Complex network key node identification method based on improved dynamic sensitive centrality

Abstract

The invention discloses a complex network key node identification method based on improved dynamic sensitive centrality, and relates to the technical field of complex network analysis. The method is used for identifying key nodes with important influence in an aviation network. A traditional method mostly focuses on analyzing local or global influence of nodes and does not fully consider interaction influence among the nodes. According to the method, a more accurate key node propagation influence evaluation model is constructed by considering the influence of nodes and the influence of neighbor nodes. Experimental results based on six actual aviation network data sets and an SIR propagation model show that the node identification accuracy of the IDS is obviously superior to that of an existing traditional method, and especially on EU air-2, the Kendall correlation coefficient of the IDS is maximally improved by 105% compared with that of DS centrality. The method provides theoretical support for stable operation of the aviation network, and is suitable for identifying key nodes in different types of complex networks.

Description

Technical Field

[0001] The present invention relates to the technical field of complex network analysis, and in particular to a complex network key node identification method based on improved dynamic sensitive centrality. Background Art

[0002] The problem of identifying key nodes in complex networks has received extensive attention in recent years. Complex networks have a wide range of applications in biology, society, transportation and other fields, and the influence of nodes is of great significance to the network structure and function. Traditional node centrality indicators (such as degree centrality, closeness centrality, eigenvector centrality, etc.) mostly consider the local or global influence of nodes, and fail to fully capture the dynamic characteristics of the network and the interaction between nodes. Summary of the invention

[0003] The purpose of the present invention is to provide a method for identifying key nodes in complex networks based on improved dynamic sensitive centrality, in order to solve the above-mentioned problems. This method constructs a more accurate key node propagation impact assessment model by considering the influence of the node itself and the influence of neighboring nodes. Experimental results based on six actual aviation network data sets and the SIR propagation model show that IDS is significantly superior to existing traditional methods in node identification accuracy, especially in the EU aviation network, where the Kendall correlation coefficient of IDS compared to DS centrality is increased by up to 105%. This method provides theoretical support for the stable operation of aviation networks and is suitable for identifying key nodes in different types of complex networks.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] A complex network key node identification method based on improved dynamic sensitive centrality includes the following steps:

[0006] Step 1: Assume an undirected and unweighted network G = (N, E), where N is the node set and E is the edge set; the connection relationship between nodes is represented by the adjacency matrix A = {a ij} means; if two nodes are connected, then a ij =1, otherwise 0; in the aviation network, airports represent nodes, and direct routes between airports represent connections in the network. The connections between different airports and routes constitute a complete network. The present invention introduces the relevant methods used in the subsequent steps, including the benchmark methods DC, CC and EC, and the improved methods DS and GSI.

[0007] Step 2: For the collected information, take degree centrality into account. Degree centrality measures the importance of a node by the number of neighboring nodes that the node is directly connected to. The specific model is as follows:

[0008]

[0009] Where n represents the number of nodes, Represents nodes i and a ij is the element in the i-th row and j-th column of the adjacency matrix A;

[0010] Step 3: Taking closeness centrality into account, determine the influential nodes through calculation; its expression is as follows:

[0011]

[0012] where d ij is the distance from node i to j;

[0013] Step 4: Eigenvector centrality describes the influence of a node in terms of the number and influence of its neighbors; the equation is expressed as:

[0014]

[0015] Where c = 1 / λ max is the proportionality constant, λ max Represents the adjacency matrix A and x=(x1,x2,…,x n ) T The eigenvector corresponding to the maximum eigenvalue of x j is the eigenvector centrality value of node j;

[0016] Step 5: Sort the nodes according to their degree and evaluate the influence of the nodes by their position attributes;

[0017] Step 6: Quantify the spread of node influence through the topological characteristics and dynamic characteristics of the network; the expression of dynamic sensitive centrality (DS) is as follows:

[0018]

