A method and apparatus for identifying key network nodes

Abstract

This invention discloses a method and apparatus for identifying key nodes in a network. The method includes: S1, acquiring a target network; S2, performing phantom decomposition on the target network to obtain N sub-phantoms and corresponding category values; S3, processing the N sub-phantoms and corresponding category values ​​to obtain K sets of statistical vectors and P category matrices; S4, performing spectral analysis on the P category matrices to obtain P influence vectors; S5, using a criticality calculation model to process the K sets of statistical vectors and the P influence vectors to obtain K criticality values. This invention can improve the accuracy of key node identification and enhance adaptability to dynamic networks.

Description

Technical Field

[0001] This invention belongs to the field of network critical node identification technology, specifically a method and apparatus for identifying network critical nodes. Background Technology

[0002] In modern information network architectures, network structures such as command and control networks, sensor networks, and communication support networks are characterized by dynamic heterogeneity, strong adversarial nature, and drastic load fluctuations. Evaluating the centrality of nodes in these networks and identifying critical nodes helps in a deeper understanding of the network's structure and function. In complex networks, nodes with high centrality often occupy key positions in information transmission and resource flow. By quantitatively analyzing indicators such as degree centrality, betweenness centrality, and proximity centrality, it is possible to accurately locate nodes that play a decisive role in network connectivity and stability. Furthermore, identifying critical nodes based on their centrality levels can provide decision support for network optimization and risk prevention. Once critical nodes are identified, on the one hand, their operational efficiency can be prioritized during resource allocation, such as increasing bandwidth investment for base stations with high centrality to improve overall communication quality; on the other hand, protection strategies can be developed in advance for critical nodes to prevent network paralysis due to the failure of a few nodes.

[0003] However, traditional centrality (such as degree centrality, betweenness centrality, and proximity centrality) only focuses on the number of a node's direct neighbors, ignoring the differences in a node's role within a repeating subgraph (motif). It fails to reflect higher-order characteristics of nodes; for example, nodes with the same number of neighbors may provide drastically different support for motif functionality. Furthermore, traditional centrality is not sensitive enough to the dynamic evolution of network structures. For instance, in dynamic networks, the incorporation of new nodes and the failure of old nodes may create or destroy multiple motifs with different functions, while the number of neighbors of their direct neighbors may not change significantly.

[0004] Therefore, key nodes identified based on traditional centrality cannot accurately reflect the higher-order characteristics of the network and are difficult to apply to rapidly changing dynamic networks. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method and apparatus for identifying key network nodes, which can improve the accuracy of key node identification and enhance the adaptability to dynamic networks.

[0006] To address the aforementioned technical problems, this invention discloses a method for identifying key network nodes, the method comprising:

[0007] S1. Obtain the target network; the target network includes K nodes and several directed edges;

[0008] S2. Perform motif decomposition on the target network to obtain N sub-motifs and their corresponding category values;

[0009] The sub-module includes a node number sequence and a sub-adjacency matrix; the sub-modules with the same category value have completely identical sub-adjacency matrices.

[0010] The node numbering sequence includes M number values; the sub-adjacency matrix is ​​an M-order square matrix;

[0011] The category value is an integer from 1 to P;

[0012] K, N, P, and M are all integers greater than 1;

[0013] S3. Process the N sub-modalities and their corresponding category values ​​to obtain K sets of statistical vectors and P category matrices;

[0014] The set of statistical vectors includes P statistical vectors; each statistical vector includes M components.

[0015] S4. Perform spectral analysis on the P category matrices to obtain P influence vectors; each influence vector includes M components.

[0016] S5. Using the criticality calculation model, process the K sets of statistical vectors and the P vectors of influence to obtain K criticality values.

[0017] As an optional implementation, in the first aspect of the present invention, processing the N sub-motifs and their corresponding category values ​​to obtain K sets of statistical vectors and P category matrices includes:

[0018] S31. Based on the corresponding category value, divide the N sub-motifs into P motif subsets; each motif subset includes several sub-motifs.

[0019] S32. Based on each of the P subsets of the aforementioned modalities, construct P numbering matrices respectively;

[0020] S33. Process the P numbering matrices to obtain the K statistical vector sets;

[0021] S34. From the P subsets of the motifs, extract any one of the sub-motifs to obtain P representative motifs; set the P category matrices as the sub-adjacency matrices of the P representative motifs.

