Method, device and storage medium for mining key nodes in a directed network

Abstract

The present invention discloses a method, device and storage medium for mining key nodes in a directed network, belonging to the field of network information mining technology. The mining method comprises: decomposing strong connectivity to obtain a strongly connected subgraph with zero in-degree, selecting a node with the smallest in-degree difference and the smallest in-degree from all strongly connected subgraphs with zero in-degree to meet the reachability condition; then using a greedy algorithm to select nodes that are farther away from the key node group and have a smaller in-degree minus out-degree and in-degree from the strongly connected subgraph with the smallest eigenvalue in each cycle and add them to the key node group; that is, using the graph theory of measurement indicators, the shortest path concept and the greedy algorithm to achieve the mining of key nodes in a large-scale directed network. Since key nodes can directly or indirectly affect all other nodes in the network, the stability of the existing complex network node importance evaluation method in the control synchronization and diffusion capabilities of the directed network is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of network information mining, and more specifically, relates to a method, device and storage medium for mining key nodes in a directed network. Background Art

[0002] Mining important information from complex networks is a key issue in complex network analysis. It primarily involves discovering important motifs within a network, such as nodes and edges, to reveal its structural, functional, and other characteristics. This research has broad applications in a variety of fields, including social networks, transportation networks, power grids, structural biology, and complex system control. For example, in social networks, key nodes may be key sources or hubs for information dissemination. By identifying these nodes, we can better understand how information propagates within the network, thereby guiding disease prevention and control, information monitoring, and more. In structural biology, complex networks are used to represent relationships between biomolecules, such as protein interactions and gene regulatory networks. Mining key nodes in these networks can help discover potential genes or proteins, providing important clues for disease treatment and drug development. Overall, research on mining important information from complex networks is of great significance for deepening our understanding of various complex systems and optimizing their performance.

[0003] Currently, some research has been conducted on mining key nodes or node groups in complex networks, such as degree centrality and K-core centrality based on node neighbors, and path-based closeness centrality and betweenness centrality. Although these methods can measure important nodes or node groups from different perspectives, their performance in determining the containment, synchronization, and diffusion capabilities of directed networks is not stable. Summary of the Invention

[0004] In response to the above-mentioned defects or improvement needs of the existing technology, the present invention provides a method, device and storage medium for mining key nodes in a directed network, which aims to solve the technical problem that the existing complex network node importance evaluation method is not stable enough in terms of the restraint synchronization and diffusion capabilities of the directed network.

[0005] To achieve the above object, according to one aspect of the present invention, a method for mining key nodes in a directed network is provided, comprising:

[0006] S1: The graph corresponding to the directed network All nodes with zero in-degree in are added to the critical node group V pin , using the graph Topological structure information and key node group V pin The node selection information constructs the corresponding preset matrix L K ;

[0007] S2: Get the preset matrix L K Relative to the figure Each strongly connected subgraph S in k The corresponding principal submatrix s is the total number of strongly connected subgraphs;

[0008] S3: From s main sub-matrices Find the M principal submatrices whose sum of all matrix elements is 0 Calculate each principal submatrix The corresponding strongly connected subgraph S m The difference between the in-degree and out-degree of each node in; from each strongly connected subgraph S m Find the node with the smallest difference and the smallest in-degree and add it to the key node group V pin And get the current key node group V after adding M nodes pin The corresponding preset matrix L K ;

[0009] S4: Get the current preset matrix L K Relative to the figure Each strongly connected subgraph S in k The principal sub-matrix Find each principal submatrix The minimum eigenvalue of , find the strongly connected subgraph S corresponding to the minimum value from the s minimum eigenvalues p ; In the figure Add node i N+1 And build i N+1 Points to the current critical section

[0010] Point Group V pin The edges of all nodes in the graph are obtained

[0011] S5: Computational Graph Slave node i N+1 To the strongly connected subgraph S p The shortest path of each node c in the node c is used to find multiple nodes i whose shortest paths are greater than the first threshold; the difference between the in-degree and out-degree of each node i is calculated, and multiple nodes whose differences are lower than the second threshold are selected to construct a node set.