[0019] Where t is the time step, β is the propagation rate, A is the adjacency matrix; L = (1,1,...,1) T is an n×1 column vector, each component H=βA+(1-μ)I; in the expanded form, μ represents the recovery rate of the network, and I represents the unit matrix;

[0020] Step 7: Global structure influence (GSI) In this invention, the influence of nodes in the network is measured by the global and local influence of the nodes; the GSI of node i is defined as

[0021]

[0022] Where Di is the degree of node i C(v i ), C(v j) is the ks value of nodes i and j, dist(v i ,v j ) are the shortest paths from point i to adjacent node j, EC(v i ) is the eigenvector centrality value of node i;

[0023] Step 8: Calculate the node's own influence;

[0024] Step 9: Consider neighbor influence by combining the DS centrality of neighbor nodes; the distance between two nodes is inversely proportional to their influence on the network; the influence values ​​of all neighbor nodes within the specified range are accumulated to evaluate the neighbor influence value of the node;

[0025] Step 10: Based on the topological characteristics and dynamic characteristics of the network, the interaction influence of node i is determined by considering the interaction influence between the node and neighbor nodes; the expression of IDS is as follows:

[0026]

[0027] Step 11: Use the Kendall correlation coefficient to measure the correlation between the two sets of ranking data;

[0028] Step 12: Using an imprecise function, calculate the average propagation capacity of the top-pN nodes in the node ranking list generated by various key node mining algorithms, thereby achieving an effective evaluation of the performance of the key node mining algorithm; thereby determining the accuracy;

[0029] Step 13: In the process of obtaining the spread of nodes within the influence range, the probability of the distribution of the sorting results is expressed by introducing CCDF:

[0030]

[0031] where n i Represents the number of nodes ranked r. When the number of nodes with different result values ​​in the ranking list is close to n, it indicates that this method can effectively distinguish the influence of each node.

[0032] In some embodiments, the step 5: sorting nodes according to their degree, and evaluating the influence of nodes by the location attributes of nodes; includes: K-shell decomposition (KS) as a coarse-grained method, sorting nodes according to their degree, and evaluating the influence of nodes by the location attributes of nodes. The present invention also needs to draw on this method, deleting nodes from the periphery to the core in sequence; deleting nodes with a degree of 1, new nodes with a degree of 1 will appear in the remaining network; the deletion process continues until there are no nodes with a degree of 1 in the network; for each node deleted, ks=1, and this operation is repeated until there are no nodes in the network, at which point each node has an associated ks value.

[0033] In some embodiments, the step 8: calculating the node's own influence includes: Inspired by the DS centrality and GSI methods, the present invention proposes a method of dynamic sensitive centrality (IDS) that considers the interaction between the self-node and the adjacent nodes. In our proposed method, the degree of the node itself is first normalized. Then the influence of the node's own DS centrality is introduced. The two parts are calculated by square root to obtain the node's own influence, which can be expressed as:

[0034]

[0035] Where D(i) is the degree of node i, N is the total number of network nodes, and DS(i) is the DS centrality value of node i.

[0036] In some embodiments, the formula used in step 9 is as follows:

[0037]

[0038] Where DS(j) represents the DS centrality value of the neighbor; j is the first-order neighbor of node i, and d(i,j) represents the shortest distance from node i to j.

[0039] In some embodiments, the step 11: using the Kendall correlation coefficient to measure the correlation between the two sets of ranking data; includes: the formula is as follows:

[0040]

[0041] Where sgn(h) is the partition function; when h>0, sgn(h)=+1; when h<0, sgn(h)=-1; when h=0, sgn(h)=0; (h i ,q i ) represent the real propagation influence capability of node i and the propagation influence capability calculated by different key node mining algorithms respectively;

[0042] When the Kendall correlation coefficient is τ=1, it indicates that the two sorted data are consistent; when τ=-1, it indicates that they are inconsistent; when τ=0, it indicates that the two sequences are neither consistent nor inconsistent; when τ is closer to 1, the performance of the method is better, indicating that the method more accurately reflects the actual propagation process.