[0022] As an optional implementation, in the first aspect of the present invention, the step of performing spectral analysis on the P category matrices to obtain P influence vectors includes:

[0023] S41. Process each of the P category matrices to obtain a set of P feature pairs;

[0024] The feature pair set includes M feature pairs; each feature pair includes a feature value and a feature vector.

[0025] S42. Perform principal feature analysis on each set of feature pairs to obtain the principal feature pairs corresponding to each set of feature pairs.

[0026] The principal feature pair includes principal feature values ​​and principal feature vectors;

[0027] S43. Process each of the P main feature pairs to obtain P influence vectors.

[0028] As an optional implementation, in the first aspect of the present invention, the step of processing the P category matrices to obtain a set of P feature pairs includes:

[0029] S411. Calculate the sum of all column vectors of each category matrix to obtain P first vectors;

[0030] S412. Calculate the sum of all row vectors of each category matrix to obtain P second vectors;

[0031] S413. Based on the feature matrix calculation model, P first vectors, P second vectors and P category matrices are processed to obtain P feature matrices;

[0032] The feature matrix calculation model is as follows:

[0033]

[0034] DA j =diag(α) j )

[0035]

[0036] In the formula, L j Let I be the j-th characteristic matrix, where j is an integer from 1 to P; I is an M-order identity matrix; AM j Let α be the category matrix for the j-th category; j and β j These are the j-th first vector and the second vector, respectively;

[0037] S414. Perform eigenvalue decomposition on each feature matrix to obtain M feature pairs corresponding to each feature matrix;

[0038] The M feature pairs corresponding to each feature matrix constitute the feature pair set corresponding to each feature matrix.

[0039] As an optional implementation, in the first aspect of the present invention, the step of performing principal feature analysis on each of the feature pair sets to obtain the principal feature pairs corresponding to each feature pair set includes:

[0040] S421. Determine whether all M feature values ​​in the feature pair set are equal to obtain the feature judgment result;

[0041] If the feature determination result is yes, execute S422;

[0042] If the feature determination result is negative, execute S423;

[0043] S422. Set the principal feature vector as the mean of the M feature vectors in the feature pair set; set the principal feature value as the modulus of any feature value in the feature pair set; execute S43;

[0044] S423. Set the main feature value to the smallest non-zero value among the moduli of the M feature values;

[0045] S424. Set the main feature vector as the mean of the feature vectors corresponding to all feature values ​​whose magnitudes are equal to the main feature value among the M feature values.

[0046] As an optional implementation, in the first aspect of the present invention, the step of processing the P pairs of principal features to obtain the P influence vectors includes:

[0047] S431. Take the reciprocal of the main feature vectors of each of the P main feature pairs to obtain P intermediate vectors;

[0048] S432. Multiply each of the P intermediate vectors by its corresponding principal feature value to obtain the P influence vectors.

[0049] As an optional implementation, in the first aspect of the present invention, the expression of the key calculation model is:

[0050]

[0051] In the formula, MSC k The key value corresponding to the k-th node of the target network, where k is an integer from 1 to K; n k,j,i S represents the i-th component of the j-th statistical vector in the k-th set of statistical vectors, where j is an integer from 1 to P and i is an integer from 1 to M;j,i Let i be the i-th component of the j-th influence vector.

[0052] A second aspect of this invention discloses a network key node identification device, the device comprising a network acquisition module, a network decomposition module, a statistics module, a spectrum analysis module, and a key node calculation module;

[0053] The network acquisition module is used to acquire the target network;

[0054] The network decomposition module is used to perform motif decomposition processing on the target network to obtain N sub-motifs and their corresponding category values.

[0055] The statistical module is used to process the N sub-modules and their corresponding category values ​​to obtain K sets of statistical vectors and P category matrices;

[0056] The spectral analysis module is used to perform spectral analysis on the P category matrices to obtain P influence vectors.

[0057] The criticality calculation module is used to process the K sets of statistical vectors and the P vectors of influence using a criticality calculation model to obtain K criticality values.

