually 0.85), N is the total number of nodes in the cross-border incoming risk network, and L(j) is the total number of nodes connected to node j.

[0127] (5) The eigenvector centrality algorithm not only considers the number of direct connections, but also gives higher weights to nodes connected to important nodes. It can identify key incoming sources or incoming nodes that connect to multiple important transmission sources. Removing these nodes can observe the overall risk characteristics of the risk network.

[0128]

[0129] Among them, C E (i) is the eigenvector centrality value of the incoming source or incoming location node i in the cross-border incoming risk network. The higher the value, the higher the A ij is the adjacency matrix element of the network. If the weight value of the biological invasion from node i to node j is not equal to 0, then A ij is 1, if it is equal to 0 then A ij is 0, C E (j) is the eigenvector centrality value of node j, and λ is the corresponding eigenvalue of the adjacency matrix.

[0130] (6) Clustering coefficient algorithm measures the degree of connectivity between node neighbors. Incoming source or incoming destination nodes with higher clustering coefficients are usually located in local high-density areas. Removing these nodes can observe the changes in the local structure of the risk network. The formula is as follows:

[0131]

[0132] Among them, e i : the actual number of edges between node i’s neighbors; k i : The degree of node i (the number of connected neighbors). Nodes with higher clustering coefficients are usually located in local high-density areas. Remove the nodes with the highest clustering coefficients one by one and observe the changes in the local structure of the network.

[0133] (7) K-Core analysis is used to identify the core source or destination nodes of the cross-border biological invasion risk network. Removing the node with the highest K-Core can observe the changes in risk characteristics after the removal of important nodes in the network (the loss of the core structure of the network).

[0134] K c =max{k|G k is the k-nucleus graph of G}

[0135] S3-2 is based on a random attack strategy. The random node removal algorithm removes incoming source or incoming destination nodes in the network by randomly selecting them, simulating the impact of random emergencies in the natural environment on network stability. By comparing the degree of damage caused by random removal and targeted attacks, the vulnerability of the cross-border risk network to random events can be analyzed. Based on the edge removal attack strategy, the maximum weight edge removal algorithm removes the edges with the largest weights (such as the number of invasive species, trade flows, etc.) to analyze the impact of high-risk paths of cross-border biological invasions on the overall risk network. The random edge removal algorithm randomly removes edges in the network to simulate changes in network connectivity under uncertain environments. By calculating indicators such as the proportion of the largest connected subgraph and global efficiency, the changes in the network under different removal strategies are observed.

[0136] S3-3 is based on the edge removal attack strategy, including:

[0137] (1) Remove the edges with the largest weights: Remove the edges with the largest weights (invasion probability, trade flow, etc.). Analyze the impact of high-propagation channels of biological invasions on the overall network.

[0138] (2) Random Edge Removal: Randomly remove edges from the network. Simulate changes in network connectivity under uncertain environments. Calculate metrics such as the maximum connected subgraph ratio and global efficiency, and observe how the network changes under different removal strategies.

[0139] Risk network vulnerability analysis is based on the importance of nodes associated with cross-border biological invasion risk. Through targeted attacks, we assess which source or destination nodes are most effective in reducing the overall characteristics of the cross-border biological invasion risk network. Consequently, we implement targeted prevention and control measures for these key risk nodes. During the random removal of nodes, the changes in the maximum connected subgraph percentage and global efficiency after each node removal are recorded. If the removal of a source or destination node results in a significant decrease in the maximum connected subgraph percentage (e.g., by more than 20%) and a significant decrease in global efficiency (e.g., by more than 15%), this node is critical to network stability and should be prioritized for prevention and control. Stricter control measures can be implemented in the region where this node is located. If the removal of the heaviest-weighted edge or random edge removal results in a significant decrease in the maximum connected subgraph percentage (e.g., by more than 25%) and a significant decrease in global efficiency (e.g., by more than 20%), this indicates that the connections between the source and destination nodes corresponding to these edges significantly impact network stability. The nodes involved in these connections should be closely monitored and monitored.