[0043] In some embodiments, the step 12: using an imprecise function to calculate the average propagation capacity of the top-pN nodes in the node ranking list generated by various key node mining algorithms, thereby achieving an effective evaluation of the performance of the key node mining algorithm; thereby determining the accuracy; includes: using the formula

[0044] Where p is the proportion of selected nodes in the entire network, Md(p) and Ms(p) represent the average transmission capacity of top-pN nodes obtained using different methods and the average transmission capacity of top-pN nodes obtained in the SIR propagation model, respectively; if Md(p) and Ms(p) are closer, it means that the average transmission capacity of top-pN nodes selected by this method is more relevant to the transmission capacity of top-pN nodes in actual situations, then ∈(p) is closer to 0.

[0045] The beneficial effects that may be brought about by a complex network key node identification method based on improved dynamic sensitive centrality disclosed in this application include but are not limited to:

[0046] This invention proposes a complex network key node identification method based on improved dynamic sensitive centrality, which effectively identifies the key nodes in the aviation network by integrating the interaction between the node itself and the neighboring nodes. Based on multiple aviation network data sets and SIR propagation models, experiments have verified the significant improvement of the IDS method in node identification accuracy. Compared with traditional methods, the IDS method performs better in multiple evaluation indicators (such as Kendall correlation coefficient, error function and complementary cumulative distribution function), especially in the EU aviation network, where the correlation coefficient of this method is improved by up to 105% compared with DS centrality. This improved method not only provides theoretical support for the operational stability of the aviation network, but also provides an effective tool for dealing with sudden failures. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 The overall flow chart of the method provided by the present invention;

[0048] Figure 2 Topological diagrams of six aviation networks provided by the present invention;

[0049] Figure 3 The SIR model of six aeronautical networks provided by the present invention evaluates the shortest distance between first to fifth order neighbors and the propagation impact of nodes;

[0050] Figure 4 A schematic diagram of comparing the IDS method with six other methods using the Kendall coefficient in six aviation networks provided by the present invention;

[0051] Figure 5 Comparison of the accuracy of the imprecise functions obtained by the seven methods provided by the present invention in different aviation networks;

[0052] Figure 6 A schematic diagram showing the comparison of seven methods using the CCDF provided by the present invention in six aviation networks. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solution and advantages of the present application more clear, the present application is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described here are only used to explain the present application and are not used to limit the present application.

[0054] On the contrary, the present application covers any substitution, modification, equivalent method and scheme made on the essence and scope of the present application as defined by the claims. Further, in order to make the public have a better understanding of the present application, some specific details are described in detail in the detailed description of the present application below. Those skilled in the art can fully understand the present application without the description of these details.

[0055] The following is a detailed description of a complex network key node identification method based on improved dynamic sensitive centrality involved in an embodiment of the present application. It should be noted that the following embodiments are only used to explain the present application and do not constitute a limitation on the present application.

[0056] like Figure 1-2 As shown, a complex network key node identification method based on improved dynamic sensitive centrality includes the following steps:

[0057] Step 1: Assume an undirected and unweighted network G = (N, E), where N is the node set and E is the edge set; the connection relationship between nodes is represented by the adjacency matrix A = {a ij} means; if two nodes are connected, then a ij =1, otherwise 0; in the aviation network, airports represent nodes, and direct routes between airports represent connections in the network. The connections between different airports and routes constitute a complete network. The present invention introduces the relevant methods used in the subsequent steps, including the benchmark methods DC, CC and EC, and the improved methods DS and GSI.

