Methods, systems, devices, and media for disintegrating complex networks based on centrality metrics

Abstract

The application discloses a complex network disintegration method and system based on centrality measurement, a device and a medium. The method comprises the following steps: constructing a complex network containing geometric structure and topological structure; constructing a geometric feature item for calculating geometric structure eigenvalues of all nodes in the geometric structure; constructing a topological feature item for calculating topological structure eigenvalues of all nodes in the topological structure; constructing a target differential equation according to the geometric feature item and the topological feature item; calculating the importance score of each node in the complex network through the target differential equation; sorting each node according to the importance score, and disintegrating the complex network according to the sorting result. The application can improve the effect and efficiency of complex network disintegration.

Description

Technical Field

[0001] This application relates to the field of network disintegration technology, and in particular to a method, system, device and medium for disintegrating complex networks based on centrality metrics. Background Technology

[0002] Complex networks are models of complex systems, widely used to describe the connections and interactions within them, such as biological networks, neural networks, and power grids. Existing centrality measures are primarily based on topological design, such as degree centrality, betweenness centrality, proximity centrality, K-core centrality, Katz centrality, and eigenvector centrality. Degree centrality considers only the number of connected nodes, neglecting the global structure, making it difficult to identify nodes that act as bridges in global connections within neural networks. While betweenness centrality assesses influence by examining the connection strength between adjacent nodes, it is essentially a recursive calculation of local features, failing to capture pivotal nodes in deep propagation paths. Proximity centrality identifies "bridge" nodes by calculating the frequency of a node's appearance in all shortest paths, but its high computational complexity leads to severe scalability issues in large-scale networks. K-core centrality reveals the core-periphery structure of the network by iteratively stripping away low-degree nodes, but this method's assessment of node importance is too discretized, failing to distinguish subtle differences between nodes within the same k-shell layer. Katz centrality measures node influence by weighting the contributions of different path lengths. While its exponential decay parameter can adjust the balance between global and local factors, the optimal decay coefficient is difficult to determine in actual neural networks. Eigenvector centrality defines node importance as the weighted sum of its neighbors, which theoretically reflects the global connectivity pattern. However, its linear superposition assumption fundamentally contradicts the nonlinear activation mechanisms prevalent in neural networks.

[0003] In complex networks, geometric and topological structures often coexist, and the network structure changes with the removal of nodes. Existing methods, which focus on a single structure type or employ static fusion strategies, struggle to adapt to the dynamic nature of complex networks. Although existing methods improve node importance measurement by integrating local and global topological features, the crucial role of network structure in system disintegration remains insufficiently quantified. Consequently, existing network disintegration methods exhibit poor disintegration performance and low efficiency. Summary of the Invention

[0004] This application aims to propose a method, system, device, and medium for dismantling complex networks based on centrality metrics, which can improve the effectiveness and efficiency of dismantling complex networks.

[0005] In a first aspect, embodiments of this application provide a method for disintegrating complex networks based on centrality metrics, the method comprising:

[0006] Constructing complex networks that include geometric and topological structures;

[0007] Construct a geometric feature term for calculating the geometric feature values ​​of all nodes in the geometric structure;

[0008] Construct a topology feature term for calculating the topology feature values ​​of all nodes in the topology;

[0009] Construct the target differential equation based on the geometric and topological feature terms;

[0010] The importance score of each node in the complex network is calculated using the objective differential equation.

[0011] Each node is ranked according to its importance score, and the complex network is dismantled based on the ranking results.

[0012] Compared with the prior art, the first aspect of this application has the following beneficial effects:

[0013] This method constructs a complex network containing geometric and topological structures; it then constructs geometric feature terms to calculate the geometric feature values ​​of all nodes in the geometric structure; it constructs topological feature terms to calculate the topological feature values ​​of all nodes in the topological structure; based on the geometric and topological feature terms, it constructs a target differential equation; it calculates the importance score of each node in the complex network using the target differential equation; it ranks each node according to its importance score and disassembles the complex network based on the ranking results. Thus, by quantifying the features of the geometric and topological structures and constructing the target differential equation based on these features, it can adapt to different types of complex networks. By using the target differential equation to calculate the importance score of each node in the complex network and then disassembling the complex network based on the importance score, it can improve the effectiveness and efficiency of complex network disassembly.

[0014] In some implementations, constructing the geometric feature terms for calculating the geometric feature values ​​of all nodes in the geometry includes:

[0015] ;

[0016] in, Represents a node The ratio of the number of participants forming triangles to the number of participants forming triangles in the entire network. Represents a node The neighborhood group, Represents a node The neighborhood group, Represents a node and nodes The number of neighbors in total. Represents a node The neighborhood group, Represents a node and nodes The number of neighbors in total. It represents the set of all nodes in a complex network.

[0017] In some implementations, constructing the topology feature terms for calculating the topology feature values ​​of all nodes in the topology includes:

[0018] ;

[0019] in, The first high-topology eigenvalue represents the value of the node that connects core neighbor nodes and is located at the intersection of redundant paths. Nodes, wherein the core neighbor nodes are neighbor nodes whose k-shell values ​​are greater than a preset value. Represents a node The neighborhood group, This represents the direct connectivity degree of neighboring nodes. Represents a node k-shell value, It represents the set of all nodes in a complex network.

