Method, system, device and storage medium for identifying important nodes in a super network based on multi-dimensional decision fusion

Abstract

The present invention relates to the field of network, especially the technical field of super network node identification, and specifically discloses a super network important node identification method, system, device and storage medium based on multi-dimensional decision fusion. The method includes the steps of: constructing a multi-dimensional index of a super network node, which at least includes a topological index, a search index and a propagation index; calculating the weight of each multi-dimensional index; according to the multi-dimensional index and its weight, adopting a decision fusion method to obtain the net dominance coefficient of each node, ranking the importance of the nodes, and identifying the important nodes therein. The present invention considers the important node identification method in multiple dimensions as the indicator of the node, and performs decision fusion through the Electre method to mine the important nodes on the super network, providing the basic conditions for the subsequent imposition of measures on the important nodes.

Description

Technical Field

[0001] The present invention relates to the field of networks, especially the technical field of supernetwork node identification, and specifically to a supernetwork important node identification method, system, device and storage medium based on multi-dimensional decision fusion. Background Art

[0002] As research into complex networks deepens, scholars have discovered that real networks contain not only one-to-one relationships between pairs of nodes, but also one-to-many, many-to-one, and many-to-many relationships in the form of communities and groups. These differences manifest as heterogeneity in nodes and edges, making it impossible to fully represent the full range of network characteristics using a standard complex network. For example, in a scientific research collaboration network, a standard network can only indicate which two authors collaborated, but cannot indicate which authors collaborated on a single paper. In a transportation network, a standard network can only indicate whether a route exists between two stations, but cannot represent situations where a route passes through multiple stations or where multiple routes exist between multiple stations. While these problems can be addressed using standard networks, they also lose the "homogeneity" of nodes, making it impossible to deeply explore certain topological properties of the network. To address this issue, hypernetworks offer several advantages over standard complex networks.

[0003] In complex networks, a hypernetwork is a graph structure used to represent more complex relationships between nodes. Unlike regular graphs, a hypernetwork allows edges (or hyperedges) to connect multiple nodes, not just two. This allows hypernetworks to more flexibly capture many-to-many relationships between nodes. In a hypernetwork, a hyperedge can connect multiple nodes, and a node can belong to multiple hyperedges simultaneously. This flexibility makes hypergraphs very useful for describing some of the complex relationship networks found in the real world.

[0004] Based on this, various real-life networks can be abstracted into complex network models through graph theory, such as road traffic networks, virus transmission networks, and rumor information networks. In road traffic networks, important nodes can be identified to improve and enhance transportation efficiency. In epidemic virus transmission networks, people can be set as network nodes to search for super-spreaders to curb the large-scale spread of the virus. In rumor information networks, important nodes can be found to block the spread of rumors and control public opinion. Therefore, identifying node influence in complex networks is a key research issue.

[0005] Current methods for identifying important nodes mainly include several categories. For example, one method divides the importance of nodes by studying the structural properties of the network; one method finds important nodes through random walks and continuously updates the importance of these nodes; and one method introduces a propagation model to initialize nodes as infected nodes to propagate in the network, and counts the number of infected nodes in the network as the importance of the nodes.

[0006] While these methods can identify important nodes, they all consider only a single dimension of the network. For example, methods based on network structure and search-based identification only explore the network structure but ignore the node's propagation capabilities. Methods that characterize node importance using propagation models ignore the structural characteristics of the network. Summary of the Invention

[0007] Purpose of the invention: The purpose of the present invention is to address the deficiencies of the existing technology and provide a method, system, device and storage medium for identifying important nodes in a super network based on multi-dimensional decision fusion. The method uses the importance of nodes in multiple dimensions as an indicator, performs decision fusion through the Electre method, and mines important nodes on the super network, providing basic conditions for subsequent measures to be taken on important nodes.