[0012] S6: From the node set Select a key node to join the current group V pin , and update the corresponding preset matrix L K ;

[0013] S7: Determine the key node group V obtained in S6 pinIs the total number of nodes in less than the third threshold? If so, return to S4; otherwise, it is considered that the target key node group V is obtained. pin .

[0014] Furthermore, the S1 includes:

[0015] The picture All nodes with zero in-degree in are added to the critical node group V pin ;

[0016] Using the formula L K =L+K builds key node group V pin Corresponding to the preset matrix L K , L is the graph Laplace matrix, K = diag{kδ1, kδ2,…, kδ N}, k is a constant, δ j is the selection information of the jth node. If the jth node is selected, δ j =1, otherwise δ j =0,j∈[1,N].

[0017] Furthermore, the S2 includes:

[0018] In the preset matrix L K Delete the directed network Except for the kth strongly connected subgraph S k The rows and columns corresponding to each node in all other strongly connected subgraphs except s is the total number of strongly connected subgraphs.

[0019] Furthermore, the S3 includes:

[0020] S31: Find the principal submatrix whose sum of all matrix elements is 0 The corresponding strongly connected subgraph S m ;

[0021] S32: For each strongly connected subgraph S m , m=1,2,…,M, calculate S m The difference between the out-degree and in-degree of each node in the node set V is added to the node with the smallest difference. Δ ; If the node set V Δ If there are multiple nodes in the , then select the one with in-degree The smallest arbitrary node is added to the current key node group V pin .

[0022] Furthermore, the S32 further includes:

[0023] If the node set V ΔIf there is only one node in the group, then add the node directly to the key node group V pin .

[0024] Furthermore, the S6 includes:

[0025] S61: Computational Graph Slave node i N+1 To the strongly connected subgraph S p The shortest path to each node c Get satisfaction The nodes are included in the node set V max middle;

[0026] S62: For the node set V max Each node, according to Sort from small to large, and select multiple nodes whose difference values ​​are lower than the second threshold to construct a node set.

[0027] Furthermore, the S62 includes:

[0028] For the node set V max Each node, according to Sort from small to large, if multiple nodes have the same Δd i , then according to Sort from small to large; select the first l c Node Set If V max Insufficient c Nodes

[0029] Furthermore, the S7 includes:

[0030] For the node set Add each of these nodes to V pin , and calculate each new V pin The corresponding strongly connected subgraph S p The principal sub-matrix The minimum eigenvalue of

[0031] All the smallest eigenvalues The largest key node group V pin Considered as the updated key node group V pin , and update the corresponding preset matrix L K .

[0032] According to another aspect of the present invention, there is provided a device for mining key nodes in a directed network, comprising:

[0033] Building module for graph corresponding to directed network All nodes with zero in-degree in are added to the critical node group V pin , using the graph Topological structure information and key node group V pin The node selection information constructs the corresponding preset matrix L K ;

[0034] Acquisition module, used to obtain the preset matrix L K Relative to the figure Each strongly connected subgraph S in k The corresponding principal submatrix s is the total number of strongly connected subgraphs;

[0035] Selection module for selecting from s main sub-matrices Find the M principal submatrices whose sum of all matrix elements is 0 Calculate each principal submatrix The corresponding strongly connected subgraph S m The difference between the in-degree and out-degree of each node in; from each strongly connected subgraph S m Find the node with the smallest difference and the smallest in-degree and add it to the key node group V pin And get the current key node group V after adding M nodes pin The corresponding preset matrix L K ;

[0036] Establish a module to obtain the current preset matrix L K Relative to the figure Each strongly connected subgraph S in k The principal sub-matrix Find each principal submatrix The minimum eigenvalue of , find the strongly connected subgraph S corresponding to the minimum value from the s minimum eigenvalues p ; In the figure Add node i N+1 And build i N+1 Points to the current key node group V pin The edges of all nodes in the graph are obtained

[0037] Computation module, used for computing graphs Slave node i N+1 To the strongly connected subgraph S p The shortest path of each node c in the node c is used to find multiple nodes i whose shortest paths are greater than the first threshold; the difference between the in-degree and out-degree of each node i is calculated, and multiple nodes whose differences are lower than the second threshold are selected to construct a node set.