[0058] A third aspect of this invention discloses another network critical node identification device, the device comprising:

[0059] Memory containing executable program code;

[0060] A processor coupled to the memory;

[0061] The processor calls the executable program code stored in the memory to execute some or all of the steps in the network key node identification method disclosed in the first aspect of the present invention.

[0062] The fourth aspect of the present invention discloses a computer storage medium storing computer instructions, which, when invoked, are used to execute some or all of the steps in the network key node identification method disclosed in the first aspect of the present invention.

[0063] Compared with the prior art, the embodiments of the present invention have the following beneficial effects:

[0064] This invention decomposes the target network to obtain a series of sub-motifs and corresponding category values, and further obtains the critical value of each node through statistical processing, spectral analysis and criticality calculation. It can accurately identify the critical value of each node from the perspective of high-order structure and functional modules, avoid over-reliance on the local connection of nodes, and improve the adaptability to dynamic networks. Attached Figure Description

[0065] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0066] Figure 1 This is a flowchart illustrating a method for identifying key network nodes disclosed in an embodiment of the present invention.

[0067] Figure 2 This is a schematic diagram of the phantom decomposition of a network key node identification method disclosed in an embodiment of the present invention.

[0068] Figure 3 This is a schematic diagram of the structure of a network key node identification device disclosed in an embodiment of the present invention.

[0069] Figure 4 This is a schematic diagram of another network key node identification device disclosed in an embodiment of the present invention. Detailed Implementation

[0070] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0072] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0073] Example 1

[0074] Please see Figure 1 and Figure 2 . Figure 1 This is a flowchart illustrating a method for identifying key network nodes disclosed in an embodiment of the present invention. Figure 2 This is a schematic diagram of the phantom decomposition of a network key node identification method disclosed in an embodiment of the present invention. Figure 1 The described network critical node identification method is applied to the identification of critical nodes in networks, such as command and control networks, sensor networks, and satellite communication networks. This invention does not limit the scope of the application. Figure 1 As shown, the method includes:

[0075] S1. Obtain the target network; the target network includes K nodes and several directed edges.

[0076] It should be noted that the target network mentioned above can be a command and control network, a sensor network, or a satellite communication network, and the embodiments of the present invention are not limited thereto.

[0077] S2. Perform motif decomposition on the target network to obtain N sub-motifs and their corresponding category values.

[0078] It should be noted that the above-mentioned motif decomposition process can employ algorithms such as ESU, Grochow-Kellis, and Mfinder, and this embodiment of the invention is not limited thereto. Decomposing the target network into a series of sub-motifs, where each sub-motif is a basic structural unit with clearly defined functional attributes, such as a data transmission motif or a routing control motif, helps to understand how the target network achieves core functions such as information interaction and resource allocation as a whole, avoiding analytical difficulties caused by the large scale of the target network.

[0079] It should be noted that the above category values ​​correspond one-to-one with the sub-motifs, and are used to describe the category to which the corresponding sub-motif belongs.

[0080] The aforementioned sub-modules include a node number sequence and a sub-adjacency matrix; for the aforementioned sub-modules with the same category value, the aforementioned sub-adjacency matrices are completely identical.

[0081] The above node numbering sequence includes M number values; the above sub-adjacency matrix is ​​an M-order square matrix.

[0082] The above category values ​​are integers from 1 to P.

[0083] K, N, P, and M are all integers greater than 1.

[0084] It should be noted that each sub-module is a sub-network of the target network containing M nodes. The i-th node number in the node numbering sequence of each sub-module represents the node number of the i-th node of that sub-module in the target network, where i is an integer from 1 to M. The sub-adjacency matrix of each sub-module describes the local adjacency relationships of the M nodes of that sub-module, and the element value in its jj-th row and kk-th column is equal to the f-value of the adjacency matrix of the target network. jj line f kk The element values ​​of the column, where f jj and f kk These are the jj-th and kk-th node numbers in the node numbering sequence of this sub-module, respectively.

[0085] S3. Process the N sub-modalities and their corresponding category values ​​to obtain K sets of statistical vectors and P category matrices.

[0086] The above set of statistical vectors includes P statistical vectors; the above statistical vectors include M components.