[0020] In some implementations, constructing the target differential equation based on the geometric feature terms and the topological feature terms includes:

[0021] Calculate the geometric structural feature values ​​of all nodes in the complex network based on the geometric feature terms;

[0022] Construct a geometric feature value matrix based on the geometric feature values ​​of all nodes in the complex network;

[0023] Calculate the topological feature values ​​of all nodes in the complex network based on the aforementioned topological feature terms;

[0024] Construct a topology feature value matrix based on the topology feature values ​​of all nodes in the complex network;

[0025] Based on the geometric eigenvalue matrix and the topological eigenvalue matrix, construct the target differential equation.

[0026] In some implementations, calculating the importance score of each node in the complex network using the target differential equation includes:

[0027] The objective differential equation is constructed into a node importance equation for calculating the importance score of each node in the complex network;

[0028] The steady-state solution of the node importance equation is obtained by iterative method, and the steady-state solution is used as the importance score of the node.

[0029] In some implementations, constructing the target differential equation into a node importance equation for calculating the importance score of each node in the complex network includes:

[0030] ;

[0031] in, Represents a node Importance score This represents the threshold time required for the target differential equation to reach a steady state. and Indicates dynamic parameters. Represents a node Geometric structural eigenvalues, Represents a node The number of neighbors, Represents a node The neighborhood group, Represents a node neighboring nodes Importance score Represents a node The topological eigenvalues.

[0032] In some implementations, after constructing the target differential equation into a node importance equation for calculating the importance score of each node in the complex network, the method further includes:

[0033] If the geometric features of a complex network are more prominent than the topological features, then the parameters... The larger the value of ;

[0034] If the characteristics of the topology in a complex network are more prominent than those of the geometric structure, then the parameters... The larger the value of ;

[0035] For the parameters and the parameters A grid search was used for selection.

[0036] Secondly, embodiments of this application also provide a complex network disintegration system based on a centrality metric, the system comprising:

[0037] Complex network building blocks are used to construct complex networks that include geometric and topological structures.

[0038] The first feature term construction unit is used to construct geometric feature terms for calculating the geometric feature values ​​of all nodes in the geometric structure;

[0039] The second feature term construction unit is used to construct topological feature terms for calculating the topological feature values ​​of all nodes in the topological structure;

[0040] A differential equation construction unit is used to construct a target differential equation based on the geometric feature terms and the topological feature terms.

[0041] Importance score calculation unit, used to calculate the importance score of each node in the complex network through the target differential equation;

[0042] A complex network disintegration unit is used to sort each node according to the importance score and disintegrate the complex network according to the sorting result.

[0043] Thirdly, embodiments of this application also provide an electronic device, including at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions executable by the at least one control processor, the instructions being executed by the at least one control processor to enable the at least one control processor to perform a complex network disintegration method based on centrality metric as described above.

[0044] Fourthly, embodiments of this application also provide a computer-readable storage medium storing computer-executable instructions for causing a computer to execute a complex network disintegration method based on centrality metrics as described above.

[0045] It is understood that the beneficial effects of the second to fourth aspects compared with the related technologies are the same as the beneficial effects of the first aspect compared with the related technologies. Please refer to the relevant description in the first aspect above, which will not be repeated here. Attached Figure Description

[0046] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0047] Figure 1 This is a flowchart illustrating an embodiment of the complex network disintegration method based on centrality metric provided in this application;

[0048] Figure 2 This is a schematic diagram of network structure competition in the best embodiment of the complex network disintegration method based on centrality metric provided in this application;

[0049] Figure 3This is a schematic diagram illustrating the removal of high G values ​​in the best embodiment of the complex network disintegration method based on centrality metric provided in this application;

[0050] Figure 4 This is a schematic diagram illustrating the removal of high T values ​​in the best embodiment of the complex network disintegration method based on centrality metric provided in this application;

[0051] Figure 5 This is a schematic diagram of an artificial network in the best embodiment of the complex network disintegration method based on centrality metric provided in this application;

[0052] Figure 6 This is a comparative diagram of network disintegration in the best embodiment of the complex network disintegration method based on centrality metric provided in this application;

[0053] Figure 7 This is a schematic diagram of parameter sensitivity analysis in the best embodiment of the complex network disintegration method based on centrality metric provided in this application;

[0054] Figure 8 This is a schematic diagram of the structure of an embodiment of the complex network disintegration system based on centrality metric provided in this application;

[0055] Figure 9 This is a schematic diagram of the structure of an embodiment of the electronic device provided in this application. Detailed Implementation

[0056] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0057] In the description of this application, the use of terms such as "first," "second," etc., is for the purpose of distinguishing technical features only and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or the order of the technical features indicated.

[0058] In the description of this application, it should be understood that the orientation descriptions, such as up, down, etc., are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and 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, and therefore should not be construed as a limitation of this application.

[0059] In the description of this application, it should be noted that, unless otherwise explicitly defined, terms such as "setup," "installation," and "connection" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this application in conjunction with the specific content of the technical solution.

