Network key node identification method and device

Abstract

The invention discloses a network key node identification method and device. The method comprises the following steps: S1, acquiring a target network; s2, performing motif decomposition processing on the target network to obtain N sub motifs and corresponding category values; s3, processing the N sub-motifs and the corresponding category values to obtain K statistical vector sets and P category matrixes; s4, performing spectral analysis processing on the P category matrixes to obtain P influence vectors; and S5, processing the K statistical vector sets and the P influence vectors by using a criticality calculation model to obtain K criticality values. According to the method, the accuracy degree of key node identification can be improved, and the adaptability to a dynamic network is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of network key node identification, and specifically relates to a method and device for identifying network key nodes. Background Art

[0002] In modern information networks, network structures such as command and control networks, sensor networks, and communication support networks are characterized by dynamic heterogeneity, strong adversarial dynamics, and significant load fluctuations. Evaluating the centrality of nodes in these networks and identifying key nodes can help deepen understanding of their structure and function. In complex networks, nodes with high centrality often play a crucial role in information transmission and resource flow. Quantitative analysis of node metrics such as degree centrality, betweenness centrality, and closeness centrality can pinpoint nodes that play a decisive role in network connectivity and stability. Furthermore, identifying key nodes based on centrality can provide decision support for network optimization and risk management. Identifying key nodes allows prioritizing their operational efficiency during resource allocation, such as increasing bandwidth allocation for base stations with high centrality to improve overall communication quality. Furthermore, proactive protection strategies can be developed for key nodes to prevent network downtime caused by the failure of a few nodes.

[0003] However, traditional centrality (such as degree centrality, betweenness centrality, closeness centrality, etc.) only focuses on the number of direct neighbors of a node, ignoring the differences in the roles of nodes in repeated subgraphs (motifs), and cannot reflect the high-order characteristics of nodes. For example, nodes with the same number of neighbors may have completely different support roles for the motif function. In addition, traditional centrality is not sensitive enough to the dynamic evolution of network structure. For example, the integration of new nodes and the failure of old nodes in a dynamic network may generate or destroy multiple motifs with different functions, while the number of neighbors of their directly adjacent nodes does not change significantly.

[0004] Therefore, the key nodes identified based on traditional centrality cannot accurately reflect the high-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 device for identifying key network nodes, which can improve the accuracy of key node identification and enhance the adaptability to dynamic networks.

[0006] In order to solve the above technical problems, an embodiment of the present invention discloses a method for identifying key network nodes, the method comprising:

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

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

[0009] The sub-motifs include a node number sequence and a sub-adjacency matrix; the sub-adjacency matrices of the sub-motifs with the same corresponding category values ​​are completely consistent;

[0010] The node number 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, processing the N sub-motifs and the corresponding category values ​​to obtain K statistical vector sets and P category matrices;

[0014] The statistical vector set includes P statistical vectors; the statistical vector includes M components;

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

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

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

[0018] S31, dividing the N sub-motifs into P motif subsets based on the corresponding category values; the motif subsets include a plurality of the sub-motifs;

[0019] S32, constructing P numbering matrices based on the P motif subsets respectively;

[0020] S33, processing the P numbering matrices to obtain K statistical vector sets;

[0021] S34. Extract any sub-motif from the P motif subsets to obtain P representative motifs; and set the P category matrices as the sub-adjacency matrices of the P representative motifs.

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

[0023] S41, processing the P category matrices respectively to obtain P feature pair sets;

[0024] The feature pair set includes M feature pairs; the feature pairs include eigenvalues ​​and eigenvectors;

[0025] S42, performing main feature analysis processing on each of the feature pair sets to obtain main feature pairs corresponding to each of the feature pair sets;

[0026] The main eigenvalue and main eigenvector are included in the main eigenvalue.

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

[0028] As an optional implementation manner, in the first aspect of the embodiment of the present invention, the processing of the P category matrices to obtain P feature pair sets includes:

[0029] S411, respectively calculating the sum of all column vectors of each category matrix to obtain P first vectors;

[0030] S412, respectively calculating the sum of all row vectors of each category matrix to obtain P second vectors;

[0031] S413: Process the P first vectors, the P second vectors, and the P category matrices based on a feature matrix calculation model to obtain P feature matrices;

[0032] The characteristic matrix calculation model is:

[0033]

[0034] DA j =diag(α j )

[0035]