[0058] Step 2: For the collected information, take degree centrality into account. Degree centrality measures the importance of a node by the number of neighboring nodes that the node is directly connected to. The specific model is as follows:

[0059]

[0060] Where n represents the number of nodes, Represents nodes i and a ij is the element in the i-th row and j-th column of the adjacency matrix A;

[0061] Step 3: Taking closeness centrality into account, determine the influential nodes through calculation; its expression is as follows:

[0062]

[0063] where d ij is the distance from node i to j;

[0064] Step 4: Eigenvector centrality describes the influence of a node in terms of the number and influence of its neighbors; the equation is expressed as:

[0065]

[0066] Where c = 1 / λ max is the proportionality constant, λ max Represents the adjacency matrix A and x=(x1,x2,…,x n ) T The eigenvector corresponding to the maximum eigenvalue of x j is the eigenvector centrality value of node j;

[0067] Step 5: Sort the nodes according to their degree, and evaluate the influence of the nodes by the location attributes of the nodes; including: K-shell decomposition (KS) as a coarse-grained method, sort the nodes according to their degree, and evaluate the influence of the nodes by the location attributes of the nodes. The present invention also needs to learn from this method, delete the nodes from the periphery to the core in sequence; delete the nodes with degree 1, and new nodes with degree 1 will appear in the remaining network; the deletion process continues until there are no nodes with degree 1 in the network; for each node deleted, ks=1, and this operation is repeated until there are no nodes in the network, at which time each node has an associated ks value.

[0068] Step 6: Quantify the spread of node influence through the topological characteristics and dynamic characteristics of the network; the expression of dynamic sensitive centrality (DS) is as follows:

[0069]

[0070] Where t is the time step, β is the propagation rate, A is the adjacency matrix; L = (1,1,...,1) T is an n×1 column vector, each component H=βA+(1-μ)I; in the expanded form, μ represents the recovery rate of the network, and I represents the unit matrix;

[0071] Step 7: Global structure influence (GSI) In this invention, the influence of nodes in the network is measured by the global and local influence of the nodes; the GSI of node i is defined as

[0072]

[0073] Where Di is the degree of node i C(v i ), C(v j) is the ks value of nodes i and j, dist(v i ,v j ) are the shortest paths from point i to adjacent node j, EC(v i ) is the eigenvector centrality value of node i;

[0074] Step 8: Calculate the node's own influence; Inspired by the DS centrality and GSI methods, this paper proposes an improved dynamic sensitive centrality (IDS) method that considers the interaction between the node and the adjacent nodes. In our proposed method, the degree of the node itself is first normalized. Then the influence of the node's own DS centrality is introduced. The two parts are calculated by square root to obtain the node's own influence, which can be expressed as:

[0075]

[0076] Where D(i) is the degree of node i, N is the total number of network nodes, and DS(i) is the DS centrality value of node i.

[0077] Step 9: Consider neighbor influence by combining the DS centrality of neighbor nodes; the distance between two nodes is inversely proportional to their influence on the network; accumulate the influence values ​​of all neighbor nodes within the specified range to evaluate the neighbor influence value of the node; the formula used is as follows:

[0078]

[0079] Where DS(j) represents the DS centrality value of the neighbor; j is the first-order neighbor of node i, and d(i,j) represents the shortest distance from node i to j.

[0080] Step 10: Based on the topological characteristics and dynamic characteristics of the network, the interaction influence of node i is determined by considering the interaction influence between the node and neighbor nodes; the expression of IDS is as follows:

[0081]

[0082] Step 11: Use the Kendall correlation coefficient to measure the correlation between the two sets of ranking data; Use the Kendall correlation coefficient to measure the correlation between the two sets of ranking data; including: The formula is as follows:

[0083]

[0084] Where sgn(h) is the partition function; when h>0, sgn(h)=+1; when h<0, sgn(h)=-1; when h=0, sgn(h)=0; (h i ,q i) represent the real propagation influence capability of node i and the propagation influence capability calculated by different key node mining algorithms; (h i ,q i ) and (h j ,q j There are three relationships between i >h j ,q i >q j or i <h j ,q i j ;h i >h j ,q i j or i <h j ,q i >q j ;h i =h j ,q i =q j , respectively, as consistent, inconsistent, consistent or inconsistent. In this paper, the Kendall coefficient will be used to analyze the correlation between the network ranking list generated by various node ranking algorithms and the SIR model. If the τ value obtained is closer to 1, it means that the ranking list generated by the complex network key node mining algorithm is more likely to reflect the node ranking in the actual propagation process, indicating that the efficiency of using this algorithm is higher.