[0060] In complex networks, geometric and topological structures often coexist, and the network structure changes with the removal of nodes. Existing methods, which focus on a single structure type or employ static fusion strategies, struggle to adapt to the dynamic nature of complex networks. Although existing methods improve node importance measurement by integrating local and global topological features, the crucial role of network structure in system disintegration remains insufficiently quantified. Consequently, existing network disintegration methods exhibit poor disintegration performance and low efficiency.

[0061] To address the issues of poor performance and low efficiency in existing network disintegration technologies, this application proposes a method, system, device, and medium for disintegrating complex networks based on centrality metrics.

[0062] Reference Figure 1 This application provides a flowchart illustrating a complex network disintegration method based on centrality metrics. This method is applied to electronic devices, such as servers or mobile terminals. Figure 1 As shown, this method for disintegrating complex networks based on centrality metrics may include the following steps:

[0063] Step S101: Construct a complex network that includes geometric and topological structures;

[0064] Step S102: Construct geometric feature terms for calculating the geometric feature values ​​of all nodes in the geometric structure;

[0065] Step S103: Construct topological feature terms for calculating the topological feature values ​​of all nodes in the topological structure;

[0066] Step S104: Construct the target differential equation based on the geometric and topological characteristic terms;

[0067] Step S105: Calculate the importance score of each node in the complex network using the objective differential equation;

[0068] Step S106: Sort each node according to its importance score, and dismantle the complex network according to the sorting results.

[0069] In this embodiment, a complex network containing geometric and topological structures is constructed; geometric feature terms are constructed to calculate the geometric feature values ​​of all nodes in the geometric structure; topological feature terms are constructed to calculate the topological feature values ​​of all nodes in the topological structure; a target differential equation is constructed based on the geometric and topological feature terms; the importance score of each node in the complex network is calculated using the target differential equation; each node is ranked according to its importance score, and the complex network is dismantled based on the ranking results. Thus, by quantifying the features of the geometric and topological structures and constructing the target differential equation based on these features, the system can adapt to different types of complex networks. Calculating the importance score of each node in the complex network using the target differential equation and then dismantling the complex network based on the importance score improves the effectiveness and efficiency of complex network dismantling.

[0070] In some implementations, a geometric feature term is constructed for calculating the geometric feature values ​​of all nodes in the geometry, including:

[0071] ;

[0072] in, Represents a node The ratio of the number of participants forming triangles to the number of participants forming triangles in the entire network. Represents a node The neighborhood group, Represents a node The neighborhood group, Represents a node and nodes The number of neighbors in total. Represents a node The neighborhood group, Represents a node and nodes The number of neighbors in total. It represents the set of all nodes in a complex network.

[0073] In this embodiment, a geometric feature term is constructed to calculate the geometric feature values ​​of all nodes in the geometric structure. The result of this geometric feature term can measure whether a node is located in a triangle-dense region. The larger the value, the more obvious the geometric feature of the node. Removing such nodes will disrupt the information transmission between local nodes and greatly reduce the local network connectivity. This design ensures that the algorithm prioritizes attacking nodes that have a greater influence in the local structure.

[0074] In some implementations, a topological feature term is constructed for calculating the topological feature values ​​of all nodes in the topology, including:

[0075] ;

[0076] in, The first high-topology eigenvalue represents the value of the node that connects core neighbor nodes and is located at the intersection of redundant paths. Nodes, where core neighbor nodes are those with k-shell values ​​greater than a preset value. Represents a node The neighborhood group, This represents the direct connectivity degree of neighboring nodes. Represents a node k-shell value, It represents the set of all nodes in a complex network.

[0077] In this embodiment, a topological feature term is constructed to calculate the topological feature value of all nodes in the topology. The result of the topological feature term indicates that the node with the high topological feature value is connected to the core neighbor and is at the intersection of redundant paths. Removing such nodes will destroy the long-range connection between modules in the complex network, thereby reducing global connectivity.

[0078] In some implementations, the target differential equation is constructed based on geometric and topological characteristic terms, including:

[0079] Calculate the geometric structural feature values ​​of all nodes in a complex network based on geometric feature terms;

[0080] Construct a geometric eigenvalue matrix based on the geometric structural eigenvalues ​​of all nodes in the complex network;

[0081] Calculate the topological characteristic values ​​of all nodes in a complex network based on the topological characteristic terms;

[0082] Construct a topological feature value matrix based on the topological feature values ​​of all nodes in the complex network;

[0083] Construct the objective differential equation based on the geometric eigenvalue matrix and the topological eigenvalue matrix.

[0084] In this embodiment, a target differential equation is constructed based on the geometric eigenvalue matrix and the topological eigenvalue matrix. This allows the target differential equation to adapt to different types of complex networks, laying a solid data foundation for subsequent network disintegration.

[0085] In some implementations, the importance score of each node in the complex network is calculated via a target differential equation, including:

[0086] The objective differential equation is constructed into a node importance equation for calculating the importance score of each node in a complex network;

[0087] The steady-state solution of the node importance equation is obtained by iterative method, and the steady-state solution is used as the importance score of the node.

[0088] In this embodiment, the steady-state solution serves as the importance score of the nodes, representing the priority of node disintegration during network collapse and balancing the contributions of geometry and topology. During network disintegration, this stable ranking guides us to prioritize the removal of nodes that have the greatest impact on network structure and function, thereby achieving efficient network disintegration. Furthermore, the proof of the existence of the steady-state solution ensures that the algorithm can obtain reliable results within a finite number of iterations in practical applications, avoiding infinite loops or unstable results.