[0008] In order to achieve the above-mentioned purpose, the present invention first provides a method for identifying important nodes in a super network based on multi-dimensional decision fusion, comprising the following steps:

[0009] S1. Constructing a multi-dimensional index of super network nodes including at least topological index, search index and propagation index;

[0010] S2. Calculate the weight of each multi-dimensional indicator;

[0011] S3. Based on the multi-dimensional indicators and their weights, the decision fusion method is used to obtain the net dominance coefficient of each node, rank the importance of the nodes, and identify the important nodes.

[0012] As a preferred technical solution, the topological index of the super network node in step S1 is established using the composite core information entropy method;

[0013] The search index of hypernetwork nodes is established using the gravity model of improved random walk;

[0014] The propagation index of the hypernetwork node adopts the SIR virus propagation model, defines each node as the initial infected node for simulation, and uses the propagation ability of each node as the propagation index.

[0015] Preferably, the topological index of the hypernetwork node is established by using a composite core information entropy method, specifically:

[0016] First, define the node composite value:

[0017] d c (i)=d(i)+d h (i);

[0018] Where d(i) is the degree of node i, d h (i) is the excess degree of node i, d c (i) is the composite degree of node i;

[0019] The composite kshell value of this node is defined as:

[0020] ks c (i)=ks(i)+ks h (i);

[0021] Among them, ks(i) is the kshell value of node i, ks h (i) is the kshell value of node i based on the hypernetwork, ks c (i) is the composite kshell value of node i;

[0022] The composite nucleus value is defined as:

[0023]

[0024] in, is the composite coreness value of node i;

[0025] The composite nuclearity information entropy is defined as:

[0026]

[0027] Then, the calculation formula for constructing the node topology index is:

[0028]

[0029] Among them, TI i is the topological index of node i, K(i) is the composite coreness information entropy of node i, Represents the sum of the composite coreness information entropy of each node in the hypernetwork.

[0030] Preferably, the search index for the hypernetwork node is established by using an improved random walk gravity model, specifically by:

[0031] The improved random walk gravity model is defined as:

[0032]

[0033] in, It represents the number of composite paths of length l between node i and node j. The number of composite paths is the sum of the number of hyperedge paths and ordinary network paths. The calculation formula is:

[0034]

[0035] here is the number of common network paths of length l between node i and node j, is the number of hyperedge paths of length l between node i and node j;

[0036] n is the number of network nodes, represents the number of all l-order paths starting from node i, d c (i) represents the composite degree of node i, and simrank(i,j) represents the SimRank similarity value between nodes i and j;

[0037] f ij represents the gravitational force between node i and node j, so the total gravitational force of node i can be obtained as:

[0038]

[0039] Where V represents the set of all nodes in the hypernetwork; the calculation formula for constructing the node search index is:

[0040]

[0041] Among them, CI i is the search index of node i, represents the sum of the total attraction of each node in the hypernetwork.

[0042] Preferably, the propagation index of the hypernetwork node adopts the SIR virus propagation model, defines each node as an initial infected node for simulation, and uses the propagation capability of each node as the propagation index. The specific method is as follows:

[0043] Using the classic SIR virus propagation model as a carrier, each node in the hypernetwork is set as the initial infected node in turn, and the infected node is defined as the node that has a normal edge relationship with it, as well as the node that has a hyperedge connection with it. Finally, after the end of the propagation, the sum of the number of infected people and the number of recovered people in the network is counted to represent the node's propagation capacity, and this propagation capacity is used as the node's propagation indicator. Here, the propagation capacity is defined as:

[0044] N(i)=I(i)+R(i);

[0045] Where I(i) represents the number of infected people in the network when node i is set as the initial infected node and until the end of the spread, and R(i) represents the number of recovered people in the network when node i is set as the initial infected node and until the end of the spread;

[0046] The calculation formula for constructing the node propagation index is:

[0047]

[0048] Among them, PI i is the propagation index of node i, Represents the sum of the propagation capabilities of each node in the hypernetwork.