[0038] Update module for updating the node set Select a key node to join the current group V pin , and update the corresponding preset matrix L K ;

[0039] The judgment module is used to judge the current key node group V pin Is the total number of nodes in the matrix less than the third threshold? If so, the current preset matrix L K Passed to the establishment module, otherwise it is regarded as obtaining the target key node group V pin .

[0040] According to another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of the above method are implemented.

[0041] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0042] (1) This solution provides a method for mining key nodes in a directed network. By strongly connected decomposition, a strongly connected subgraph with zero in-degree is obtained. Nodes with the smallest in-degree minus out-degree and in-degree are selected from all strongly connected subgraphs with zero in-degree to meet the reachability condition. Since the reachability condition is met, it can be guaranteed that the key node group can directly or indirectly affect all other nodes in the network. Then, a greedy algorithm is used to select nodes that are farther away from the key node group and have smaller in-degree minus out-degree and in-degree from the strongly connected subgraph with the smallest eigenvalue in each loop and add them to the key node group. Since only the eigenvalues ​​of the principal submatrix corresponding to the strongly connected subgraph need to be calculated in each loop, the computational complexity can be reduced. At the same time, since a greedy algorithm is used, it can be applied to large-scale complex network application scenarios. In addition, the satisfaction of the reachability condition can also solve the technical problem that the existing complex network node importance evaluation method is not stable in terms of the restraint synchronization and diffusion capabilities of directed networks.

[0043] (2) In this scheme, the formula L is used K =L+K builds key node group V pin Corresponding to the preset matrix L K , considering the directed graph The topology and V pin The node selection information, based on theoretical derivation, can prove that λ1(L K ) can measure the synchronization and diffusion capabilities of the network.

[0044] (3) In this solution, the preset matrix L K Delete the directed network Except for the k-th strongly connected subgraph Sk The rows and columns corresponding to the remaining nodes in the matrix are obtained by We can get each strongly connected subgraph S k The corresponding principal submatrix This method makes the main sub-matrix Carrying strongly connected subgraph S k Path information and preset matrix L K Medium V pin The node selection information of the matrix L K Decompose into multiple low-dimensional sub-matrices, thereby reducing the computational complexity of calculating the matrix eigenvalues.

[0045] (4) In this scheme, if the node set V Δ If there are multiple nodes in the , then select the one with in-degree The smallest arbitrary node is added to the current key node group V pin By selecting the node with the smallest in-degree minus out-degree and the smallest in-degree, it is beneficial to improve λ1(L K ), that is, to improve the synchronization and diffusion capabilities of the network. In addition, considering the scenario where there are multiple nodes with the same minimum in- and out-degree differences, this scheme is more logical and rigorous.

[0046] (5) In this scheme, if the node set V Δ If there is only one node in the i The smallest node is added to the key node group V pin Considering each strongly connected subgraph S m In the common scenario where there is only one node with the minimum in-degree minus out-degree, the computational logic of its execution process is simple.

[0047] (6) This solution finds the way to obtain satisfaction The nodes are included in the node set V max In; Considering the key nodes to the strongly connected subgraph S p The distance information of all nodes in the graph is obtained by selecting nodes with farther distances, thereby reducing the number of key nodes to the strongly connected subgraph S. p The minimum distance between all nodes in .

[0048] (7) In this solution, for the node set V max Each node, according to Sort from small to large, if multiple nodes have the same Δd i , then according to Sort from small to large; select the first l c Node Set If V max Insufficient c Nodes Considering that if V max Insufficientc In the special scenario of each node, this solution is more logical and rigorous.