[0089] In some implementations, the objective differential equation is constructed as a node importance equation for computing the importance score of each node in a complex network, including:

[0090] ;

[0091] in, Represents a node Importance score This represents the threshold time required for the target differential equation to reach a steady state. and Indicates dynamic parameters. Represents a node Geometric structural eigenvalues, Represents a node The number of neighbors, Represents a node The neighborhood group, Represents a node neighboring nodes Importance score Represents a node The topological eigenvalues.

[0092] In this embodiment, the objective differential equation is constructed as a node importance equation for calculating the importance score of each node in a complex network, and dynamic parameters are adjusted accordingly. and It can dynamically adjust the competition intensity between geometric and topological features in the network. The introduction of these two parameters makes the objective differential equation more adaptable to different types of networks, laying a good data foundation for network disintegration in the later stage.

[0093] In some implementations, after constructing the target differential equation into a node importance equation for computing the importance score of each node in the complex network, the method further includes:

[0094] If the geometric features of a complex network are more prominent than the topological features, then the parameters... The larger the value of ;

[0095] If the characteristics of the topology in a complex network are more prominent than those of the geometric structure, then the parameters... The larger the value of ;

[0096] For parameters and parameters A grid search was used for selection.

[0097] In this embodiment, the parameters are determined through a grid search. and parameters By making selections, the target differential equation can automatically adapt to the structural characteristics of complex networks, select the optimal disintegration parameters, and thus achieve better disintegration results.

[0098] To facilitate understanding by those skilled in the art, a set of preferred embodiments is provided below:

[0099] Identifying key nodes in complex networks is crucial for robust control, information propagation, and structural analysis of complex systems. While existing methods have improved node importance measurement by integrating local and global topological features, the critical role of network structure in system collapse remains insufficiently quantified. To address this challenge, this embodiment proposes a centrality metric, TripRank, based on dynamic competition between geometry and topology. This method constructs a competition mechanism for node influence using differential equations, simultaneously integrating the spatial relationships of nodes in geometric features with the local and global structural attributes in topological features, and introducing dynamic parameters to adaptively adjust the structural competition intensity for different complex networks. Experimental results show that TripRank outperforms several baseline methods in complex network collapse, achieving a performance improvement of 10%-15%. Parameter sensitivity analysis further reveals a non-linear correlation between network density and optimal competition intensity, providing a basis for the adaptability of TripRank in different networks.

[0100] The method in this embodiment specifically includes the following:

[0101] In real-world scenarios, many complex systems can be described using complex networks. For example, biological networks can be used to describe dominance relationships between species, with nodes representing a species; power networks can be used to describe a city's power supply system, where each node represents a transformer; and social networks are used to describe social relationships between people, where nodes represent individuals. The method in this embodiment can be applied to different types of complex networks, and this embodiment does not impose any specific limitations. By studying influential nodes in these networks, important people or things within these systems can be mapped. For these complex networks, this embodiment can categorize their structure into local geometric structures and global topological structures.

[0102] like Figure 2 As shown, black represents the geometric structure region in the network, and gray represents the topological structure region. The structural characteristics of the network are determined by the relative magnitudes of these two structural features, indicating a competitive relationship between geometric and topological structures in terms of network characteristics. In this embodiment, the G value represents the magnitude of the geometric structure feature value in a complex network, and the T value represents the magnitude of the topological structure feature value. If the T value in a complex network is greater than the G value, it indicates that the complex network has strong topological features, making it suitable for key node identification using a topology-based design method. Conversely, if the T value in a complex network is less than the G value, it indicates that the complex network has strong geometric features, making it suitable for key node identification using a geometric structure-based design method. The basic idea of ​​network structure competition, as seen in the figure, is to first measure the structural feature values ​​of each node, then simplify regions with obvious geometric features into a single node, and then judge the structural characteristics of the complex network from the simplified network. Finally, a centrality metric suitable for the network's structural characteristics is used for key node identification.

[0103] 1. Design the TripRank equation (i.e., the objective differential equation).

[0104] To achieve this goal, this embodiment designs the TripRank equation. The TripRank equation mainly consists of geometric feature terms. and topological feature terms constitute( ), where geometric feature terms It mainly measures the local geometric characteristics of nodes, and its specific calculation formula is given in equation (1); topological characteristic term It mainly measures the global topological characteristic value of the node, and its specific calculation formula is shown in equation (2).

[0105] (1);

[0106] (2);

[0107] In equation (1), Represents a node The ratio of the number of participants forming triangles to the number of participants forming triangles in the entire network. This represents the set of all nodes in the network. Represents a node The neighborhood group, Represents a node The neighborhood group, Represents a node and nodes The number of shared neighbors. This result can measure the number of nodes. Whether a node is located in a dense triangular region indicates a more pronounced geometric feature. Removing such nodes disrupts local information transmission and significantly reduces local network connectivity. This design ensures that the algorithm prioritizes attacking nodes with significant influence in the local structure, such as... Figure 3 As shown.