[0140] Example 1

[0141] The data requirements for cross-border introduction risk analysis of biological invasions are to construct a basic dataset for cross-border introduction risk analysis based on a triplet network data structure. This dataset contains three core fields: (1) the source of introduction (from), which refers to the origin of the cross-border introduction of invasive species. It can be represented by a country / region name (e.g., United States / New York) or a custom code (e.g., 1, 2); (2) the destination of introduction (to), which refers to the destination of the cross-border introduction of invasive species. It can also be represented by a region name or code; (3) the transmission weight (weight), which is used to quantify the risk intensity of each transmission path. The specific value can be based on indicators such as invasion probability and trade flow. For example, if the number of invasive species transmitted from the United States to China is 10, the weight value is 10.

[0142] As shown in Table 1 below, the initial data for the three modules—risk node centrality analysis, risk network cluster analysis, and risk network vulnerability analysis—are all formatted in a three-column format. The "from" and "to" fields can be specific region names or codes. The data is stored in an Excel spreadsheet with three columns, each row representing a cross-border risk path and containing the fields "from," "to," and "weight." This format is suitable for risk node centrality analysis, risk network cluster analysis, and risk network vulnerability analysis. This data structure, defined by standardized network edge attributes, provides a structured data foundation for constructing risk analysis models for cross-border biological invasions, identifying key risk nodes, delineating risk clusters, and assessing network vulnerability.

[0143] Table 1

[0144] from to weight USA Shanghai 1 1 2 0.31 … … …

[0145] Taking the cross-border introduction risk network analysis of the major invasive species pine wood nematode as an example, the importance of risk nodes was quantitatively evaluated through the centrality analysis module; and the clustering characteristics of different risk nodes were identified through the grouping clustering analysis module of the cross-border introduction risk network; finally, the risk network vulnerability analysis module was used to identify the robustness characteristics of the cross-border introduction risk network of pine wood nematode, as shown below.

[0146] 1.1 Analysis of key nodes in the risk network of cross-border introduction of pine wood nematodes

[0147] The system converts the input edge list data into a network graph model and calculates multiple centrality indicators to identify key propagation nodes. Specifically, they include:

[0148] Degree centrality measures the number of direct connections between nodes, revealing which regions are potential sources of invasion due to frequent trade or transportation. Closeness centrality calculates the average shortest path distance between a node and all other nodes, identifying the nodes with the fastest transmission speeds in the risk network. Betweenness centrality focuses on the bridge role of a node in the network, helping to locate key countries / regions that may pose a high risk of cross-border introduction. Eigenvector centrality and PageRank value further consider the connection relationship between a node and important nodes and its overall influence, thereby accurately identifying high-risk introduction areas. By combining these multi-dimensional centrality indicators, we can comprehensively analyze the key nodes in the pine wood nematode cross-border introduction risk network, providing a scientific basis for formulating targeted management measures.

[0149] The risk levels of source nodes and destination nodes of cross-border introduction of pine wood nematodes were quantitatively assessed using five algorithms: degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, and PageRank value. For example, the source nodes of the United States (outdegree centrality 0.85) and Japan (0.78) have become the main sources of transmission due to large trade flows and frequent import quarantines. The destination nodes of Shanghai, China (indegree centrality 0.92) and Jiangsu (0.88) are vulnerable to invasion due to large trade flows and frequent interceptions. Hong Kong, China (proximity centrality 0.75) and Singapore (0.72) are located at the core nodes of the risk network with high transmission frequency. Taiwan, China (betweenness centrality 0.68) and Germany (0.65) are key transit / bridgehead nodes. The United States (eigenvector centrality 0.89) and Japan (0.87) are core risk sources. Among the source nodes, the United States (PR=0.91) and Canada (PR=0.83) are high-risk sources of transmission. Among the destination nodes, Shanghai (PR=0.93) and Zhejiang (PR=0.88) face high invasion risks. The key nodes are comprehensively analyzed through multi-dimensional centrality indicators.