[0036] Where, L j is the jth characteristic matrix, j is an integer from 1 to P; I is the M-order unit matrix; AM j is the j-th category matrix; α j and β j are the j-th first vector and the j-th second vector respectively;

[0037] S414, performing eigenvalue decomposition processing on each of the feature matrices to obtain M feature pairs corresponding to each of the feature matrices;

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

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

[0040] S421, judging whether all the M feature values ​​in the feature pair set are equal, and obtaining a feature judgment result;

[0041] When the feature judgment result is yes, execute S422;

[0042] When the feature judgment result is no, execute S423;

[0043] S422, setting the main eigenvector to the mean of the M eigenvectors in the feature pair set; setting the main eigenvalue to the modulus of any eigenvalue in the feature pair set; and executing S43;

[0044] S423, setting the main eigenvalue to the smallest non-zero value among the moduli of the M eigenvalues;

[0045] S424: Set the main eigenvector to the mean of the eigenvectors corresponding to all the eigenvalues ​​whose moduli are equal to the main eigenvalue among the M eigenvalues.

[0046] As an optional implementation manner, in the first aspect of the embodiment of the present invention, the processing of the P main feature pairs to obtain the P influence vectors includes:

[0047] S431, performing reciprocal processing on the main eigenvectors of the P main eigenvector pairs to obtain P intermediate vectors;

[0048] S432: Multiply the P intermediate vectors by the corresponding main eigenvalues ​​respectively to obtain P influence vectors.

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

[0050]

[0051] Where, MSC k is the critical value corresponding to the kth node of the target network, where k is an integer from 1 to K; n k,j,i is the i-th component of the j-th statistical vector of the k-th statistical vector set, j is an integer from 1 to P, and i is an integer from 1 to M; Sj,i is the i-th component of the j-th influence vector.

[0052] A second aspect of an embodiment of the present 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 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 corresponding category values;

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

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

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

[0058] A third aspect of an embodiment of the present invention discloses another device for identifying key network nodes, the device comprising:

[0059] a memory storing executable program code;

[0060] a processor coupled to the memory;

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

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

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

[0064] The present 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 excessive dependence on the local connection status of the node, and at the same time improve the adaptability to dynamic networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

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

[0067] Figure 2 This is a schematic diagram of a motif decomposition of a method for identifying key network nodes disclosed in an embodiment of the present invention.

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

[0069] Figure 4 It is a structural diagram of another network key node identification device disclosed in an embodiment of the present invention. DETAILED DESCRIPTION

[0070] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0071] In the description of the present invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present 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 the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0073] Example 1

[0074] See also Figure 1 and Figure 2 . Figure 1 The present invention is a flowchart of a method for identifying key network nodes disclosed in an embodiment of the present invention. Figure 2 : is a schematic diagram of a motif decomposition of a method for identifying key network nodes disclosed in an embodiment of the present invention. Figure 1 The described network key node identification method is applied to network key node identification, such as identification of key nodes in a command and control network, a sensor network, and a satellite communication network, and the embodiment of the present invention does not limit this. Figure 1 As shown, the method includes:

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

[0076] It should be noted that the target network may be a command and control network, a sensor network or a satellite communication network, which is not limited in the embodiment of the present invention.

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

[0078] It should be noted that the above-mentioned motif decomposition process can adopt the ESU algorithm, Grochow-Kellis algorithm, Mfinder algorithm, etc., and is not limited in the embodiments of the present invention. Decomposing the target network into a series of sub-motifs, where each sub-motif is a basic structural unit with clear functional attributes, such as a data transmission motif and a routing control motif, helps to understand how the target network implements core functions such as information exchange and resource allocation from a holistic perspective, avoiding the 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 to the sub-motifs, and are respectively used to describe the category to which the corresponding sub-motifs belong.

[0080] The above-mentioned sub-motifs include node number sequences and sub-adjacency matrices; for the above-mentioned sub-motifs with the same corresponding category values, the above-mentioned sub-adjacency matrices are completely consistent.

[0081] The node number sequence includes M number values; the 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-motif is a sub-network of the target network containing M nodes. The ii-th number value in the node number sequence of each sub-motif represents the node number corresponding to the ii-th node of the sub-motif in the target network, where ii is an integer from 1 to M. The sub-adjacency matrix of each sub-motif describes the local adjacency relationship of the M nodes of the sub-motif, and the element value of its jj-th row and kk-th column is equal to the f of the adjacency matrix of the target network. jj Line f kk The element value of the column, where f jj and f kk are the jj-th and kk-th number values ​​in the node number sequence of the sub-motif respectively.