[0108] In equation (2), Represents a node The neighborhood group, This represents the direct connectivity of neighboring nodes and can be used to measure their propagation ability. It is a node The k-shell value is calculated using the k-core decomposition algorithm. It should be noted that the k-core decomposition algorithm is existing technology and will not be described in detail in this embodiment. The k-shell value reflects the hierarchical position of a node in a complex network; a higher value indicates that the node is closer to the network core. The physical meaning it represents is high. Nodes that connect to core neighbors and are located at the intersection of redundant paths will disrupt long-range connections between modules in the network, thereby reducing global connectivity. Figure 4 As shown.

[0109] By synthesizing and rearranging the differential equations, we obtain the TripRank equation (i.e., the target differential equation), as shown in equation (3):

[0110] (3);

[0111] in, This represents a matrix of TripRank scores for all nodes in the network. This represents the geometric eigenvalue matrix of all nodes. This represents the topological eigenvalue matrix of all nodes. This represents the threshold time required for the differential equation to reach a steady state. and For dynamic parameters ( The TripRank equation can dynamically adjust the competition intensity between geometric and topological features in complex networks. The introduction of these two parameters makes the TripRank equation adaptable to different types of complex networks. Therefore, for each node... Its node importance equation can be described as:

[0112] (4);

[0113] in, Represents a node TripRank score, Represents a node Geometric eigenvalues, Represents a node The number of neighbors, Represents a node neighboring nodes The TripRank score (i.e., importance score). Represents a node The topological eigenvalues. Parameters in equation (4) and Used to control the competition intensity of geometric and topological structures in a network, when When, the equation focuses on local geometric attacks; when At this time, the focus is on global topology attacks. This depends on the network's structural characteristics; generally, in networks with distinct geometric features, The larger the value of , the more accurately the equation identifies the key nodes; however, in networks with obvious topological characteristics... The larger the value of , the more accurately the equation identifies the key nodes. It should be noted that, in order to achieve a good disintegration effect, this embodiment... and The parameters are selected through a grid search method. This method allows the target differential equation to automatically adapt to the structural characteristics of the complex network and select the optimal disintegration parameters, thereby achieving a better network disintegration effect.

[0114] The basic steps for network disintegration using TripRank in this embodiment are as follows:

[0115] (1) Set the geometric feature weight parameters and topological feature weight parameters Initialize the node importance score vector The initial value can be set to 0 or a random value.

[0116] (2) Calculate the geometric and topological eigenvalues ​​of each node.

[0117] (3) Obtain the importance score by solving the steady-state solution of the objective differential equation using the iterative method. .

[0118] (4) According to the steady-state solution The importance of each node is ranked, and the complex network is dismantled based on the ranking results.

[0119] 2. Proof that the equation has a solution.

[0120] As mentioned earlier, the steady-state solution of the TripRank equation represents the importance score of a node. From a mathematical perspective, equation (3) is a differential equation if and only if At this point, the equation has a steady-state solution. For the nodes within it... In other words, assuming Then we obtain the steady-state equation:

[0121] (5);

[0122] Summarized as follows:

[0123] (6);

[0124] Define a diagonal matrix ( ), adjacency matrix , Then equation (6) can be expressed as:

[0125] (7);

[0126] To prove that the equation has a solution, we need to further simplify the equation by letting... Then the original expression becomes:

[0127] (8);

[0128] make Its iteration format is:

[0129] (9);

[0130] Assuming the network is strongly connected, the adjacency matrix... Unrepeatable (meaning irreducible from any node in the network) To any node (All paths exist), and their corresponding normalized matrices A matrix that satisfies nonnegativity and has a row sum of 1 is, according to the Perron-Frobenius theorem, a nonnegative irreducible matrix. The largest eigenvalue is 1, corresponding to a unique positive eigenvector. At this point, the iterative equation (9) can converge to the steady-state solution:

[0131] (10);

[0132] because Since it is reversible, a unique steady-state solution exists. This value represents the node disintegration priority in network collapse, balancing the contributions of geometric and topological structures. In the process of complex network disintegration, this stable ranking guides this embodiment to prioritize the removal of nodes that have the greatest impact on network structure and function, thereby achieving efficient network disintegration. Furthermore, the proof of the existence of the steady-state solution ensures that the TripRank algorithm in this embodiment can obtain reliable results within a finite number of iterations in practical applications, without encountering infinite loops or unstable results.

[0133] 3. Time complexity analysis.

[0134] The time complexity of the TripRank algorithm mainly consists of three parts: geometric competition, topological competition, and iterative solution of differential equations. The core of the geometric competition is counting the number of triangles a node participates in; for each node... It is necessary to check whether all possible pairs of nodes in its neighbor set are connected, assuming the average degree of the network is . The time complexity is then O(n). For topology competition terms, it is necessary to calculate the degree of each neighboring node. The time complexity of the k-shell value is as follows: and For nodes The time complexity of the topological term is Finally, there is the iterative calculation part of the equation, assuming the complexity of a single iteration is O(n). It needs to be iterated Then the time complexity of the equation iteration is . Therefore, the total time complexity is Although TripRank has a slightly higher time complexity, the algorithm's time complexity increases linearly with the network size n, making it suitable for networks of various sizes.

[0135] 4. Case studies.