[0049] (8) This solution targets the node set Add each of these nodes to V pin , and calculate each new V pin The corresponding strongly connected subgraph S p The principal sub-matrix The minimum eigenvalue of Based on graph theory with the help of measurement indicators The theoretically obtained optimization The characteristics of key node groups are used to mine key node groups. Compared with key node mining strategies based on network node importance ranking methods, such as degree centrality, page-rank, betweenness centrality, and closeness centrality, the mined key node groups have better performance in synchronization and propagation in directed networks, and are particularly suitable for selecting key nodes in key control systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Flowchart of the directed network key node mining method based on graph theory provided in Example 1 of the present invention;

[0051] Figure 2 A topological diagram of a directed network and a flow chart of its point selection in Example 1 of the present invention;

[0052] Figure 3 The out-degree algorithm, in-degree algorithm, PageRank, betweenness centrality algorithm, closeness centrality algorithm and the point selection result of the present invention in Example 1 are compared with the measurement index λ1(L K ) below;

[0053] Figure 4 This is a state error curve diagram of five pinning nodes selected by different point selection algorithms and applied to the pinning control system in Example 1 of the present invention;

[0054] Figure 5 This is a topological structure diagram of the real directed network physicians in Example 2 of the present invention, in which the number of nodes is 117 and the number of directed edges is 542;

[0055] Figure 6 This is a comparison chart of the super-spreader's influence in Example 2 of the present invention, where p is the ratio of infected nodes to total nodes, and the experimental results are the average of 50 experiments;

[0056] Figure 7The results of point selection in different point selection algorithms for the directed network Edinburgh Associative Thesaurus in Example 3 of the present invention are shown, where the index λ1 (L K ) where k=5;

[0057] Figure 8 The results of the point selection of the directed network NewYork City under different point selection algorithms in Example 3 of the present invention are shown, where the synchronization capability measurement index λ1 (L K ) where k=5. DETAILED DESCRIPTION

[0058] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the figures and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0059] Example 1

[0060] like Figure 1 As shown, this embodiment provides a method for mining key nodes in a directed network, including the following steps.

[0061] S1: Add all nodes with zero in-degree in the directed network to the key node group V pin , and according to the key node group V pin Get a directed network The preset matrix L K , L K =L+K, L is the Laplace matrix of the directed network, K=diag{kδ1,kδ2,…,kδ N}, k is a constant, δ j is the selection information of the jth node. If the jth node is selected, δ j =1, otherwise δ j =0,j∈[1,N].

[0062] S2: Get all strongly connected subgraphs S of the directed network k , k=1,2,…,s; s is the total number of strongly connected subgraphs; get each strongly connected subgraph S k The corresponding preset matrix L K The principal sub-matrix To delete the matrix L K The matrix obtained by the rows and columns corresponding to the node i, are all nodes in the directed network, is the kth strongly connected subgraph S k Nodes in .

[0063] S3: From s main sub-matrices Find the M principal submatrices whose sum of all matrix elements is 0 Calculate each principal submatrix The corresponding strongly connected subgraph S m The difference between the in-degree and out-degree of each node in; from each strongly connected subgraph S m Find the node with the smallest difference and the smallest in-degree and add it to the key node group V pin And get the current key node group V after adding M nodes pin The corresponding preset matrix L K ;

[0064] S4: Get each strongly connected subgraph S k The corresponding current preset matrix L K ′'s principal submatrix From each master matrix Find the smallest eigenvalue among the eigenvalues ​​of , k = 1, 2, ..., s; find each principal submatrix The minimum eigenvalue of , find the strongly connected subgraph S corresponding to the minimum value from the S minimum eigenvalues p , although the matrix L K as well as Asymmetric, but the smallest eigenvalue can be proven is a real number; in a directed network Add a node i N+1 and with the current key node group V pin All nodes in the network establish edges, and the direction is determined by node i N+1 Point to the nodes in the key node group to form a graph

[0065] S5: Computational Graph Slave node i N+1 To the strongly connected subgraph S p The shortest path to each node c and get satisfaction The node set V max ; For node set V max ,according to Sort from small to large, if multiple nodes have the same Δd i , then according to Sort from small to large; select the first l c nodes, forming a node set If V max Insufficient c Nodes

[0066] S6: For node sets Add each of these nodes to V pin , and calculate each new V pin The corresponding strongly connected subgraph S p The principal sub-matrix The minimum eigenvalue of Each new V pin The key node group V corresponding to the largest one among the corresponding minimum eigenvalues pin Considered as the updated key node group V pin , and update the matrix L K .