[0085] S3. Process the N sub-motifs and the corresponding category values ​​to obtain K statistical vector sets and P category matrices.

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

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

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

[0089] It should be noted that the K criticality values ​​respectively 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] Take M equal to 3 as an example, Figure 2 As shown in the figure, the target network on the left is decomposed into 13 types of 3-element sub-motifs M1-M13 with different connection methods (there is only one sub-motif in each type in the figure), that is, P is equal to 13, and the detailed structure and position relationship of each sub-motif are shown on the right. In the figure on the right, the internal node position relationship of each sub-motif is represented by the mark on the right side of the sub-motif. For example, nodes 1, 2, and 3 of sub-motif M1 are marked as 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 corresponding to them.

[0091] In an optional embodiment, the N sub-motifs and the corresponding category values ​​are processed to obtain K statistical vector sets and P category matrices, including:

[0092] S31 . Based on the corresponding category values, the N sub-motifs are divided into P motif subsets; the motif subsets include a plurality of the sub-motifs.

[0093] It should be noted that the category values ​​corresponding to the sub-motifs in the same motif subset are equal, and the category values ​​corresponding to the sub-motifs in different motif subsets are not equal.

[0094] S32. Construct P numbering matrices based on the P motif subsets mentioned above.

[0095] Optionally, the node number sequences of all sub-motifs in each motif subset are used as row vectors and sequentially concatenated to obtain a number matrix.

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

[0097] S34. Extract any of the above sub-motifs from the P motif subsets to obtain P representative motifs; set the P category matrices as the sub-adjacency matrices of the P representative motifs.

[0098] It should be noted that the above P-th category matrix corresponds to P types of sub-motifs.

[0099] In another optional embodiment, the P number matrices are processed to obtain the K statistical vector sets, including:

[0100] S331, initialize the number of cycles ic to 1.

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

[0102] S333. In the P statistical matrices above, all elements not equal to ic are replaced with 0, and all elements equal to ic are replaced with 1.

[0103] S334. Perform compression and summation processing on the P statistical matrices to obtain P statistical vectors; the P statistical vectors constitute the icth statistical vector set.

[0104] Optionally, the above-mentioned compressed summation processing is to calculate the sum of all row vectors of the corresponding statistical matrix to obtain the corresponding statistical vector.

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

[0106] S335. Add 1 to the value of ic.

[0107] S336. Repeat S332 to S335 until ic is greater than K, and obtain K statistical vector sets.

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

[0109] In yet another optional embodiment, the spectral analysis is performed on the P category matrices to obtain P influence vectors, including:

[0110] S41. Process the P category matrices mentioned above respectively to obtain P feature pair sets.

[0111] The above-mentioned feature pair set includes M feature pairs; the above-mentioned feature pairs include eigenvalues ​​and eigenvectors.

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

[0113] The above-mentioned principal eigenpair includes principal eigenvalue and principal eigenvector.

[0114] S43. Process the P main feature pairs mentioned above respectively to obtain the 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 P category matrices are processed separately to obtain P feature pair sets, including:

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

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

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

[0120] The above feature matrix calculation model is:

[0121]

[0122] DA j =diag(α j )

[0123]

[0124] Where, L j is the jth characteristic matrix above, j is an integer from 1 to P; I is the M-order unit matrix; AM j is the j-th category matrix above; α j and β j are the jth first vector and the jth second vector respectively.

[0125] S414 , performing eigenvalue decomposition processing on each of the above-mentioned characteristic matrices to obtain the M above-mentioned characteristic pairs corresponding to each of the above-mentioned characteristic matrices.

[0126] It should be noted that, by performing eigenvalue decomposition on each characteristic matrix, M eigenvalues ​​and M corresponding eigenvectors are obtained, wherein each eigenvalue and the corresponding eigenvector constitute an eigenpair of the characteristic matrix.

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

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

[0129] S421, judging whether all the M feature values ​​in the feature pair set are equal, and obtaining a feature judgment result;

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

[0131] When the result of the above feature judgment is no, execute S423.

[0132] S422. Set the main eigenvector as the mean of the M eigenvectors in the feature pair set; set the main eigenvalue as the modulus of any eigenvalue in the feature pair set; and execute S43.

[0133] S423. Set the main eigenvalue as the smallest non-zero value among the moduli of the M eigenvalues.