[0136] To further explain the basic principles and process of TripRank breakdown, this example demonstrates it using a simple artificial network. This artificial network has 10 nodes and 17 edges (e.g., ...). Figure 5As shown in the diagram, the network contains numerous triangular structures, with only node 2 not participating in the formation of any triangle. Overall, the network can be abstracted as one with node 4 as the bridge node, the left side representing the geometric region, and the right side representing the topological region.

[0137] After solving the artificial network using the TripRank equation, the parameters are obtained. The optimal trip-disintegration effect indicates that geometric features are slightly stronger than topological features in this network, and theoretically, nodes with strong geometric features should be removed first. Table 1 shows the normalized TripRank scores of each node as the number of iterations increases. As the number of iterations increases, the TripRank scores of nodes 1 and 4 also gradually increase. This indicates that the importance of nodes 1 and 4 gradually increases before the network structure competition reaches a steady state. When the equation solution reaches a steady state, the important nodes in the network are ranked as follows: 4, 3, 8, 1, 6, 7, 5, 10, 9, and 2. Among them, node 4 replaces node 3 as the most important node. Although node 4 is not the node with the strongest geometric features, it has very strong topological features. During the equation iteration process, this feature advantage weakens the influence of node 3, making node 4 the most influential node. This shows that the TripRank solution gradually identifies hidden important nodes in the network.

[0138] Table 1. Scores for each node

[0139]

[0140] 5. Experiments using the method described in this embodiment.

[0141] 5.1 Data Introduction.

[0142] In the experiment testing the effectiveness of the TripRank algorithm, this embodiment used four real-world networks: a Highschool network (representing friendships among boys in a small high school in Illinois); a Caenorhabditis elegans network (representing the metabolic network of Caenorhabditis elegans); a Bitcoin OTC network (representing trust relationships between users); and a Chess network (representing the outcome of a chess game). These networks were undirected and unweighted, and their feature statistics are shown in Table 2. Indicates the number of nodes. Indicates the number of edges. This represents the average degree of a node. This represents the maximum degree of a node. This represents the average distance of the network. Indicates the diameter of the network. This indicates the number of triangles in the network. This indicates the number of clusters in the network. This indicates network density.

[0143] Table 2 Statistical Table of Real Network Characteristics

[0144]

[0145] 5.2 Network Disintegration Experiment.

[0146] In this section, this embodiment evaluates the structural stability of different networks under sequential node attacks based on different centrality metrics and compares the results with those obtained based on TripRank. To evaluate the superiority of TripRank, this embodiment uses the relative size evolution of the maximum connected component (LCC), a fundamental concept in graph theory, as the evaluation metric. The maximum connected component refers to a connected subgraph of a network containing the largest number of nodes, where any two nodes can reach each other via a path and no other nodes can be added without disrupting connectivity. In network robustness research, the relative size evolution of the maximum connected component is often used as a key indicator of overall network connectivity. By comparing the maximum connected component change curves obtained by sequentially removing nodes using different algorithms, the merits and performance of network disintegration algorithms can be intuitively reflected. Its disintegration effect is as follows: Figure 6 As shown, Figure 6 In this embodiment, TripRank is the method used, Tricentrality is a triangle centrality measurement method, and DomiRank is a DomiRank centrality measurement method. Tricentrality and DomiRank are algorithms known to those skilled in the art and are not specifically described in this embodiment. Figure 6 (a) shows the breakdown effect of the three methods in the Highschool network. Figure 6 (b) shows the breakdown effect of three methods in the Caenorhabditis elegans network. Figure 6 (c) is a diagram illustrating the destructive effects of the three methods on the Bitcoin OTC network. Figure 6 (d) shows the breakdown effect of the three methods in the Chess network.

[0147] from Figure 6 As can be seen, TripRank performs well in all four networks. When the proportion of removed nodes reaches 40%, TripRank can reduce the maximum connectivity of the network to below 20%, causing the network to collapse much faster than the other two methods, highlighting the superiority of TripRank. In addition, from... Figure 6 (a) to Figure 6As shown in (d), the speed of TripRank network disintegration increases with the size of the network, and the efficiency also gradually improves. This indicates that TripRank is not only suitable for small-scale networks, but also has good results in disintegrating large-scale networks. This reflects that compared to the other two algorithms, TripRank, by quantifying the geometric and topological features of the network and using differential equation modeling to create dynamic competition, can more accurately and quickly identify key nodes in the network. Setting the maximum network connectivity to 20% as the mark of successful disintegration, TripRank removes an average of 40% of the nodes to successfully disintegrate the network, while the other two methods remove an average of 50% to 55% of the nodes to reduce the maximum network connectivity to 20%. This shows that TripRank improves disintegration efficiency by 10% to 15% compared to the other two methods.

[0148] 5.3 Parameter sensitivity analysis.