[0049] Preferably, in step S2, the weights of the multi-dimensional indicators are calculated based on entropy theory, and the specific method is:

[0050] S21. Use the obtained node indices to establish the indicator matrix P:

[0051]

[0052] S22. Based on Shannon entropy theory, the entropy value of the jth indicator is calculated as:

[0053]

[0054] Among them, a ij Represents the element in the i-th row and j-th column of the matrix P;

[0055] S23, according to the index entropy value e j The weight of each indicator is calculated as:

[0056]

[0057] in, Represents the sum of the entropy values ​​of each indicator in the network.

[0058] Preferably, in step S3, based on the multi-dimensional indicators and their weights, a decision fusion method is used to obtain the net dominance coefficient of each node, rank the importance of the nodes, and identify the important nodes. The specific method is:

[0059] S31, perform weighted calculation on the indicator matrix P to obtain the n×2 order weighted decision matrix R, {r ij ∈R|i=1,2,…,n,j=1,2,…,n}, the calculation formula is:

[0060]

[0061] S32. For any pair of nodes i and j in the network, and the indicators of this pair of nodes, let the indicator set be L = {TI, SI, PI};

[0062] Then the indicator set is divided into two non-overlapping subsets. The former consists of indicators whose weighted values ​​in node i are not less than those in node j, which is called the harmony set H of node i for node j. ij The latter consists of the indicators in node i whose weighted value is lower than that of node j, which is called the discord set B of node i to node j ij ;

[0063] S33, based on the harmonious set H ij , construct an n×n order harmony matrix C, {c ij ∈C|i=1,2,…,n,j=1,2,…,n}, where c ij It represents the harmony index of node i to node j, and its calculation formula is:

[0064]

[0065] S34, based on the discordant set B ij , construct an n×n order inharmony matrix D, {d ij ∈D|i=1,2,…,n,j=1,2,…,n}, d ij It represents the disharmony index of node i to node j, and its calculation formula is:

[0066]

[0067] Among them, r il is the element in the i-th row and l-th column of the weighted decision matrix R, r jl is the element in the jth row and lth column of the weighted decision matrix R;

[0068] S35. Based on the harmony matrix C and the disharmony matrix D, construct an n×n order comprehensive dominating matrix U, {u ij ∈U|i=1,2,…,n,j=1,2,…,n}, which reflects the relative advantages and disadvantages of the comprehensive effects of multi-method fusion decision-making at different nodes, where u ij It represents the dominance coefficient of node i to node j, and its calculation formula is:

[0069] u ij =c ij -d ij ;

[0070] u ij The larger it is, the stronger the dominance of node i over node j is, and the better node i is at evaluating node j.

[0071] S36. Calculate the net dominance coefficient of each node based on the comprehensive dominance matrix The calculation formula is:

[0072]

[0073] Among them, u ik represents the dominance coefficient of node i to node k, u ki represents the dominance coefficient of node k to node i;

[0074] Reflects the comprehensive utility of node i after fusion using the Electre method, The larger the value, the better the utility of the node, that is, the greater the influence of the node. Sort the nodes from large to small, and finally select important nodes based on the sorting results.

[0075] The present invention further provides a super network important node identification system based on multi-dimensional decision fusion, comprising:

[0076] An indicator construction module is used to construct multi-dimensional indicators of hypernetwork nodes, including at least topological indicators, search indicators and propagation indicators;

[0077] The indicator weight acquisition module is used to calculate the weight of each multi-dimensional indicator;

[0078] The node evaluation module is used to obtain the net dominance coefficient of each node based on multi-dimensional indicators and their weights, rank the importance of the nodes, and identify the important nodes.

[0079] The present invention also provides an electronic device, comprising a processor, a communication interface, a memory and a communication bus;

[0080] Among them, the processor, communication interface, and memory communicate with each other through a communication bus;

[0081] The processor is used to call the logic instructions in the memory to execute the above-mentioned super network important node identification method based on multi-dimensional decision fusion.

[0082] Another aspect of the present invention provides a non-transitory computer-readable storage medium having computer instructions stored thereon, which enable a computer to execute the above-mentioned method for identifying important nodes in a supernetwork based on multi-dimensional decision fusion.