[0134] S424. Set the main eigenvector as the mean of the eigenvectors corresponding to all the eigenvalues ​​whose moduli are equal to the main eigenvalue among the M eigenvalues.

[0135] It should be noted that the above eigenvalue can be a real number or a complex number. When it is a real number, the modulus is its absolute value.

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

[0137] In yet another optional embodiment, the P main feature pairs are processed separately to obtain the P influence vectors, including:

[0138] S431. Perform reciprocal processing on the principal eigenvectors of the P principal eigenvectors to obtain P intermediate vectors.

[0139] It should be noted that the above-mentioned reciprocal processing is to replace each component of the corresponding main eigenvector with the reciprocal of the component.

[0140] S432. Multiply the P intermediate vectors by the corresponding main eigenvalues ​​to obtain the P influence vectors.

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

[0142]

[0143] Where, MSC k is the critical value corresponding to the k-th node of the target network, where k is an integer from 1 to K; n k,j,i is the i-th component of the j-th statistical vector of the k-th statistical vector set, j is an integer from 1 to P, and i is an integer from 1 to M; S j,i is the i-th component of the j-th influence vector mentioned above.

[0144] In another optional embodiment, the above criticality calculation model adopts a nonlinear weighting method, and its expression is:

[0145]

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

[0147] It can be seen that through the criticality calculation model, based on the influence of the M node positions of the P-type sub-motif, the number of times each node in the target network appears in the M node positions of the P-type sub-motif 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-motif.

[0148] It can be seen that the network key node identification method described in the embodiment of the present invention can accurately identify the critical value of each node from the perspective of high-order structure and functional modules, avoid excessive dependence on the local connection status of the node, and at the same time, because it can identify dynamic changes that affect high-order structures, it improves the adaptability to dynamic networks.

[0149] Example 2

[0150] See also 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 key node identification device can be applied to network key node identification, such as identification of key nodes in a command and control network, a sensor network, and a satellite communication network, and the embodiment of the present invention does not limit this. Figure 3 As shown, the apparatus 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 is used to acquire a target network.

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

[0153] The statistical module 203 is used to process the N sub-motifs and the corresponding category values ​​to obtain K statistical vector sets and P category matrices.

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

[0155] The criticality calculation module 205 is configured to process the K statistical vector sets and the P influence vectors using a criticality calculation model to obtain K criticality values.

[0156] It can be seen that the network key node identification device described in the embodiment of the present invention can be implemented.

[0157] Example 3

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

[0159] A memory 301 storing executable program code;

[0160] a processor 302 coupled to the memory 301;

[0161] The processor 302 calls the executable program code stored in the memory 301 to execute the steps of the method for identifying key network nodes described in the first embodiment.

[0162] Example 4

[0163] An embodiment of the present invention discloses a computer-readable storage medium storing a computer program for electronic data exchange, wherein the computer program enables a computer to execute the steps of the method for identifying key network nodes described in the first embodiment.

[0164] The device embodiments described above are merely illustrative. Modules described as separate components may or may not be physically separate, and components shown as modules may or may not be physical modules, i.e., they may be located in one place or distributed across multiple network modules. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0165] Through the detailed description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus the necessary general hardware platform, or of course, by means of hardware. Based on this understanding, the above technical solution, in essence, or the portion that contributes to the prior art, can be embodied in the form of a software product, which can be stored in a computer-readable storage medium, including a read-only memory (ROM), a random access memory (RAM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), a one-time programmable read-only memory (OTPROM), an electronically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM) or other optical disc storage, magnetic disk storage, magnetic tape storage, or any other computer-readable medium capable of carrying or storing data.

[0166] Finally, it should be noted that the network key node identification method and device disclosed in the embodiments of the present invention are only preferred embodiments of the present invention, and are only used to illustrate the technical solutions of the present invention, rather than to limit them. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments can still be modified, or some of the technical features therein can be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for identifying key network nodes, characterized in that: include: S1. Obtain the target network; The target network includes K nodes and a plurality of directed edges; S2. Perform motif decomposition processing on the target network to obtain N sub-motifs and corresponding category values; The sub-motifs include a node number sequence and a sub-adjacency matrix; the sub-adjacency matrices of the sub-motifs with the same corresponding category values ​​are completely consistent; The node number 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, processing the N sub-motifs and the corresponding category values ​​to obtain K statistical vector sets and P category matrices; The statistical vector set includes P statistical vectors; the statistical vector includes M components; S4. Perform spectral analysis on the P category matrices to obtain P influence vectors; the influence vectors include M components; S5. Using a criticality calculation model, process the K statistical vector sets and the P influence vectors to obtain K criticality values.