[0149] This section primarily explores the impact of parameter values ​​on network collapse performance. We selected the area under the LCC curve (AUC) as the evaluation metric, with each parameter corresponding to an AUC value. By comparing the optimal parameter values ​​for different network collapses, we attempt to find the underlying relationship between parameter values ​​and network size. (Refer to...) Figure 7 , Figure 7 In this embodiment, TripRank AUC represents the area under the AUC curve, and best alpha represents the optimal parameter. Values, Figure 7 In Figure (a), the area under the AUC curve and the optimal parameters of the method in this embodiment are shown. A diagram illustrating the possible values. Figure 7 (b) shows the area under the AUC curve and the optimal parameters of the method in this embodiment in the Caenorhabditis elegans network. A diagram illustrating the possible values. Figure 7 In the middle (c), the area under the AUC curve and the optimal parameters of the method in this embodiment are shown. A diagram illustrating the possible values. Figure 7 In the middle (d), the area under the AUC curve and the optimal parameters of the method in this embodiment are represented in the Chess network. A diagram illustrating the possible values.

[0150] from Figure 7 This shows the AUC and its changing trends for each network under different parameter values, revealing... Figure 7 (a) and Figure 7 In (b), the optimal parameters lie within the interval [a certain range]. Figure 7 (c) and Figure 7The optimal parameter values ​​for (d) fall within the range [insert range here]. Referring to Table 2, this embodiment shows that the higher the network density, the higher the optimal parameter value; conversely, the lower the network density, the lower the optimal parameter value, indicating a positive correlation. From the perspective of the TripRank equation, a larger optimal parameter means a stronger competitive advantage in the network's geometric structure, i.e., more prominent geometric features.

[0151] In addition, this embodiment also shows that the collapse effect of the Bitcoin OTC network and the Chess network is most affected by the parameters, with their AUC variation range around 0.07, while the AUC variation of other networks is all below 0.05. This indicates that the intensity of network structure competition varies among different types of networks, and this method can further test the robustness of the network. In comparison, the Highschool network and the Caenorhabditis elegans network have the strongest robustness among these types of networks, while the Bitcoin OTC network and the Chess network have the weakest robustness. Combining the data in Table 2, it can be found that the network density of the network is lower in the network sensitive to parameters. This indicates that the network with acyclic and simple topology is more susceptible to the influence of parameter selection, that is, the acyclic structure is less stable than the cyclic structure.

[0152] Compared with the prior art, the method of this embodiment has the following advantages:

[0153] The TripRank algorithm proposed in this embodiment provides a new theoretical framework and practical tool for identifying key nodes in complex networks by introducing a dynamic competition mechanism between geometric and topological structures. Based on the modeling method of objective differential equations, TripRank achieves a quantitative balance between local geometric features and global topological features for the first time, and adjusts the competition intensity through dynamic parameters, enabling the method to adapt to the structural characteristics of different networks. Theoretical analysis shows that the steady-state solution of the method in this embodiment is mathematically unique and stable, providing a reliable basis for ranking node importance. Experimental verification shows that TripRank exhibits significant advantages in four different networks, improving the descent rate of the maximum connected component (LCC) by 10% to 15% compared to other algorithms. This breakthrough not only confirms the effectiveness of the structural competition mechanism but also provides new ideas for optimizing network disintegration strategies.

[0154] Reference Figure 8 This application also provides a complex network disintegration system based on centrality metric. The system includes a complex network construction unit 801, a first feature term construction unit 802, a second feature term construction unit 803, a differential equation construction unit 804, an importance score calculation unit 805, and a complex network disintegration unit 806, wherein:

[0155] Complex network building unit 801 is used to build complex networks that include geometric and topological structures;

[0156] The first feature term construction unit 802 is used to construct geometric feature terms for calculating the geometric feature values ​​of all nodes in the geometric structure;

[0157] The second feature term construction unit 803 is used to construct topological feature terms for calculating the topological feature values ​​of all nodes in the topological structure;

[0158] Differential equation construction unit 804 is used to construct the target differential equation based on geometric and topological characteristic terms;

[0159] Importance score calculation unit 805 is used to calculate the importance score of each node in a complex network through the objective differential equation;

[0160] Complex network disintegration unit 806 is used to sort each node according to its importance score and disintegrate the complex network according to the sorting results.

[0161] In some implementations, the first feature construction unit 802 may be specifically used for:

[0162] ;

[0163] in, Represents a node The ratio of the number of participants forming triangles to the number of participants forming triangles in the entire network. Represents a node The neighborhood group, Represents a node The neighborhood group, Represents a node and nodes The number of neighbors in total. Represents a node The neighborhood group, Represents a node and nodes The number of neighbors in total. It represents the set of all nodes in a complex network.

[0164] In some implementations, the second feature construction unit 803 may be specifically used for:

[0165] ;

[0166] in, The first eigenvalue representing the high topological structure The node connects to its core neighbor nodes and is located at the intersection of redundant paths. The core neighbor nodes are those with k-shell values ​​greater than a preset value. Represents a node The neighborhood group, This represents the direct connectivity degree of neighboring nodes. Represents a node k-shell value, It represents the set of all nodes in a complex network.

[0167] In some implementations, the differential equation building unit 804 can be specifically used for:

[0168] Calculate the geometric structural feature values ​​of all nodes in a complex network based on geometric feature terms;

[0169] Construct a geometric eigenvalue matrix based on the geometric structural eigenvalues ​​of all nodes in the complex network;

[0170] Calculate the topological characteristic values ​​of all nodes in a complex network based on the topological characteristic terms;

[0171] Construct a topological feature value matrix based on the topological feature values ​​of all nodes in the complex network;

[0172] Construct the objective differential equation based on the geometric eigenvalue matrix and the topological eigenvalue matrix.