[0150] 1.2 Cluster analysis of risk nodes in the pine wood nematode cross-border introduction risk network

[0151] The risk network cluster analysis module was used to perform cluster analysis on the risk nodes of the cross-border introduction risk network of pine wood nematodes.

[0152] In the risk node clustering analysis of the pine wood nematode cross-border introduction risk network, five algorithms, including K-Means, hierarchical clustering, density clustering (DBSCAN), spectral clustering and Gaussian mixture model (GMM), were used. Based on the centrality characteristics and link weight clustering, the process was to input the cross-border introduction data of pine wood nematodes (from = the United States, Japan, etc.; to = Shanghai, Jiangsu, China, etc.; weight = trade volume / number of interceptions), and based on the centrality characteristics of the introduction source node and the introduction destination node and the weight value of the introduction source and introduction destination link (such as trade volume, pine wood nematode interception volume, etc.), five algorithms were used for grouping and clustering: through K-Means clustering, risk nodes with similar characteristics were merged into the same cluster according to the weight value of the introduction source and introduction destination link (such as trade volume, interception volume); using hierarchical clustering , the incoming source nodes are gradually merged based on the trade volume and interception volume characteristics of their links with the incoming destinations, and the incoming destination nodes are hierarchically merged based on the trade volume and interception volume characteristics of their links with the incoming source; density-based clustering analysis is used to identify core nodes and abnormal nodes that deviate from the normal density distribution according to the characteristic density of the trade volume and interception volume of the incoming source nodes and the incoming destination links; with the help of spectral clustering, combined with the network structure characteristics such as the trade volume and interception volume of the incoming source nodes and the incoming destination links, clustering is performed after extracting hidden features through the Laplace matrix eigenvector; Gaussian mixture model analysis is used to probabilistically group risk nodes based on the number of Gaussian distribution components according to the trade volume and interception volume of the incoming source nodes and the incoming destination nodes, and finally the clustering of high-risk nodes is evaluated by combining the clustering results of the five algorithms with the link weight value.

[0153] Five clustering algorithms were used. K-Means divided the sources of introduction into high-risk clusters (the United States, Japan, and Canada) and medium- and low-risk clusters, and the introduction areas into high-risk clusters (Shanghai, Jiangsu, and Zhejiang), medium-risk clusters, and low-risk clusters. Hierarchical clustering divided the source countries outside of China into two levels: "North America-East Asia" and "Europe-Oceania." The "North America-East Asia" level includes countries such as the United States, Canada, Japan, and South Korea that have frequent trade with China and are the main exporters of pine wood nematodes. The "Europe-Oceania" level includes countries such as Germany and Australia, where the introduction risk is relatively dispersed. Among the introduction areas in China, Shanghai and Zhejiang are the main risk nodes for the introduction of pine wood nematodes. Density clustering identified the United States (which has frequent trade with many coastal provinces in China) among the sources of introduction and Shanghai among the introduction areas as core nodes, serving as the "source of introduction risk" and "high-risk introduction area," respectively. It also found that the routes from Brazil to Guangdong, China, and Vietnam (a Southeast Asian country) to Guangxi, China, were abnormal nodes and may be potential introduction risk nodes. Spectral clustering divides the sources of transmission into a "trans-Pacific transmission group" (countries with trans-oceanic trade, such as the United States and Japan) and a "regional transmission group" (Southeast Asian countries), and the locations of transmission into a "coastal cluster" (such as Shanghai, Guangdong, and Fujian) and an "inland cluster" (such as Anhui and Hubei). The GMM model divides the sources of transmission into high-risk sources (such as the United States and Japan), medium-risk sources (South Korea and some Southeast Asian countries), and low-risk sources (Europe and Oceania countries). The locations of transmission are divided into high-risk areas (Yangtze River Delta provinces, such as Shanghai, Zhejiang, and Jiangsu) and medium-risk areas (coastal provinces, such as Guangdong and Fujian). A comprehensive assessment shows that the high-risk cluster is composed of the "North America-East Asia cluster" of transmission sources connected to the "Yangtze River Delta cluster" of transmission areas through high-weight trade edges (such as the transmission routes from the United States to Shanghai and Japan to Zhejiang), representing key prevention and control pathways. The outlier clusters are composed of non-traditional pathways, such as Brazil to Guangdong, which warrant vigilance as emerging risk pathways.