[0085] When the Kendall correlation coefficient is τ=1, it indicates that the two sorted data are consistent; when τ=-1, it indicates that they are inconsistent; when τ=0, it indicates that the two sequences are neither consistent nor inconsistent; when τ is closer to 1, the performance of the method is better, indicating that the method more accurately reflects the actual propagation process.

[0086] Step 12: Use an imprecise function to calculate the average propagation capacity of the top-pN nodes in the node ranking list generated by various key node mining algorithms, thereby effectively evaluating the performance of the key node mining algorithm; thereby determining the accuracy; using the formula

[0087] Where p is the proportion of selected nodes in the entire network, Md(p) and Ms(p) represent the average transmission capacity of top-pN nodes obtained using different methods and the average transmission capacity of top-pN nodes obtained in the SIR propagation model, respectively; if Md(p) and Ms(p) are closer, it means that the average transmission capacity of top-pN nodes selected by this method is more relevant to the transmission capacity of top-pN nodes in actual situations, then ∈(p) is closer to 0. ​​

[0088] Step 13: In the process of obtaining the spread of nodes within the influence range, the probability of the distribution of the sorting results is expressed by introducing CCDF:

[0089]

[0090] where n i Represents the number of nodes ranked r. When the number of nodes with different result values ​​in the ranking list is close to n, it indicates that this method can effectively distinguish the influence of each node.

[0091] Table 1 gives the relevant topological properties of six aviation networks, introducing six real aviation networks, namely EU air-1, EU air-2, US air, CA, CZ and MU. EU air-1 constitutes a comprehensive aviation network composed of five European airlines, and EU air-2 represents a comprehensive aviation network composed of 15 European airlines. US air represents the American Airlines network, CA is the Air China route network, CZ is the China Southern Airlines route network, and MU is the China Eastern Airlines route network. N represents the total number of nodes in the network, E is the total number of edges in the network, <k>represents the average degree, β th represents the propagation threshold, γ represents the expansion threshold, C is the clustering coefficient, <d>represents the average distance, and D represents the network diameter.

[0092] Table 1 Related topological attributes

[0093]

[0094] Figure 2 A topological diagram of six aviation networks provided as an example of the present invention;

[0095] Topological graphs of six different aviation networks, where each node represents an airport and an edge between two nodes represents a route. Each node in the graph represents an airport and an edge between two nodes represents a route. The six aviation networks show similar topological characteristics, presenting a layout characterized by dense centers and sparse edges. Observations show that a few nodes have a large number of connected edges, while most nodes have only a small number of edges. It can be seen that nodes with many directly connected neighbors are more important than nodes with only a few neighbors.

[0096] Figure 3 An SIR model through six aeronautical networks is provided for an example of the invention, and the shortest distances within the 1st, 2nd, 3rd, 4th and 5th order neighbors of the selected nodes in the IDS and the diffusion impact of the nodes are evaluated.

[0097] We set the propagation speed β = 0.5, the time step t = 10 and the recovery rate μ = 1 for the propagation process of six different airline networks. EU Airlines 1, EU Airlines 2, American Airlines, CZ (China Southern Airlines), CA (Air China) and MU (China Eastern Airlines). The shortest distance within the 1st, 2nd, 3rd, 4th and 5th order neighbors of the node was selected as the variable. The Kendall correlation coefficient was used to compare the accuracy of IDS under different conditions. The Kendall correlation coefficient for the first order neighbor range selected as the shortest distance performed best, and the accuracy of IDS was the highest. When the second order neighbors were considered, the Kendall τ decreased significantly. However, for the third, fourth and fifth order neighbor ranges, the Kendall's τ value tended to be stable.