[0083] Beneficial effects: The present invention proposes a method, system, device and storage medium for identifying important nodes in a super network based on multi-dimensional decision fusion. By considering the important node identification methods in multiple dimensions as node indicators and performing decision fusion through the Electre method, important nodes on the super network are excavated, providing basic conditions for subsequent measures to be taken on important nodes. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 This is a flow chart of the method for identifying important nodes in a supernetwork based on multi-dimensional decision fusion of the present invention. DETAILED DESCRIPTION

[0085] In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the embodiments described are part of the embodiments of the present invention, not all of the embodiments, and they should not be understood as limitations on the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. In the description of the present invention, it should be understood that the terms used are only for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0086] The following combination Figure 1 The present invention describes a method, system, device, and storage medium for identifying important nodes in a supernetwork based on multi-dimensional decision fusion.

[0087] Example: This example provides a method for identifying important nodes in a super network based on multi-dimensional decision fusion. Figure 1 As shown in the figure, we first use the composite nuclearity information entropy, the improved random walk gravity model, and the SIR epidemic model to construct the topological index, search index, and propagation index of the hypernetwork nodes, then use the Shannon entropy theory to determine the weight of each index, and finally use the Electre decision fusion method to obtain the ranking results. It includes:

[0088] S1. Constructing a multi-dimensional index of super network nodes, including at least topological index, search index and propagation index:

[0089] This example uses three dimensional indicators as an example. These include: using the hypernetwork-based composite coreness information entropy to obtain the topological indicator of a node in the hypernetwork, which represents the importance score of the node in the topological structure dimension; using the improved random walk gravity model to construct the node search indicator, which represents the importance score of the node in the search dimension; and using the SIR virus propagation model to construct the node propagation indicator, which represents the importance score of the node in the propagation dimension.

[0090] (1) Using the composite core information entropy based on the hypernetwork to obtain the topological index of the nodes in the hypernetwork, the specific method is as follows:

[0091] First, define the node composite value:

[0092] d c (i)=d(i)+d h (i);

[0093] Where d(i) is the degree of node i, d h (i) is the excess degree of node i, d c (i) is the composite degree of node i;

[0094] Since the Kshell method is a node importance ranking algorithm based on the global structure of the network, it recursively deletes nodes with a degree less than or equal to k from the network from k = 1 to k = N, and assigns their kshell value to k. The algorithm is executed until all nodes in the network are assigned a value, and the larger the value, the more important the node. The same theory is also applicable to hypernetworks. The kshell method based on superdegree also recursively deletes nodes with a superdegree less than or equal to k from the network from k = 1 to k = N, and assigns their kshell value to k. The algorithm is executed until all nodes in the network are assigned a value, and the larger the value, the more important the node.

[0095] The composite kshell value of this node is defined as:

[0096] ks c (i) = ks(i) + ks h (i);

[0097] Among them, ks(i) is the kshell value of node i, ks h (i) is the kshell value of node i based on the hypernetwork, ks c (i) is the composite kshell value of node i;

[0098] The composite nucleus value is defined as:

[0099]

[0100] in, is the composite coreness value of node i;

[0101] The composite nuclearity information entropy is defined as:

[0102]

[0103] Then, the calculation formula for constructing the node topology index is:

[0104]

[0105] Among them, TI i is the topological index of node i, k(i) is the composite coreness information entropy of node i, Represents the sum of the composite coreness information entropy of each node in the hypernetwork.