[0154] 1.3 Identification of robustness characteristics of the pine wood nematode cross-border introduction risk network

[0155] The resilience analysis module is used to simulate the changes in the robustness characteristics of the cross-border incoming risk network under different attack strategies to evaluate its stability.

[0156] Through two scenarios, targeted attack and random attack, the network structure is gradually destroyed and the changes in key indicators are recorded in real time. Specifically, in the targeted attack, the nodes with the highest degree centrality, betweenness centrality or PageRank values ​​are removed first, and the changing trends of indicators such as global efficiency, the maximum proportion of connected subgraphs and the average shortest path length are observed; while in the random attack, risk nodes are randomly removed to simulate the impact of uncertainty in the natural environment. By analyzing these dynamic curves, the weak links in the risk network of cross-border introduction of pine wood nematodes and the impact of key nodes on the overall stability can be clearly identified. The K-Core analysis method is used to further evaluate the anti-destruction ability of the core structure of the network. This multi-angle robustness feature assessment provides decision makers with a comprehensive risk prediction tool, which helps to optimize resource allocation and improve the overall effectiveness of biological invasion prevention and control.

[0157] Network stability was evaluated based on topological attack, random attack, and edge removal strategies. Removing the node with the highest degree centrality, the United States, in the topological attack reduced the proportion of the largest connected subgraph from 92% to 65%, decreased global efficiency by 28%, and increased the average shortest path length by 40%. Removing the node with the highest betweenness centrality, Hong Kong, disrupted the trans-Pacific transmission path and reduced global efficiency by 22%. In the random attack, after randomly removing 10% of the nodes, the proportion of the largest connected subgraph only decreased by 5%, and global efficiency remained stable. In the edge removal attack, removing the heaviest-weighted edge, the United States → Shanghai, reduced the number of routes for pine wood nematode transmission into China by 35% and decreased the proportion of the largest connected subgraph by 18%. Randomly removing edges had little impact on network connectivity. K-Core analysis showed that the network core layer (k=5) included nodes such as the United States, Japan, Shanghai, and Hong Kong. Removing nodes with k-core ≥ 5 collapsed the network structure. Comprehensive analysis concluded that targeted attacks on key incoming risk nodes can significantly reduce the stability of the pine wood nematode cross-border transmission risk network, and priority should be given to controlling key incoming risk nodes and high-weight risk paths.

[0158] This systematic approach supports the quantitative analysis of key risk nodes and risk paths in the cross-border biological invasion risk network, and quantitatively evaluates the overall risk characteristics of the risk network. This method can not only quantitatively identify the topological structure of the cross-border biological invasion risk network (such as node connection relationships and edge weights), but also combine the importance of different risk nodes (such as centrality indicators) and the overall risk characteristics of the cross-border risk network (such as robustness characteristics) and other multi-dimensional characteristics to achieve accurate identification of key entry paths and risk nodes.

Claims

1. A method for analyzing the risk network of cross-border biological invasions, characterized by: The method comprises the following steps: S1 Quantitatively assess the importance of risk nodes: using a network centrality assessment algorithm, quantitatively assess the risk levels of the source nodes and destination nodes in the cross-border introduction risk network of invasive species; S2 performs group cluster analysis on the risk network of cross-border introduction of invasive species: by clustering the source nodes and the destination nodes based on their respective centrality characteristics, combining the weight values ​​of the links between the source and the destination, and then evaluating the high-risk node clusters; S3 Risk Network Vulnerability Analysis: Use vulnerability analysis methods to assess the stability of the cross-border introduction risk network of invasive species under different prevention and control strategies to identify key nodes and paths in the network.