[0087] S4. Perform spectral analysis on the P category matrices to obtain P influence vectors; each influence vector has M components.

[0088] S5. Using the criticality calculation model, process the K sets of statistical vectors and P vectors of influence mentioned above to obtain K criticality values.

[0089] It should be noted that the K criticality values ​​reflect the criticality of the K nodes in the target network. The higher the criticality value, the more critical the corresponding node is in the target network.

[0090] Taking M equals 3 as an example, such as Figure 2 As shown, the target network on the left undergoes motif decomposition, resulting in 13 different ternary sub-motifs M1-M13 with varying connection patterns (each sub-motif has only one instance), i.e., P equals 13. The detailed structure and positional relationships of each sub-motif are shown on the right. In the right-hand diagram, the internal node positional relationships of each sub-motif are represented by labels on the right side of the sub-motif. For example, nodes 1, 2, and 3 of sub-motif M1 are labeled L1, L2, and L1, respectively, indicating that the positions of nodes 1 and 3 are symmetrical. Furthermore, since there are 13 types of sub-motifs, there are 13 different sub-adjacency matrices.

[0091] In an optional embodiment, the above processing of the N sub-motifs and their corresponding category values ​​yields K sets of statistical vectors and P category matrices, including:

[0092] S31. Based on the corresponding category values ​​mentioned above, divide the N sub-motifs into P motif subsets; each motif subset includes several of the aforementioned sub-motifs.

[0093] It should be noted that sub-motifs within the same motif subset have the same category value, while sub-motifs within different motif subsets have different category values.

[0094] S32. Based on the P subsets of the above-mentioned modalities, construct P numbering matrices respectively.

[0095] Optionally, the node number sequence of all sub-motifs in each motif subset can be used as a row vector and concatenated sequentially to obtain a numbering matrix.

[0096] S33. Process the P numbered matrices to obtain the K statistical vector sets.

[0097] S34. From the P subsets of the above-mentioned motifs, extract any of the above-mentioned sub-motifs to obtain P representative motifs; set the P above-mentioned category matrices as the above-mentioned sub-adjacency matrices of the P above-mentioned representative motifs.

[0098] It should be noted that the Pth category matrix mentioned above corresponds to each of the P sub-models.

[0099] In another optional embodiment, the above processing of the P numbering matrices yields the K sets of statistical vectors, including:

[0100] S331 initializes the loop count ic to 1.

[0101] S332. Initialize the P statistical matrices into the P numbered matrices mentioned above.

[0102] S333. Replace all elements not equal to ic in the P statistical matrices above with 0, and replace all elements equal to ic with 1.

[0103] S334. Compress and sum the P statistical matrices mentioned above to obtain P statistical vectors; the P statistical vectors mentioned above constitute the set of the i-th statistical vector.

[0104] Optionally, the above compression and summation process involves calculating the sum of all row vectors of the corresponding statistical matrix to obtain the corresponding statistical vector.

[0105] It should be noted that the m-th component of each of the above statistical vectors represents the number of times that the m-th component of the node number sequence of the corresponding motif subset is equal to ic, where m is an integer from 1 to M.

[0106] S335, Increment the value of ic by 1.

[0107] S336. Repeat S332 to S335 until ic is greater than K, to obtain a set of K statistical vectors.

[0108] It can be seen that the P statistical vectors in the above set of K statistical vectors can represent the number of times each node position of the K nodes of the target network appears in the P sub-modules obtained after the module decomposition.

[0109] In another optional embodiment, the above-described spectral analysis of the P category matrices yields P influence vectors, including:

[0110] S41. Process each of the P category matrices to obtain a set of P feature pairs.

[0111] The aforementioned feature pair set includes M feature pairs; each feature pair includes an eigenvalue and an eigenvector.

[0112] S42. Perform principal feature analysis on each of the above feature pair sets to obtain the principal feature pairs corresponding to each of the above feature pair sets.

[0113] The aforementioned principal feature pairs include principal feature values ​​and principal feature vectors.

[0114] S43. Process each of the P main feature pairs mentioned above to obtain P influence vectors mentioned above.

[0115] It should be noted that the M components of the P influence vectors represent the influence of the M node positions of the P sub-motifs. Furthermore, the P influence vectors represent the influence of the spectrum corresponding to the P sub-motifs.