[0106] (2) Use the improved random walk gravity model to construct the node search index. The gravity between each pair of nodes is calculated through this model, so that the sum of the gravity of each node on all other nodes can be obtained, and then the importance score of the node is obtained. The importance score is used to establish the node search index. The specific method is:

[0107] The improved random walk gravity model is defined as:

[0108]

[0109] in, It represents the number of composite paths of length l between node i and node j. The number of composite paths is the sum of the number of hyperedge paths and ordinary network paths. The calculation formula is:

[0110]

[0111] here is the number of common network paths of length l between node i and node j, is the number of hyperedge paths of length l between node i and node j;

[0112] n is the number of network nodes, represents the number of all l-order paths starting from node i, d c (i) represents the composite degree of node i, and simrank(i,j) represents the SimRank similarity value between nodes i and j;

[0113] f ij represents the gravitational force between node i and node j, so the total gravitational force of node i can be obtained as:

[0114]

[0115] Where V represents the set of all nodes in the hypernetwork; the calculation formula for constructing the node search index is:

[0116]

[0117] Among them, CI i is the search index of node i, represents the sum of the total attraction of each node in the hypernetwork.

[0118] (3) Use the SIR virus propagation model to construct the node propagation index. The specific method is as follows:

[0119] In order to construct the node propagation index, since the propagation between nodes in traditional networks is carried out through the edge relationship between them, this is actually not in line with the characteristics of some real networks. For example, the virus is transmitted through the air in the crowd, so two unrelated people may be infected by an infected person at the same time. Therefore, the classic SIR virus propagation model is used as a carrier here. Each node in the hypernetwork is set as the initial infected node in turn, and it is defined that the infected node at the current moment can not only infect the susceptible nodes with ordinary edge relationships at the infection rate β, but also infect the susceptible nodes with hyperedge connections at the infection rate θ. After the end of the propagation, the sum of the number of infected people (S) and the number of recovered people (I) in the network is counted to represent the propagation ability of the node, and the propagation ability is used as the propagation index of the node, where the infection rate is set The recovery rate is fixed at 0.25. For node i, in each SIR simulation, the sum of the number of infected nodes I and recovered nodes R in the network is counted after a given number of propagation days. The propagation capacity is defined as:

[0120] N(i)=I(i)+R(i);

[0121] Where I(i) represents the number of infected people in the network when node i is set as the initial infected node and until the end of the spread, and R(i) represents the number of recovered people in the network when node i is set as the initial infected node and until the end of the spread;

[0122] The calculation formula for constructing the node propagation index is:

[0123]

[0124] Among them, PI i is the propagation index of node i, Represents the sum of the propagation capabilities of each node in the hypernetwork.

[0125] S2. Since the present invention uses the multi-attribute decision-making fusion method, it is extremely important to determine the weights between multi-dimensional indicators. Here, the weights of each indicator are obtained by calculating the Shannon information entropy of each indicator, and then the weights are added to the Electre method for decision fusion. The weights of each multi-dimensional indicator are calculated based on entropy theory:

[0126] S21. Use the obtained node indices to establish the indicator matrix P:

[0127]

[0128] S22. In order to obtain a good weight between each indicator in the subsequent decision fusion, the weight of each indicator is determined based on the Shannon entropy theory. According to this theory, the smaller the information entropy of an indicator, the greater the degree of variation of the indicator, the more information it provides, and the higher its corresponding weight. Based on the Shannon entropy theory, the entropy value of the jth indicator is calculated as:

[0129]

[0130] Among them, a ij Represents the element in the i-th row and j-th column of the matrix P;

[0131] S23, according to the index entropy value e j The weight of each indicator is calculated as:

[0132]

[0133] in, Represents the sum of the entropy values ​​of each indicator in the network.

[0134] S3. The obtained weights and indicators are fused using the Electre method to obtain the importance scores of the nodes in the hypernetwork. The importance scores are then used to sort the nodes and identify the important nodes.

[0135] The ELectre method is a multi-criteria decision analysis method that supports decision makers in making choices by comparing the differences between a set of alternative options. This method is implemented through two steps: elimination and selection transformation. In the elimination step, a filtering strategy is used to gradually eliminate clearly unsuitable or infeasible options based on their performance scores across all criteria, thereby narrowing the decision space. In the selection transformation step, the remaining alternatives are ranked to determine the optimal solution.