2. The method for analyzing the risk network of cross-border biological invasion according to claim 1, characterized in that: In the step of quantitatively evaluating the importance of risk nodes in S1, the network centrality evaluation algorithm includes: S1-1: Degree centrality analysis, respectively calculate the out-degree centrality of the incoming source node and the in-degree centrality of the incoming land node. Among them, the incoming source node with high out-degree centrality indicates that the incoming source node will become the main source of transmission in the cross-border spread of biological invasion; and the incoming land node with high in-degree centrality indicates that the incoming land node is susceptible to the impact of biological invasion. The calculation formula of degree centrality is as follows: Among them, C D (i) is the degree centrality of node i at the incoming source or incoming destination, deg(i) is the degree of node i (the incoming source is the out-degree and the incoming destination is the in-degree), and N is the total number of nodes in the cross-border incoming risk network; S1-2: Closeness centrality analysis. For incoming source nodes and incoming destination nodes, higher closeness centrality values ​​indicate that the incoming source nodes and incoming destination nodes propagate faster in the cross-border incoming network and are located in the core area of ​​the cross-border incoming risk network. The calculation formula for closeness centrality is as follows: Where Cc(i) is the closeness centrality of node i of the incoming source or incoming destination, d(i,j) is the shortest path length from node i to node j, and N is the total number of nodes in the cross-border incoming risk network; S1-3: Betweenness centrality. In the cross-border introduction risk network of invasive species, the source nodes or the introduction destination nodes with high betweenness centrality are located at transportation hubs, or play a key transit role in the cross-border introduction risk network. By controlling these nodes, the introduction path of biological invasion can be cut off. The calculation formula of betweenness centrality is as follows: Among them, C B (i) is the betweenness centrality of the incoming source or incoming destination node i, σ st (i) is the number of nodes passing through i in the shortest path from s to t, σ st is the total number of shortest paths from node s to t; S1-4: Eigenvector centrality analysis: By calculating the eigenvector centrality, we can identify the incoming source nodes and incoming destination nodes directly associated with the high-risk nodes. The formula is as follows: Among them, C E (i) is the eigenvector centrality value of the incoming source or incoming location node i in the cross-border incoming risk network. The higher the value, the higher the A ij is the adjacency matrix element of the network. If the weight value of the biological invasion from node i to node j is not equal to 0, then A ij is 1, if it is equal to 0 then A ij is 0, C E (j) is the eigenvector centrality value of node j, and λ is the corresponding eigenvalue of the adjacency matrix; S1-5: By comprehensively considering the incoming probability / weight and random jumps, the overall influence of the node is measured. The incoming source node with a high PageRank value is a high-risk incoming source, and the incoming destination node with a high PageRank value faces a high risk of biological invasion. The formula is as follows: Where PR(i) is the PageRank value of node i at the incoming source or incoming destination, d is the damping factor (usually 0.85), N is the total number of nodes in the cross-border incoming risk network, and L(j) is the total number of nodes connected to node j.