[0116] In another optional embodiment, the above processing is performed on each of the P category matrices to obtain a set of P feature pairs, including:

[0117] S411. Calculate the sum of all column vectors of each of the above category matrices to obtain P first vectors.

[0118] S412. Calculate the sum of all row vectors of each of the above category matrices to obtain P second vectors.

[0119] S413. Based on the feature matrix calculation model, process the P first vectors, P second vectors and P category matrices mentioned above to obtain P feature matrices.

[0120] The above feature matrix calculation model is as follows:

[0121]

[0122] DA j =diag(α) j )

[0123]

[0124] In the formula, L j Let I be the j-th characteristic matrix mentioned above, where j is an integer from 1 to P; I is an M-order identity matrix; AM j Let α be the j-th category matrix above; j and β j These are the j-th first vector and the j-th second vector mentioned above, respectively.

[0125] S414. Perform eigenvalue decomposition on each of the above feature matrices to obtain M feature pairs corresponding to each of the above feature matrices.

[0126] It should be noted that eigenvalue decomposition is performed on each feature matrix to obtain M eigenvalues ​​and M corresponding eigenvectors, where each eigenvalue and its corresponding eigenvector constitute a feature pair of the feature matrix.

[0127] The M feature pairs corresponding to each of the above feature matrices constitute the feature pair set corresponding to each of the above feature matrices.

[0128] In another optional embodiment, the principal feature analysis is performed on each of the P sets of the above feature pairs to obtain P principal feature pairs, including:

[0129] S421. Determine whether all M feature values ​​in the feature pair set are equal, and obtain the feature judgment result;

[0130] If the above feature judgment result is yes, execute S422;

[0131] If the above feature judgment result is negative, execute S423.

[0132] S422. Set the aforementioned principal feature vector to the mean of the M feature vectors in the aforementioned feature pair set; set the aforementioned principal feature value to the modulus of any of the aforementioned feature values ​​in the aforementioned feature pair set; execute S43.

[0133] S423. Set the above principal feature value to the smallest non-zero value among the moduli of the M feature values.

[0134] S424. Set the aforementioned principal feature vector as the mean of the feature vectors corresponding to all the aforementioned feature values ​​whose magnitudes are equal to the aforementioned principal feature values ​​among the M aforementioned feature values.

[0135] It should be noted that the above eigenvalues ​​can be real or complex numbers. When they are real numbers, the modulus is their absolute value.

[0136] It should be noted that the eigenvector corresponding to the aforementioned eigenvalue refers to the eigenvector that belongs to the same eigenpair as the eigenvalue.

[0137] In another optional embodiment, the above processing of P pairs of principal features to obtain P influence vectors includes:

[0138] S431. Take the reciprocal of the main feature vectors of the P main feature pairs respectively to obtain P intermediate vectors.

[0139] It should be noted that the above reciprocal processing involves replacing each component of the corresponding main feature vector with its reciprocal.

[0140] S432. Multiply each of the P intermediate vectors mentioned above by its corresponding principal feature value to obtain the P influence vectors mentioned above.

[0141] In another optional embodiment, the above-mentioned key calculation model adopts a linear weighting method, and its expression is:

[0142]

[0143] In the formula, MSC k The key value is the value corresponding to the k-th node of the target network, where k is an integer from 1 to K; n k,j,i Let S be the i-th component of the j-th statistical vector in the k-th set of the aforementioned statistical vectors, where j is an integer from 1 to P and i is an integer from 1 to M; j,i It is the i-th component of the j-th influence vector mentioned above.

[0144] In another optional embodiment, the above-mentioned key calculation model adopts a non-linear weighting method, and its expression is:

[0145]

[0146] It should be noted that, compared to linear weighting, nonlinear weighting can better highlight the criticality of nodes that appear multiple times at the same node position in multiple sub-modules.

[0147] As can be seen, by using the criticality calculation model, based on the influence of the M node positions of the P-type sub-modules, the number of times each node in the target network appears at the M node positions of the P-type sub-modules is weighted and summed, so that the criticality value can comprehensively reflect the centrality of the corresponding node in the spectrum composed of the P-type sub-modules.