[0136] S31, perform weighted calculation on the indicator matrix P to obtain the n×2 order weighted decision matrix R, {r ij ∈R|i=1,2,…,n,j=1,2,…,n}, the calculation formula is:

[0137]

[0138] S32. For any pair of nodes i and j in the network, and the indicators of this pair of nodes, let the indicator set be L = {TI, SI, PI};

[0139] Then the indicator set is divided into two non-overlapping subsets. The former consists of indicators whose weighted values ​​in node i are not less than those in node j, which is called the harmony set H of node i for node j. ij The latter consists of the indicators in node i whose weighted value is lower than that of node j, which is called the discord set B of node i to node jij ;

[0140] S33, based on the harmonious set H ij , construct an n×n order harmony matrix C, {c ij ∈C|i=1,2,…,n,j=1,2,…,n}, where c ij It represents the harmony index of node i to node j, and its calculation formula is:

[0141]

[0142] S34, based on the discordant set B ij , construct an n×n order inharmony matrix D, {d ij ∈D|i=1,2,…,n,j=1,2,…,n}, d ij It represents the disharmony index of node i to node j, and its calculation formula is:

[0143]

[0144] Among them, r il is the element in the i-th row and l-th column of the weighted decision matrix R, r jl is the element in the jth row and lth column of the weighted decision matrix R;

[0145] S35. Based on the harmony matrix C and the disharmony matrix D, construct an n×n order comprehensive dominating matrix U, {u ij ∈U|i=1,2,…,n,j=1,2,…,n}, which reflects the relative advantages and disadvantages of the comprehensive effects of multi-method fusion decision-making at different nodes, where u ij It represents the dominance coefficient of node i to node j, and its calculation formula is:

[0146] u ij =c ij -d ij ;

[0147] u ij The larger it is, the stronger the dominance of node i over node j is, and the better node i is at evaluating node j.

[0148] S36. Calculate the net dominance coefficient of each node based on the comprehensive dominance matrix The calculation formula is:

[0149]

[0150] Among them, u ik represents the dominance coefficient of node i to node k, u ki represents the dominance coefficient of node k to node i;

[0151] Reflects the comprehensive utility of node i after fusion using the Electre method, The larger the value, the better the utility of the node, that is, the greater the influence of the node. Sort the nodes from large to small, and finally select important nodes based on the sorting results.

[0152] In one embodiment, a super network important node identification system based on multi-dimensional decision fusion is provided, including:

[0153] An indicator construction module is used to construct multi-dimensional indicators of hypernetwork nodes, including at least topological indicators, search indicators and propagation indicators;

[0154] The indicator weight acquisition module is used to calculate the weight of each multi-dimensional indicator;

[0155] The node evaluation module is used to obtain the net dominance coefficient of each node based on multi-dimensional indicators and their weights, rank the importance of the nodes, and identify the important nodes.

[0156] Among them, the indicator construction module includes three sub-parts: the first sub-part uses the composite nuclearity information entropy based on the hypernetwork to obtain the topological index of the node in the hypernetwork, which represents the importance score of the node in the topological structure dimension; the second sub-part uses the improved random walk gravity model to construct the search index of the node, which represents the importance score of the node in the search dimension; the third sub-part uses the SIR virus propagation model to construct the propagation index of the node, which represents the importance score of the node in the propagation dimension.

[0157] In one embodiment, an electronic device is provided, comprising a processor, a communication interface, a memory, and a communication bus;

[0158] Among them, the processor, communication interface, and memory communicate with each other through a communication bus;

[0159] The processor is used to call logic instructions in the memory to execute a super network important node identification method based on multi-dimensional decision fusion;

[0160] The super network important node identification method based on multi-dimensional decision fusion includes:

[0161] S1. Constructing a multi-dimensional index of super network nodes including at least topological index, search index and propagation index;

[0162] S2. Calculate the weight of each multi-dimensional indicator;

[0163] S3. Based on the multi-dimensional indicators and their weights, the decision fusion method is used to obtain the net dominance coefficient of each node, rank the importance of the nodes, and identify the important nodes.