[0067] S7: Check the key node group V updated in S6 pin Is the number of nodes in less than l? If so, return to S3, otherwise end the loop to obtain the target key node group V pin .

[0068] The present invention provides a method for mining key nodes in directed networks, which uses the graph theory of measurement indicators and integrates the shortest path idea and greedy algorithm to complete the task of mining key nodes in large-scale directed networks.

[0069] Below is Figure 2 As shown, the directed network 1 with 11 nodes and 14 directed edges is the bottom information interaction topology of the control system. The task of selecting the controlled node set in the control system is completed. The specific process includes the following steps.

[0070] First: Refer to Figure 2 As shown, the underlying directed network topology for containment control Use graph partitioning method to obtain the basic pinning node set V pin .

[0071] S1: The picture All zero-indegree nodes in are added to the pinning node set V pin , and according to V pin Update matrix L K At this time, V pin ={10}.

[0072] S2: Get the graph All strongly connected subgraphs S in k , and corresponding to the matrix L K The principal sub-matrix And for each k=1,2,…,s, calculate Among them, in the preset matrix L K Delete the directed network Except for the kth strongly connected subgraph S k The rows and columns corresponding to each node in all other strongly connected subgraphs except s is the total number of strongly connected subgraphs.

[0073]

[0074] S3: For each A strongly connected subgraph S k , get S k middle Minimum node set V Δ In this embodiment, only V Δ ={4}. Since the node set V Δ There is only one node in , so add it to the pinning node set. pin ={10,4}. Based on V pin ={10,4} Update matrix L K .

[0075] Then, refer to Figure 2 As shown, in the pinning node set V pin ={10,4}, based on the shortest path principle and graph theory, a greedy algorithm is used to gradually obtain key node groups with more nodes.

[0076] S4: Calculate the principal submatrix The minimum eigenvalue of In this embodiment Get the strongly connected subgraph S p , where S p satisfy In the figure Add a node i N+1 and with key node group V pin All nodes in the network establish edges, and the direction is determined by node i N+1 Point to the nodes in the key node group to form a graph

[0077] S5: Computational Graph Slave node i N+1 The shortest path to node i And get satisfaction The node set V max For the node set V max ,according to Sort from small to large, if multiple nodes have the same Δd i, then according to Sort from small to large. Select the first l c >0 nodes, forming a node set If V max Insufficient c Nodes In this embodiment, select 1 c =5.

[0078] S6: For node sets Add each of these nodes to V pin and calculate Get A key node group V with the maximum value pin , and update the matrix L K .

[0079] S7: Check key node group V pin Is the number of nodes in less than l? If so, return to S4, otherwise end the loop and get the restraining node set V pin In this embodiment, l=5. The point selection results are shown in Table 1, where the measurement index λ1(L K ) where k=5.

[0080] Table 1 Point selection results of directed network 1

[0081]

[0082] Furthermore, the selected pinning node set V pin Applicable to the following pinning control system configured in a directed network 1: Where i = 1, 2, ..., N, in this embodiment N = 11, vector is the state vector of the i-th node; parameter c = 5 is the coupling strength of the network; u i =ck(x i -s) is a linear feedback controller, k = 5, when i∈V pin When δ i =1, otherwise δ i =0; f(·): is the nonlinear self-dynamics of node i. In this embodiment, the following third-order Chua system is considered:

[0083]

[0084] Among them, γ=10, ε=14.87, a=-1.27, b=-0.68.

[0085] The desired target trajectory is the solution of the following isolated nodes: s(0)=s0, where the initial state of the desired target trajectory is s0=(1,0.15,0) T .

[0086] Figure 3 It shows that the key node mining method in this invention can obtain a larger λ1(L K ). Figure 4 It is verified that the present invention can be applied to the selection of the control node set in the directed network control, and can obtain a faster control synchronization effect. Figure 4 (a) is the state error curve under the point selection result of the present invention, Figure 4 (b) - The state error curve under the point selection result of the in-degree algorithm, Figure 4 (c) - State error curve under the point selection result of the close centrality algorithm.