[0098] Figure 4 A schematic diagram of comparing the IDS method with six other methods using the Kendall correlation coefficient in six aviation networks is provided for an example of the invention;

[0099] Six methods including DC, CC, EC, KS, DS and GSI are used for comparison with IDS. At the same time, the time step is set to t=10, the recovery rate μ=1, the diffusion rate β=(0,0.1], and the red dotted line indicates the diffusion threshold β th .like Figure 3 As shown in the figure, IDS performs exceptionally well in four aviation networks: EU air-1, USair, CA, and CZ. In most cases, the Kendall τ obtained by IDS is closest to 1 compared to other methods. In addition, IDS also shows superior performance in EU air-2 and MU networks. EC, DS, and GSI perform relatively well, but DC, CC, and KS perform slightly worse. In the EU air-2 network, the IDS results are significantly improved compared to DS centrality, with a maximum improvement of 105% when β = 0.1. In different aviation networks, IDS has higher accuracy than other methods, indicating that this method can more accurately identify potential nodes in the network.

[0100] Figure 5 For the purpose of an example of the invention, a comparison of the accuracy of the imprecise functions obtained by seven methods in different aeronautical networks is provided.

[0101] At the same time, we use the imprecise function ∈(p) to further evaluate the accuracy of the method. During the experiment, the propagation rate and time step are set to β = 0.05, t = 10 and μ = 1, and the p value is 0.1~0.3. Figure 4 It can be seen that the imprecision function value of IDS is generally lower than that of other methods. Under different P values, the results obtained by the proposed method are consistently close to or equal to 0. In particular, in the EU air-2 aggregated aviation network, IDS outperforms all other methods. DC and CC show poor performance in these six networks, and the KS method shows the largest fluctuation in the imprecision function value among the seven methods. This shows that IDS can effectively and accurately have a significant influence on the top 10% to 30% of nodes in the aviation network.

[0102] Figure 6 The present invention provides an example of the comparison of seven methods using CCDF in six aviation networks.

[0103] Finally, CCDF is used to further verify the superiority of this method. Figure 5 As shown in the figure, we set β = 0.05, μ = 1 and t = 10. KS decays the fastest due to its poor ability to identify key nodes in the network, and finally decays to 0, followed by DC and CC. Compared with the other four methods (EC, DS, GSI and IDS), these three methods decay faster. Among DS, GSI and IDS, IDS shows a slower decay rate and outperforms the other methods. The comparison with other methods proves the effectiveness of this method in evaluating the propagation influence of each node in the network. This method can identify key nodes more accurately and avoid the problem of multiple nodes getting the same centrality value in the same ranking.

[0104] In the experimental verification process, we introduced six different methods to compare with IDS: four baseline methods (DC, CC, EC and KS) and two improved methods (DS and GSI). We used the actual data of airlines to construct the topology graphs of six different aviation networks. Figure 1 As shown in the figure, each node in the graph represents an airport, and an edge between two nodes represents a route. The six aviation networks show similar topological characteristics, presenting a layout characterized by central density and edge sparseness. Observations show that a few nodes have a large number of connected edges, while most nodes have only a small number of edges. It can be seen that nodes with many directly connected neighbors are more important than nodes with only a few neighbors.