3. The method for analyzing the risk network of cross-border biological invasion according to claim 1, characterized in that: Clustering the incoming source nodes and the incoming destination nodes is performed by the following method: S2-1K-Means clustering: For the incoming source nodes, clustering is performed based on the weight values ​​of the links between the incoming source and the incoming destination. For the incoming destination nodes, clustering is performed based on the weight values ​​of their links with the incoming source. Incoming destination nodes with large weight values ​​of their links with the incoming source are grouped together, and risk nodes with similar characteristics are merged into the same cluster. The formula is as follows: Where N is the total number of nodes in the cross-border risk network, X i is the characteristic of the i-th risk node, μ i is the feature of the center point of the i-th cluster, x∈C i Indicates whether node x belongs to cluster C i ; S2-2 hierarchical clustering: when clustering incoming source nodes, incoming source nodes with similar characteristics to incoming land links are gradually merged; for incoming land nodes, clustering is performed based on the number of invasive species and trade flows linked to the incoming land nodes and incoming sources to find groups of incoming land nodes with similar susceptibility; when merging clusters, incoming source and incoming land nodes with similar propagation relationships are gradually merged based on these link characteristics. The hierarchical clustering formula is as follows: Where A and B represent different clusters, i and j represent risk nodes belonging to i and j respectively, d(i, j) represents the distance between risk nodes i and j, and d(A, B) is the minimum distance between clusters A and B, which is used to judge the similarity between clusters, determine the merging order, and reveal the propagation hierarchical relationship of risk nodes. S2-3 density-based cluster analysis, in which, when analyzing incoming source nodes, clustering is performed based on the number of invasive species and the characteristic density of trade flows linked to the incoming source nodes and the incoming land, and the incoming source nodes with higher characteristic density are classified into one category. At the same time, abnormal incoming source nodes that deviate from the normal density distribution are identified, representing new sources of invasion risks; for incoming land nodes, clustering is performed based on the number of invasive species and the characteristic density of trade flows linked to the incoming land nodes and the incoming source, and abnormal incoming land nodes are detected, indicating the presence of sudden biological invasion events. Based on density, The incoming source and incoming ground nodes with similar link feature density are clustered into one category. The core parameters of density-based clustering are the neighborhood radius ε and the minimum number of neighbors MinPts, which are used to detect abnormal biological invasion events and sudden areas. The neighborhood radius ε: defines the neighborhood range of the risk node. If the number of neighbor nodes within the ε radius of a risk node meets the minimum requirement, it becomes a core node. The minimum number of neighbors (MinPts) is the threshold for judging whether a risk node is a core node. If the number of neighbors of a risk node in the ε neighborhood is ≥MinPts, the node is a core node, otherwise it is a boundary point or a noise point. S2-4 spectral clustering analysis: When clustering incoming source nodes, the connection strength and propagation probability of the incoming source nodes with other nodes, as well as the number of invasive species and trade flow characteristics linked to the incoming destination, are combined to identify groups of incoming source nodes with similar propagation influence in the complex network structure. For incoming destination nodes, the location of the incoming destination node in the network, the closeness of the connection with different incoming sources, and the number of invasive species and trade flow characteristics linked to the incoming destination are considered to cluster incoming destination nodes with similar network characteristics. When merging clusters, incoming source and incoming destination nodes with similar network characteristics and propagation relationships are clustered based on the entire network structure and link characteristics. S2-5 Gaussian mixture model analysis: When clustering source nodes, the source nodes are classified according to the number of invasive species linked to the destination during the cross-border introduction of invasive species and trade flow factors; for destination nodes, the destination nodes are clustered according to the number of invasive species linked to the source and trade flow characteristics; if merge clustering is performed, the source and destination nodes are grouped according to the similarity in uncertainty characteristics and link characteristics. The formula is as follows: Among them, x is the risk node in the cross-border risk network, represented by the eigenvector, K is the number of preset Gaussian distribution components, that is, the risk nodes are planned to be divided into K categories, π i The weight of the i-th Gaussian distribution represents the prior probability that the risk node belongs to the i-th category, μ i is the mean vector of the i-th Gaussian distribution.