[0087] Example 2

[0088] This invention can also be applied to discovering super-spreaders in complex networks for disease prevention and control. Specifically, in this embodiment, the invention combines the SIR infectious disease model to discover super-spreaders in disease transmission networks. Nodes are individuals, edges are contacts between individuals, and the key nodes ultimately identified are super-spreading individuals.

[0089] The SIR model assumes that nodes in a network have three states: susceptible (S), infected (I), and recovered (R). Within a unit of time, when a susceptible state S comes into contact with an infected state I (there is a directed edge from infected state I to susceptible state S), it will change to infected state I with probability β. An infected state S will change to immune state R with probability γ. The immune state will no longer be infected.

[0090] This embodiment uses Figure 5 The real directed network physicians is the contact relationship network between individuals, and the key node group mining algorithm in the present invention is used (l c =20, l=15, k=5), completing the excavation of super spreaders.

[0091] In the SIR model, let the infection rate β = 0.3, the immunity rate γ = 0.15, the super spreader be in the initial infected state I, and the remaining nodes be in the susceptible state S. The transmission ability of the super spreader is verified by the ratio of infected nodes to total nodes in the network at each time step.

[0092] Figure 6It shows that the super spreaders obtained by the present invention have a faster spread speed and a wider spread range than the out-degree algorithm, PageRank, betweenness centrality algorithm and closeness centrality algorithm, and have obvious beneficial effects.

[0093] Example 3

[0094] This embodiment uses two real-world directed networks, as shown in Table 2, to further verify that the key node group mining method in the present invention can be applied to large-scale directed networks. c =1 to increase the calculation speed. K ) can effectively measure the restraint synchronization capability of the key node group, so λ1(L K ) to measure the quality of site selection. The Edinburgh Associative Thesaurus refers to the Edinburgh Associative Dictionary. Nodes represent English words, and directed links from A to B indicate that in user experiments, when stimulus word A is given, word B is given as the response. New York City: Directed road network data from the 9th IMACS Implementation Challenge in New York City, with nodes as points and edges as roads.

[0095] Table 2 Directed network statistics

[0096]

[0097]

[0098] In this embodiment, when the out-degree algorithm, PageRank, close centrality algorithm, etc. are used for key node group mining, it is difficult to ensure the measurement index λ1(L K )>0, so this embodiment uses the out-degree algorithm, in-degree algorithm, PageRank, betweenness centrality algorithm and closeness centrality algorithm to further mine the key node group based on the basic key node group obtained by the graph partitioning algorithm. Figure 7 and Figure 8 The results show that the key node group mining method of the present invention can be effectively applied to directed networks with tens of thousands of nodes, and compared with the out-degree algorithm, in-degree algorithm, PageRank, betweenness centrality algorithm and closeness centrality algorithm, it has a better performance in terms of the measurement index λ1(L K ), has certain beneficial effects.

[0099] Example 4

[0100] The directed network in this embodiment refers to the power grid, where the nodes are power plants, substations and load centers, the edges are power transmission lines, and the key nodes finally obtained refer to the key nodes in the power grid risk assessment.

[0101] Example 5

[0102] The directed network in this embodiment refers to a structural biology network, which is used to represent the relationship between biological molecules such as protein interactions and gene regulatory networks. The nodes are biological macromolecules, the edges are the interactions between biological macromolecules, and the key nodes finally obtained refer to the central position of biological signal transduction.

[0103] Example 6

[0104] The directed network in this embodiment refers to a transportation network, where the nodes are intersections or transition locations in the network, the edges are roads between nodes, and the key nodes ultimately obtained refer to key transportation hubs.

[0105] Example 7

[0106] This embodiment provides a device for mining key nodes in a directed network, including: a construction module, an acquisition module, a selection module, an establishment module, a calculation module, an update module and a judgment module.

[0107] Building module for graph corresponding to directed network All nodes with zero in-degree in are added to the critical node group V pin , using the graph Topological structure information and key node group V pin The node selection information constructs the corresponding preset matrix L K .