[0105] The study of key node identification in complex networks can provide valuable insights into understanding and analyzing the structure and propagation characteristics of networks. This is of great significance for optimizing network performance. To identify key nodes, this paper proposes an improved method, IDS, based on network topology and dynamic characteristics, which takes into account the influence of both the node itself and neighbor nodes. First, the node's self-influence degree is calculated using the node's own degree centrality and DS centrality. Second, the node's first-order neighbor influence is considered, and the node's interaction influence is determined by combining these two aspects. To verify the accuracy and reliability of the proposed method, three evaluation indicators are used: Kendall correlation coefficient, imprecise function, and complementary cumulative distribution function. (1) The intrusion detection method proposed in this paper outperforms the other six methods by Kendall correlation coefficient. In the EU air-2 network, when β = 0.1, the Kendall correlation coefficient is increased by 105% compared with DS centrality. (2) In 6 different air networks, using the imprecise function, the value of IDS is lower than that of other methods. Especially in the EU air-2 network, the fluctuation range of the IDS detection result value is smaller than that of other methods and is closer to 0. (3) In the evaluation of CCDF, the results of IDS decrease more slowly than those of other methods. In all six networks, the slope of the CCDF line follows the diagonal line. Therefore, IDS can more effectively distinguish nodes with different influence orders. All the above evaluation indicators show that the performance of this method is better than that of other methods. This intrusion detection system can provide a reference for accurately identifying key nodes in the network.

[0106] Due to the continuous increase in global air traffic and the increasing number of routes, the complexity of network topology is also rising. When unforeseen factors cause delays or closures of certain airports, it may affect the normal operation of the aviation network. Theoretically, an intrusion detection system based on a diffusion dynamics model can be used to identify important airports in the aviation network. Identifying important nodes in the aviation network helps to accurately optimize the layout of routes and airports and improve the resilience and anti-interference ability of the network. In addition to aviation networks, it can also be extended to email, electricity, protein, social and various other networks to identify basic nodes. With the development of society, complex networks have evolved from single-layer networks to multi-layer networks, weighted networks and temporal networks. Therefore, future research will focus on these networks to further expand the applicability of intrusion detection systems.

[0107] The above description is only a preferred embodiment of the present invention and is used to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.< / d> < / k>

Claims

1. A complex network key node identification method based on improved dynamic sensitive centrality, characterized in that: The following steps are involved: Step 1: Assume an undirected and unweighted network G = (N, E), where N is the node set and E is the edge set; the connection relationship between nodes is represented by the adjacency matrix A = {a ij } means; if two nodes are connected, then a ij =1, otherwise 0; Step 2: For the collected information, take degree centrality into account. Degree centrality measures the importance of a node by the number of neighboring nodes that the node is directly connected to. The specific model is as follows: Where n represents the number of nodes, Represents nodes i and a ij is the element in the i-th row and j-th column of the adjacency matrix A; Step 3: Taking closeness centrality into account, determine the influential nodes through calculation; Its expression is as follows: where d ij is the distance from node i to j; Step 4: Eigenvector centrality describes the influence of a node in terms of the number and influence of its neighbors; the equation is expressed as: Where c = 1 / λ max is the proportionality constant, λ max Represents the adjacency matrix A and x=(x1,x2,...,x n ) T The eigenvector corresponding to the maximum eigenvalue of x j is the eigenvector centrality value of node j; Step 5: Sort the nodes according to their degree and evaluate the influence of the nodes by their position attributes; Step 6: Quantify the spread of node influence through the topological characteristics and dynamic characteristics of the network; the expression of dynamic sensitive centrality (DS) is as follows: Where t is the time step, β is the propagation rate, A is the adjacency matrix; L = (1,1,…,1) T is an n×1 column vector, each component H=βA+(1-μ)I; in the expanded form, μ represents the recovery rate of the network, and I represents the unit matrix; Step 7: Calculate GSI to measure the influence of nodes in the network by their global and local influence; the GSI of node i is defined as Where Di is the degree of node i C(v i ), C(v j ) is the ks value of nodes i and j, dist(v i ,v j ) are the shortest paths from point i to adjacent node j, EC(v i ) is the eigenvector centrality value of node i; Step 8: Calculate the node's own influence; Step 9: Consider neighbor influence by combining the DS centrality of neighbor nodes; the distance between two nodes is inversely proportional to their influence on the network; the influence values ​​of all neighbor nodes within the specified range are accumulated to evaluate the neighbor influence value of the node; Step 10: Based on the topological characteristics and dynamic characteristics of the network, the interaction influence of node i is determined by considering the interaction influence between the node and neighbor nodes; the expression of IDS is as follows: Step 11: Use the Kendall correlation coefficient to measure the correlation between the two sets of ranking data; Step 12: Using an imprecise function, calculate the average propagation capacity of the top-pN nodes in the node ranking list generated by various key node mining algorithms, thereby achieving an effective evaluation of the performance of the key node mining algorithm; thereby determining the accuracy; Step 13: In the process of obtaining the spread of nodes within the influence range, the probability of the distribution of the sorting results is expressed by introducing CCDF: where n i Represents the number of nodes ranked r. When the number of nodes with different result values ​​in the ranking list is close to n, it indicates that this method can effectively distinguish the influence of each node.