4. The method for analyzing the risk network of cross-border biological invasion according to claim 1, characterized in that: In the S3 risk network vulnerability analysis step, the risk network vulnerability is analyzed based on the following strategies: S3-1 is a topology-based attack strategy that includes the following algorithms: (1) Degree centrality algorithm: The degree of direct interaction of a node in the network is measured by calculating the number of connections between nodes. For an incoming source node, a larger out-degree means that it has a stronger ability to spread biological invasions outward and is an important source of transmission; for an incoming ground node, a larger in-degree means that it receives biological invasions more frequently and is more likely to become an invasion target. The formula is as follows: Among them, C D (i) is the degree centrality of node i at the incoming source or incoming destination, deg(i) is the degree of node i, where the incoming source is the out-degree and the incoming destination is the in-degree, and N is the total number of nodes in the cross-border incoming risk network. (2) The proximity centrality algorithm measures the average shortest path distance from a node to all other nodes in the network, indicating the node's propagation efficiency in the network. Nodes with high proximity centrality are at the core of the risk network for cross-border introduction of invasive species and are more likely to cause rapid spread of biological invasions. By removing the nodes with the highest proximity centrality in turn, their impact on network connectivity is evaluated. The calculation formula for proximity centrality is as follows: Among them, C C (i) is the closeness centrality of node i of the incoming source or incoming destination, d(i,j) is the shortest path length from node i to node j, N is the total number of nodes in the cross-border incoming risk network, (3) Betweenness centrality algorithm measures the frequency of a node on all shortest paths. Nodes with high betweenness centrality are "critical control points" in the network and have a great impact on the cross-border risk network of biological invasions. Removing these nodes can assess their impact on the stability of the cross-border risk network. The formula is: Among them, C B (i) is the betweenness centrality of the incoming source or incoming destination node i, σst(i) is the number of shortest paths from node s to t that pass through i, and σst is the total number of shortest paths from node s to t. (4) PageRank algorithm: The incoming source or incoming destination node with a high PageRank value is the key risk node. The formula is: Where PR(i) is the PageRank value of the incoming source or incoming destination node i, d is the damping factor, N is the total number of nodes in the cross-border incoming risk network, L(j) is the total number of nodes connected to node j, (5) The eigenvector centrality algorithm not only considers the number of direct connections, but also gives higher weights to nodes connected to important nodes, identifying key incoming sources or incoming nodes that connect to multiple important transmission sources. Removing these nodes can observe the overall risk characteristics of the risk network. The formula is: Among them, C E (i) is the eigenvector centrality value of the incoming source or incoming location node i in the cross-border incoming risk network. The higher the value, the higher the risk importance of the node in the cross-border incoming risk network. ij is the adjacency matrix element of the network. If the weight value of the biological invasion from node i to node j is not equal to 0, then A ij is 1, if it is equal to 0 then A ij is 0, C E (j) is the eigenvector centrality value of node j, λ is the eigenvalue corresponding to the adjacency matrix, (6) Clustering coefficient algorithm measures the degree of connectivity between node neighbors. Nodes with high clustering coefficients are located in local high-density areas. By removing these nodes, we can observe the changes in the local structure of the risk network. The formula is as follows: Among them, e i : the actual number of edges between node i’s neighbors; k i : degree of node i, (7) K-Core analysis is used to identify the core source or entry point nodes of the cross-border biological invasion risk network. By removing the nodes with the highest K-Core, the changes in risk characteristics after the important nodes of the network are observed. K c =max{k|G k is a k-core subgraph of G}; S3-2 is based on a random attack strategy. By randomly selecting incoming source nodes or incoming destination nodes in the network and removing them, it simulates the impact of random emergencies in the natural environment on network stability. By comparing the damage degree of random removal and targeted attacks, it analyzes the vulnerability of cross-border incoming risk networks to random events. S3-3 is based on the edge removal attack strategy, including: (1) Remove the edge with the largest weight: Remove the edge with the largest weight and analyze the impact of the high propagation channel of biological invasion on the overall network. (2) Randomly remove edges: Randomly remove the propagation paths in the network to simulate the changes in network connectivity under uncertain environments and observe the changes in the network under different removal strategies.

5. An analysis system for the risk network of cross-border biological invasions, characterized by: The system includes a centrality analysis module, a cluster analysis module, and a vulnerability analysis module, wherein: The centrality analysis module is used to quantitatively assess the importance of risk nodes and quantitatively assess the risk levels of the source nodes and the destination nodes in the cross-border introduction risk network of invasive species through a network centrality assessment algorithm; The cluster analysis module performs group cluster analysis on the cross-border introduction risk network of invasive species, and evaluates high-risk node clusters by clustering the introduction source nodes and the introduction destination nodes based on their respective centrality characteristics and combining the weight values ​​of the introduction source and introduction destination links; The vulnerability analysis module is used to analyze the vulnerability of the risk network: assess the stability of the cross-border introduction risk network of invasive species under different prevention and control strategies to identify key nodes and paths in the network.

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