[0108] Acquisition module, used to obtain the preset matrix L K Relative to the figure Each strongly connected subgraph S in k The corresponding principal submatrix s is the total number of strongly connected subgraphs.

[0109] Selection module for selecting from s main sub-matrices Find the M principal submatrices whose sum of all matrix elements is 0 Calculate each principal submatrix The corresponding strongly connected subgraph S m The difference between the in-degree and out-degree of each node in; from each strongly connected subgraph S m Find the node with the smallest difference and the smallest in-degree and add it to the key node group V pin and obtain the current key node group V pin The corresponding preset matrix L K .

[0110] Establish a module to obtain the current preset matrix L K Relative to the figure Each strongly connected subgraph S in kThe principal sub-matrix Find each principal submatrix The minimum eigenvalue of , find the strongly connected subgraph S corresponding to the minimum value from the s minimum eigenvalues p ; In the figure Add node i N+1 And build i N+1 Points to the current key node group V pin The edges of all nodes in the graph are obtained

[0111] Computation module, used for computing graphs Slave node i N+1 To the strongly connected subgraph S p The shortest path of each node c in the node c is obtained, and multiple nodes i whose shortest paths are greater than the first threshold are found. The difference between the in-degree and out-degree of each node i is calculated, and multiple nodes whose difference is lower than the second threshold are selected to construct a node set.

[0112] Update module for slave node sets Select a key node to join the current group V pin , and update the corresponding preset matrix L K .

[0113] The judgment module is used to judge the current key node group V pin Is the total number of nodes in the matrix less than the third threshold? If so, the current preset matrix L K Pass it to the establishment module, otherwise it is regarded as obtaining the target key node group V pin .

[0114] Example 8

[0115] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the method described above are implemented.

[0116] Those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of protection of the present invention, the present invention is also intended to include these modifications and variations.

Claims

1. A method for mining key nodes in a power grid, characterized in that: include: S1: The corresponding diagram of the power grid All nodes with zero in-degree in are added to the critical node group V pin , using the graph Topological structure information and key node group V pin The node selection information constructs the corresponding preset matrix L K ;Nodes are power plants, substations and load centers; S2: Get the preset matrix L K Relative to the figure Each strongly connected subgraph S in k The corresponding principal submatrix k=1,2,…,s; s is the total number of strongly connected subgraphs; S3: From s main sub-matrices Find the M principal submatrices whose sum of all matrix elements is 0 Calculate each principal submatrix The corresponding strongly connected subgraph S m The difference between the in-degree and out-degree of each node in; from each strongly connected subgraph S m Find the node with the smallest difference and the smallest in-degree and add it to the key node group V pin And get the current key node group V after adding M nodes pin The corresponding preset matrix L K ; S4: Get the current preset matrix L K Relative to the figure Each strongly connected subgraph S in k The principal sub-matrix Find each principal submatrix The minimum eigenvalue of , find the strongly connected subgraph S corresponding to the minimum value from the s minimum eigenvalues p ; In the figure Add node i N+1 And build i N+1 Points to the current key node group V pin The edges of all nodes in the graph are used to represent the power transmission lines, and the graph is obtained. S5: Computational Graph Slave node i N+1 To the strongly connected subgraph S p The shortest path of each node c in , find multiple nodes i whose shortest paths are greater than the first threshold; Calculate the difference between the in-degree and out-degree of each node i, and select multiple nodes whose difference is lower than the second threshold to construct a node set S6: From the node set Select a key node to join the current group V pin , and update the corresponding preset matrix L K ; S7: Determine the key node group V obtained in S6 pin Is the total number of nodes in less than the third threshold? If so, return to S4. Otherwise, it is considered that the target key node group V consisting of the key nodes in the power grid risk assessment is obtained. pin .

2. The method for mining key nodes in a power grid according to claim 1, characterized in that: Said S1 comprises: The picture All nodes with zero in-degree in are added to the critical node group V pin ; Using the formula L K =L+K builds key node group V pin Corresponding to the preset matrix L K , L is the graph Laplace matrix, K = diag{kδ1, kδ2,…, kδ N }, k is a constant, δ j is the selection information of the jth node. If the jth node is selected, then δ j =1, otherwise δ j =0,j∈[1,N].