2. The method for identifying key network nodes according to claim 1, wherein: The N sub-motifs and the corresponding category values ​​are processed to obtain K statistical vector sets and P category matrices, including: S31, dividing the N sub-motifs into P motif subsets based on the corresponding category values; the motif subsets include a plurality of the sub-motifs; S32, constructing P numbering matrices based on the P motif subsets respectively; S33, processing the P numbering matrices to obtain K statistical vector sets; S34. Extract any sub-motif from the P motif subsets to obtain P representative motifs; and set the P category matrices as the sub-adjacency matrices of the P representative motifs.

3. The method for identifying key network nodes according to claim 1, wherein: The performing spectral analysis on the P category matrices to obtain P influence vectors includes: S41, processing the P category matrices respectively to obtain P feature pair sets; The feature pair set includes M feature pairs; the feature pairs include eigenvalues ​​and eigenvectors; S42, performing main feature analysis processing on each of the feature pair sets to obtain main feature pairs corresponding to each of the feature pair sets; The main eigenvalue and main eigenvector are included in the main eigenvalue. S43. Process the P main feature pairs respectively to obtain P influence vectors.

4. The method for identifying key network nodes according to claim 3, wherein: The P category matrices are processed respectively to obtain P feature pair sets, including: S411, respectively calculating the sum of all column vectors of each category matrix to obtain P first vectors; S412, respectively calculating the sum of all row vectors of each category matrix to obtain P second vectors; S413: Process the P first vectors, the P second vectors, and the P category matrices based on a feature matrix calculation model to obtain P feature matrices; The characteristic matrix calculation model is: Yes j =diag(a j ) Where, L j is the jth characteristic matrix, j is an integer from 1 to P; I is the M-order unit matrix; AM j is the j-th category matrix; α j and β j are the j-th first vector and the j-th second vector respectively; S414, performing eigenvalue decomposition processing on each of the feature matrices to obtain M feature pairs corresponding to each of the feature matrices; The M feature pairs corresponding to each feature matrix constitute a feature pair set corresponding to each feature matrix.

5. The method for identifying key network nodes according to claim 3, wherein: The performing main feature analysis processing on each of the feature pair sets to obtain the main feature pairs corresponding to each of the feature pair sets includes: S421, judging whether all the M feature values ​​in the feature pair set are equal, and obtaining a feature judgment result; When the feature judgment result is yes, execute S422; When the feature judgment result is no, execute S423; S422, setting the main eigenvector to the mean of the M eigenvectors in the feature pair set; setting the main eigenvalue to the modulus of any eigenvalue in the feature pair set; and executing S43; S423, setting the main eigenvalue to the smallest non-zero value among the moduli of the M eigenvalues; S424: Set the main eigenvector to the mean of the eigenvectors corresponding to all the eigenvalues ​​whose moduli are equal to the main eigenvalue among the M eigenvalues.

6. The method for identifying key network nodes according to claim 3, wherein: The processing of the P main feature pairs to obtain the P influence vectors includes: S431, performing reciprocal processing on the main eigenvectors of the P main eigenvector pairs to obtain P intermediate vectors; S432: Multiply the P intermediate vectors by the corresponding main eigenvalues ​​respectively to obtain P influence vectors.

7. The method for identifying key network nodes according to claim 1, wherein: The expression of the key calculation model is: Where, MSC k is the critical value corresponding to the kth node of the target network, where k is an integer from 1 to K; n k,j,i is the i-th component of the j-th statistical vector of the k-th statistical vector set, where j is an integer from 1 to P, and i is an integer from 1 to M; S j,i is 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 spectrum 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 corresponding category values; The statistical module is used to process the N sub-motifs and the corresponding category values ​​to obtain K statistical vector sets and P category matrices; The spectrum analysis module is used to perform spectrum analysis on the P category matrices to obtain P influence vectors; The criticality calculation module is used to process the K statistical vector sets and the P influence vectors using a criticality calculation model to obtain K criticality values.

9. A network key node identification device, characterized in that: The device comprises: a memory storing executable program code; a processor coupled to the memory; The processor calls the executable program code stored in the memory to execute the network key node identification method according to any one of claims 1 to 7.

10. A computer storable medium, characterized in that The computer storable medium stores computer instructions, and when the computer instructions are called, they are used to execute the network key node identification method according to any one of claims 1 to 7.

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