[0148] As can be seen, the network key node identification method described in the embodiments of the present invention can accurately identify the key values ​​of each node from the perspective of higher-order structure and functional modules, avoid over-reliance on the local connection of nodes, and improve the adaptability to dynamic networks by identifying dynamic changes that affect higher-order structure.

[0149] Example 2

[0150] Please see Figure 3 , Figure 3 This is a schematic diagram of the structure of a network key node identification device disclosed in an embodiment of the present invention. Figure 3 The described network critical node identification device can be applied to the identification of critical nodes in networks, such as command and control networks, sensor networks, and satellite communication networks. This invention does not limit the application of this device. Figure 3 As shown, the device may include a network acquisition module 201, a network decomposition module 202, a statistics module 203, a spectrum analysis module 204, and a criticality calculation module 205.

[0151] The network acquisition module 201 mentioned above is used to acquire the target network.

[0152] The network decomposition module 202 described above is used to perform motif decomposition processing on the target network to obtain N sub-motifs and their corresponding category values.

[0153] The aforementioned statistical module 203 is used to process the N sub-modules and their corresponding category values ​​to obtain K sets of statistical vectors and P category matrices.

[0154] The aforementioned spectral analysis module 204 is used to perform spectral analysis on the P category matrices to obtain P influence vectors; the influence vectors include M components.

[0155] The aforementioned criticality calculation module 205 is used to process the K sets of statistical vectors and P influence vectors mentioned above using a criticality calculation model to obtain K criticality values.

[0156] It is evident that implementing the network critical node identification device described in the embodiments of the present invention is capable of [achieving this goal].

[0157] Example 3

[0158] Please see Figure 4 , Figure 4 This is a schematic diagram of another network key node identification device disclosed in an embodiment of the present invention. Figure 4 The described network critical node identification device can be applied to the identification of critical nodes in networks, such as command and control networks, sensor networks, and satellite communication networks. This invention does not limit the application of this device. Figure 4 As shown, the network key node identification device may include the following parts:

[0159] Memory 301 storing executable program code;

[0160] Processor 302 coupled to memory 301;

[0161] The processor 302 calls the executable program code stored in the memory 301 to execute the steps in the network key node identification method described in Embodiment 1.

[0162] Example 4

[0163] This invention discloses a computer read storage medium that stores a computer program for electronic data interchange, wherein the computer program causes a computer to execute the steps in the network critical node identification method described in Embodiment 1.

[0164] The device embodiments described above are merely illustrative. The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical modules; that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0165] Through the detailed description of the above embodiments, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, including read-only memory (ROM), random access memory (RAM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), one-time programmable read-only memory (OTPROM), electrically-erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc storage, disk storage, magnetic tape storage, or any other computer-readable medium that can be used to carry or store data.

[0166] Finally, it should be noted that the network key node identification method and apparatus disclosed in the embodiments of the present invention are merely preferred embodiments of the present invention, and are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for identifying key nodes in a network, characterized in that, include: S1. Obtain the target network; The target network includes K nodes and several directed edges; S2. Perform motif decomposition on the target network to obtain N sub-motifs and their corresponding category values; The sub-module includes a node number sequence and a sub-adjacency matrix; the sub-modules with the same category value have completely identical sub-adjacency matrices. The node numbering sequence includes M number values; the sub-adjacency matrix is ​​an M-order square matrix; The category value is an integer from 1 to P; K, N, P, and M are all integers greater than 1; S3. Process the N sub-modalities and their corresponding category values ​​to obtain K sets of statistical vectors and P category matrices; The set of statistical vectors includes P statistical vectors; each statistical vector includes M components. S4. Perform spectral analysis on the P category matrices to obtain P influence vectors; each influence vector includes M components. S5. Using the criticality calculation model, process the K sets of statistical vectors and the P vectors of influence to obtain K criticality values.

2. The network key node identification method according to claim 1, characterized in that, The process of processing the N sub-motifs and their corresponding category values ​​to obtain K sets of statistical vectors and P category matrices includes: S31. Based on the corresponding category value, divide the N sub-motifs into P motif subsets; each motif subset includes several sub-motifs. S32. Based on each of the P subsets of the aforementioned modalities, construct P numbering matrices respectively; S33. Process the P numbering matrices to obtain the K statistical vector sets; S34. From the P subsets of the motifs, extract any one of the sub-motifs to obtain P representative motifs; set the P category matrices as the sub-adjacency matrices of the P representative motifs.