[0164] In addition, the logical instructions in the above-mentioned memory can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0165] In one embodiment, a non-transitory computer-readable storage medium is provided, on which computer instructions are stored, the computer instructions causing a computer to execute a method for identifying important nodes in a supernetwork based on multi-dimensional decision fusion;

[0166] The method for identifying important nodes in a super network based on multi-dimensional decision fusion includes:

[0167] S1. Constructing a multi-dimensional index of super network nodes including at least topological index, search index and propagation index;

[0168] S2. Calculate the weight of each multi-dimensional indicator;

[0169] S3. Based on the multi-dimensional indicators and their weights, the decision fusion method is used to obtain the net dominance coefficient of each node, rank the importance of the nodes, and identify the important nodes.

[0170] In one embodiment, the present invention further provides a computer program product, comprising a computer program, which may be stored on a non-transitory computer-readable storage medium, and when the computer program is executed by a processor, the computer is capable of performing a supernetwork important node identification method based on multi-dimensional decision fusion;

[0171] The method for identifying important nodes in a super network based on multi-dimensional decision fusion includes:

[0172] S1. Constructing a multi-dimensional index of super network nodes including at least topological index, search index and propagation index;

[0173] S2. Calculate the weight of each multi-dimensional indicator;

[0174] S3. Based on the multi-dimensional indicators and their weights, the decision fusion method is used to obtain the net dominance coefficient of each node, rank the importance of the nodes, and identify the important nodes.

[0175] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. 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.

[0176] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, or of course, by hardware. Based on this understanding, the essence of the above technical solution or the part that contributes to the existing technology can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or certain parts of the embodiments.

[0177] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes may be made to it in form and detail without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A method for identifying important nodes in a super network based on multi-dimensional decision fusion, characterized in that: The steps include: S1. Constructing a multi-dimensional index of super network nodes including at least topological index, search index and propagation index; The topological index of the hypernetwork node is established using the composite core information entropy method; specifically: First, define the node composite value: ； in, is the degree of node i, For nodes of salvation, For nodes The degree of complexity; The composite kshell value of this node is defined as: ； in, For nodes kshell value, For nodes Based on the kshell value of the hypernetwork, For nodes The composite kshell value of The composite nucleus value is defined as: ； in, is the composite coreness value of node i; The composite nuclearity information entropy is defined as: ； Then, the calculation formula for constructing the node topology index is: ； in, is the topological index of node i, is the composite coreness information entropy of node i, represents the sum of the composite coreness information entropy of each node in the hypernetwork; The search index of the hypernetwork node is established using the improved random walk gravity model; specifically: The improved random walk gravity model is defined as: ； in, It represents the number of composite paths of length l between node i and node j. The number of composite paths is the sum of the number of hyperedge paths and ordinary network paths. The calculation formula is: ； here is the number of common network paths of length l between node i and node j, is the number of hyperedge paths of length l between node i and node j; n is the number of network nodes, represents the number of all l-order paths starting from node i, represents the composite degree of node i, represents the SimRank similarity value between node i and node j; represents the gravitational force between node i and node j, so the total gravitational force of node i can be obtained as: ； Where V represents the set of all nodes in the hypernetwork; the calculation formula for constructing the node search index is: ； in, is the search index of node i, represents the sum of the total gravitational forces of each node in the hypernetwork; The propagation index of the hypernetwork node adopts the SIR virus propagation model, defines each node as the initial infected node for simulation, and uses the propagation ability of each node as the propagation index; specifically: Using the classic SIR virus propagation model as a carrier, each node in the hypernetwork is set as the initial infected node in turn, and the infected node is defined as the node that has a normal edge relationship with it, as well as the node that has a hyperedge connection with it. Finally, after the end of the propagation, the sum of the number of infected people and the number of recovered people in the network is counted to represent the node's propagation capacity, and this propagation capacity is used as the node's propagation indicator. Here, the propagation capacity is defined as: ； in, It represents the number of infected people in the network when node i is set as the initial infected node and until the propagation is completed. It represents the number of people who have recovered in the network when node i is set as the initial infected node and until the spread is completed; The calculation formula for constructing the node propagation index is: ； in, is the propagation index of node i, represents the sum of the propagation capabilities of each node in the hypernetwork; S2. Calculate the weight of each multi-dimensional indicator; S3. Based on the multi-dimensional indicators and their weights, the decision fusion method is used to obtain the net dominance coefficient of each node, rank the importance of the nodes, and identify the important nodes.