3. The method for mining key nodes in a power grid according to claim 1, wherein: The S2 includes: In the preset matrix L K Delete the power grid Except for the kth strongly connected subgraph S k The rows and columns corresponding to each node in all other strongly connected subgraphs except 4. The method for mining key nodes in a power grid according to claim 1, wherein: The S3 includes: S31: Find the principal submatrix whose sum of all matrix elements is 0 The corresponding strongly connected subgraph S m ; S32: For each strongly connected subgraph S m , m=1,2,…,M, calculate S m The difference between the out-degree and in-degree of each node in the node set V is added to the node with the smallest difference. Δ ; If the node set V Δ If there are multiple nodes in the , then select the one with in-degree The smallest arbitrary node is added to the current key node group V pin .

5. The method for mining key nodes in a power grid according to claim 4, characterized in that: The S32 further includes: If the node set V Δ If there is only one node in the group, then add the node directly to the key node group V pin .

6. The method for mining key nodes in a power grid according to claim 1, characterized in that: The S6 includes: S61: Computational Graph Slave node i N+1 To the strongly connected subgraph S p The shortest path to each node c Get satisfaction The nodes are included in the node set V max middle; S62: For the node set V max Each node, according to Sort from small to large, and select multiple nodes whose difference values ​​are lower than the second threshold to construct a node set.

7. The method for mining key nodes in a power grid according to claim 6, characterized in that: The S62 includes: For the node set V max Each node, according to Sort from small to large, if multiple nodes have the same Δd i , then according to Sort from small to large; select the first l c Node Set If V max Insufficient c Nodes 8. The method for mining key nodes in a power grid according to any one of claims 1 to 7, characterized in that: The S7 includes: For the node set Add each of these nodes to V pin , and calculate each new V pin The corresponding strongly connected subgraph S p The principal sub-matrix The minimum eigenvalue of All the smallest eigenvalues The largest key node group V pin Considered as the updated key node group V pin , and update the corresponding preset matrix L K .

9. A device for mining key nodes in a power grid, characterized in that: include: Building module for mapping the grid to the All nodes with zero in-degree in are added to the critical node group V pin , using the graph Topological structure information and key node group V pin The node selection information constructs the corresponding preset matrix L K ; Acquisition module, used to obtain the preset matrix L K Relative to the figure Each strongly connected subgraph S in k The corresponding principal submatrix k=1,2,…,s; s is the total number of strongly connected subgraphs; Selection module for selecting from s main sub-matrices Find the M principal submatrices whose sum of all matrix elements is 0 Calculate each principal submatrix The corresponding strongly connected subgraph S m The difference between the in-degree and out-degree of each node in; from each strongly connected subgraph S m Find the node with the smallest difference and the smallest in-degree and add it to the key node group V pin And get the current key node group V after adding M nodes pin The corresponding preset matrix L K ; Establish a module to obtain the current preset matrix L K Relative to the figure Each strongly connected subgraph S in k The principal sub-matrix Find each principal submatrix The minimum eigenvalue of , find the strongly connected subgraph S corresponding to the minimum value from the s minimum eigenvalues p ; In the figure Add node i N+1 And build i N+1 Points to the current key node group V pin The power transmission lines of all nodes in the graph are obtained. Computation module, used for computing graphs Slave node i N+1 To the strongly connected subgraph S p The shortest path of each node c in , find multiple nodes i whose shortest paths are greater than the first threshold; Calculate the difference between the in-degree and out-degree of each node i, and select multiple nodes whose difference is lower than the second threshold to construct a node set Update module for updating the node set Select a key node to join the current group V pin , and update the corresponding preset matrix L K ; The judgment module is used to judge the current key node group V pin Is the total number of nodes in the matrix less than the third threshold? If so, the current preset matrix L K The result is transmitted to the establishment module, otherwise it is regarded as obtaining the target key node group V of the key nodes in the power grid risk assessment. pin .

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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