2. According to claim 1, a complex network key node identification method based on improved dynamic sensitive centrality is characterized in that: The step 5: sorting the nodes according to their degrees, and evaluating the influence of the nodes by the location attributes of the nodes; including: deleting nodes from the periphery to the core; deleting nodes with a degree of 1, and new nodes with a degree of 1 will appear in the remaining network; the deletion process continues until there are no nodes with a degree of 1 in the network; for each node deleted, ks=1, and this operation is repeated until there are no nodes in the network, at which point each node has an associated ks value.

3. The complex network key node identification method based on improved dynamic sensitive centrality according to claim 1 is characterized in that: The step 8: calculating the node's own influence includes: normalizing the node's own degree; introducing the influence of the node's own DS centrality; the two parts are calculated by square root to obtain the node's own influence, which is expressed as: Where D(i) is the degree of node i, N is the total number of network nodes, and DS(i) is the DS centrality value of node i.

4. The complex network key node identification method based on improved dynamic sensitive centrality according to claim 1 is characterized in that: The formula used in step 9 is as follows: Where DS(j) represents the DS centrality value of the neighbor; j is the first-order neighbor of node i, and d(i,j) represents the shortest distance from node i to j.

5. The complex network key node identification method based on improved dynamic sensitive centrality according to claim 1 is characterized in that: Step 11: using the Kendall correlation coefficient to measure the correlation between the two sets of ranking data; including: the formula is as follows: Where sgn(h) is the partition function; when h>0, sgn(h)=+1; when h<0, sgn(h)=-1; when h=0, sgn(h)=0; (h i ,q i ) represent the real propagation influence capability of node i and the propagation influence capability calculated by different key node mining algorithms respectively; When the Kendall correlation coefficient is τ=1, it indicates that the two sorted data are consistent; when τ=-1, it indicates that they are inconsistent; when τ=0, it indicates that the two sequences are neither consistent nor inconsistent; when τ is closer to 1, the performance of the method is better, indicating that the method more accurately reflects the actual propagation process.

6. The complex network key node identification method based on improved dynamic sensitive centrality according to claim 1 is characterized in that: Step 12: using an imprecise function to calculate the average propagation capacity of top-pN nodes in the node ranking list generated by various key node mining algorithms, thereby achieving an effective evaluation of the performance of the key node mining algorithm; To determine the accuracy; including: using the formula Where p is the proportion of selected nodes in the entire network, Md(p) and Ms(p) represent the average transmission capacity of top-pN nodes obtained using different methods and the average transmission capacity of top-pN nodes obtained in the SIR propagation model, respectively; if Md(p) and Ms(p) are closer, it means that the average transmission capacity of top-pN nodes selected by this method is more relevant to the transmission capacity of top-pN nodes in actual situations, then ∈(p) is closer to 0.

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