2. The method for identifying important nodes in a super network based on multi-dimensional decision fusion according to claim 1 is characterized in that: In step S2, the weights of the multi-dimensional indicators are calculated based on the entropy theory. The specific method is: S21. Use the obtained node indices to establish the indicator matrix P: P= ； S22. Based on Shannon entropy theory, the entropy value of the jth indicator is calculated as: ； in, Represents the element in the i-th row and j-th column of the matrix P; S23, according to the index entropy value The weight of each indicator is calculated as: ； in, Represents the sum of the entropy values ​​of each indicator in the network.

3. The method for identifying important nodes in a super network based on multi-dimensional decision fusion according to claim 2 is characterized in that: In step S3, based on the multi-dimensional indicators and their weights, the decision fusion method is used to obtain the net dominance coefficient of each node, rank the importance of the nodes, and identify the important nodes. The specific method is: S31. Perform weighted calculation on the indicator matrix P to obtain the n×2 order weighted decision matrix R. , the calculation formula is: ； S32. For any pair of nodes i and j in the network, and the various indicators of this pair of nodes, let the indicator set be ; Then the indicator set is divided into two non-overlapping subsets. The former consists of indicators in node i whose weighted value is not less than that of node j, which is called the harmonious set of node i for node j. The latter consists of the indicators in node i whose weighted value is lower than that of node j, which is called the discord set of node i to node j ; S33, based on harmonious set , construct an n×n order harmony matrix C, ,in It represents the harmony index of node i to node j, and its calculation formula is: ； S34, based on the discordant set , construct an n×n order inharmony matrix D, , It represents the disharmony index of node i to node j, and its calculation formula is: ； in, is the element in the i-th row and l-th column of the weighted decision matrix R, is the element in the jth row and lth column of the weighted decision matrix R; S35. Based on the harmony matrix C and the disharmony matrix D, construct an n×n order comprehensive dominance matrix U. , reflecting the relative advantages and disadvantages of the comprehensive effects of multi-method fusion decision-making at different nodes, among which It represents the dominance coefficient of node i to node j, and its calculation formula is: ； The larger it is, the stronger the dominance of node i over node j is, and the better node i is at evaluating node j. S36. Calculate the net dominance coefficient of each node based on the comprehensive dominance matrix , and its calculation formula is: ； in, represents the dominance coefficient of node i to node k, represents the dominance coefficient of node k to node i; Reflects the comprehensive utility of node i after fusion using the Electre method, The larger the value, the better the utility of the node, that is, the greater the influence of the node. Sort the nodes from large to small, and finally select important nodes based on the sorting results.

4. A super network important node identification system using the super network important node identification method based on multi-dimensional decision fusion according to claim 1, characterized in that: include: An indicator construction module, used to construct multi-dimensional indicators of hypernetwork nodes including at least topological indicators, search indicators and propagation indicators; The indicator weight acquisition module is used to calculate the weight of each multi-dimensional indicator; The node evaluation module is used to obtain the net dominance coefficient of each node based on multi-dimensional indicators and their weights, rank the importance of the nodes, and identify the important nodes.

5. An electronic device, characterized in that: including a processor, a communication interface, a memory and a communication bus; Among them, the processor, communication interface, and memory communicate with each other through a communication bus; The processor is used to call the logic instructions in the memory to execute the super network important node identification method based on multi-dimensional decision fusion as described in any one of claims 1 to 3.

6. A non-transitory computer-readable storage medium, characterized in that Computer instructions are stored thereon, which enable the computer to execute the super network important node identification method based on multi-dimensional decision fusion as described in any one of claims 1 to 3.

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