3. The network key node identification method according to claim 1, characterized in that, The spectral analysis of the P category matrices yields P influence vectors, including: S41. Process each of the P category matrices to obtain a set of P feature pairs; The feature pair set includes M feature pairs; each feature pair includes a feature value and a feature vector. S42. Perform principal feature analysis on each set of feature pairs to obtain the principal feature pairs corresponding to each set of feature pairs. The principal feature pair includes principal feature values ​​and principal feature vectors; S43. Process each of the P main feature pairs to obtain P influence vectors.

4. The network key node identification method according to claim 3, characterized in that, The process of processing each of the P category matrices yields a set of P feature pairs, including: S411. Calculate the sum of all column vectors of each category matrix to obtain P first vectors; S412. Calculate the sum of all row vectors of each category matrix to obtain P second vectors; S413. Based on the feature matrix calculation model, P first vectors, P second vectors and P category matrices are processed to obtain P feature matrices; The feature matrix calculation model is as follows: Yes j =diag(a j ) In the formula, L j Let I be the j-th characteristic matrix, where j is an integer from 1 to P; I is an M-order identity matrix; AM j Let α be the category matrix for the j-th category; j and β j These are the j-th first vector and the second vector, respectively; S414. Perform eigenvalue decomposition on each feature matrix to obtain M feature pairs corresponding to each feature matrix; The M feature pairs corresponding to each feature matrix constitute the feature pair set corresponding to each feature matrix.

5. The network key node identification method according to claim 3, characterized in that, The step of performing principal feature analysis on each of the feature pair sets to obtain the principal feature pairs corresponding to each feature pair set includes: S421. Determine whether all M feature values ​​in the feature pair set are equal to obtain the feature judgment result; If the feature determination result is yes, execute S422; If the feature determination result is negative, execute S423; S422. Set the principal feature vector as the mean of the M feature vectors in the feature pair set; set the principal feature value as the modulus of any feature value in the feature pair set; execute S43; S423. Set the main feature value to the smallest non-zero value among the moduli of the M feature values; S424. Set the main feature vector as the mean of the feature vectors corresponding to all feature values ​​whose magnitudes are equal to the main feature value among the M feature values.

6. The network key node identification method according to claim 3, characterized in that, The process of processing each of the P main feature pairs to obtain P influence vectors includes: S431. Take the reciprocal of the main feature vectors of each of the P main feature pairs to obtain P intermediate vectors; S432. Multiply each of the P intermediate vectors by its corresponding principal feature value to obtain the P influence vectors.

7. The network key node identification method according to claim 1, characterized in that, The expression for the key computational model is: In the formula, MSC k The key value corresponding to the k-th node of the target network, where k is an integer from 1 to K; n k,j,i S represents the i-th component of the j-th statistical vector in the k-th set of statistical vectors, where j is an integer from 1 to P and i is an integer from 1 to M; j,i Let i be the i-th component of the j-th influence vector.

8. A network key node identification device, characterized in that, The device includes a network acquisition module, a network decomposition module, a statistics module, a spectral analysis module, and a key calculation module; The network acquisition module is used to acquire the target network; The network decomposition module is used to perform motif decomposition processing on the target network to obtain N sub-motifs and their corresponding category values. The statistical module is used to process the N sub-modules and their corresponding category values ​​to obtain K sets of statistical vectors and P category matrices; The spectral analysis module is used to perform spectral analysis on the P category matrices to obtain P influence vectors. The criticality calculation module is used to process the K sets of statistical vectors and the P vectors of influence using a criticality calculation model to obtain K criticality values.

9. A network critical node identification device, characterized in that, The device includes: Memory containing executable program code; A processor coupled to the memory; The processor calls the executable program code stored in the memory to execute the network critical node identification method as described in any one of claims 1-7.

10. A computer-storable medium, characterized in that, The computer storage medium stores computer instructions, which, when invoked, are used to execute the network critical node identification method as described in any one of claims 1-7.

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