[0173] In some implementations, the importance score calculation unit 805 may be specifically used for:

[0174] The objective differential equation is constructed into a node importance equation for calculating the importance score of each node in a complex network;

[0175] The steady-state solution of the node importance equation is obtained by iterative method, and the steady-state solution is used as the importance score of the node.

[0176] In some implementations, the importance score calculation unit 805 may be specifically used for:

[0177] ;

[0178] in, Represents a node Importance score This represents the threshold time required for the target differential equation to reach a steady state. and Indicates parameters, Represents a node Geometric structural eigenvalues, Represents a node The number of neighbors, Represents a node The neighborhood group, Represents a node neighboring nodes Importance score Represents a node The topological eigenvalues.

[0179] In some implementations, the importance score calculation unit 805 may be specifically used for:

[0180] If the geometric features of a complex network are more prominent than the topological features, then the parameters... The larger the value of ;

[0181] If the characteristics of the topology in a complex network are more prominent than those of the geometric structure, then the parameters... The larger the value of ;

[0182] For parameters and parameters A grid search was used for selection.

[0183] It should be noted that since the complex network disintegration system based on centrality metric in this embodiment is based on the same inventive concept as the complex network disintegration method based on centrality metric described above, the corresponding content in the method embodiment is also applicable to this system embodiment, and will not be described in detail here.

[0184] Reference Figure 9 This application also provides an electronic device, which includes:

[0185] At least one memory;

[0186] At least one processor;

[0187] At least one program;

[0188] The program is stored in memory, and the processor executes at least one program to implement the above-described method for disintegrating complex networks based on centrality metrics.

[0189] This electronic device can be any smart terminal, including mobile phones, tablets, personal digital assistants (PDAs), and in-vehicle computers.

[0190] The electronic devices according to embodiments of this application will now be described in detail.

[0191] The processor 1600 can be implemented using a general-purpose central processing unit (CPU), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this disclosure.

[0192] The memory 1700 can be implemented as a read-only memory (ROM), static storage device, dynamic storage device, or random access memory (RAM). The memory 1700 can store the operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 1700 and is called and executed by the processor 1600 to execute the complex network disintegration method based on centrality metric of the embodiments of this disclosure.

[0193] The input / output interface 1800 is used to implement information input and output.

[0194] The communication interface 1900 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0195] Bus 2000 transmits information between various components of the device (e.g., processor 1600, memory 1700, input / output interface 1800, and communication interface 1900);

[0196] The processor 1600, memory 1700, input / output interface 1800 and communication interface 1900 are connected to each other within the device via bus 2000.

[0197] This disclosure also provides a storage medium, which is a computer-readable storage medium storing computer-executable instructions for causing a computer to perform the above-described method for disintegrating complex networks based on centrality metrics.

[0198] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0199] The embodiments described in this disclosure are for the purpose of more clearly illustrating the technical solutions of this disclosure and do not constitute a limitation on the technical solutions provided by this disclosure. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by this disclosure are also applicable to similar technical problems.

[0200] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this disclosure, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0201] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0202] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0203] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0204] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0205] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0206] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0207] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0208] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks. The embodiments of this application have been described in detail above with reference to the accompanying drawings, but this application is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of this application.

[0209] The embodiments of this application have been described in detail above with reference to the accompanying drawings. However, this application is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of this application.

Claims

1. A method for complex network disintegration based on centrality measures, characterized in that, The method comprises: constructing a complex network comprising a geometric structure and a topological structure, wherein the complex network is any one of a biological network for describing the dominance relationship between species and a power network for describing a power supply system, each node in the complex network constructed by the biological network represents a biological organism, and each node in the complex network constructed by the power network represents a transformer; constructing a geometric feature item for calculating geometric feature values of all nodes in the geometric structure, comprising: ； wherein, denotes a node participates in the most triangles, denotes a node a neighbor set of denotes a node a neighbor set of denotes a node a number of neighbors common to a number of neighbors common to denotes a node a neighbor set of denotes a node a number of neighbors common to a number of neighbors common to denotes a set of all nodes in a complex network; constructing a topological feature item for calculating topological feature values of all nodes in the topological structure, comprising: ； wherein, represents the first k-shell value of the node, represents the k-shell value of the node, represents the neighbor set of the node, represents the direct connectivity degree of the neighbor node, represents the k-shell value of the node, represents the k-shell value of the node, represents the k-shell value of the node, represents the set of all nodes in the complex network; constructing a target differential equation according to the geometric feature item and the topological feature item; calculating an importance score of each node in the complex network through the target differential equation; ranking each node according to the importance score, and disintegrating the complex network according to the ranking result to destroy the connectivity of the network.

2. The centrality measure based complex network disintegration method according to claim 1, wherein, The method comprises: calculating geometric feature values of all nodes in the complex network according to the geometric feature item; constructing a geometric feature value matrix according to the geometric feature values of all nodes in the complex network; calculating topological feature values of all nodes in the complex network according to the topological feature item; constructing a topological feature value matrix according to the topological feature values of all nodes in the complex network; constructing a target differential equation according to the geometric feature value matrix and the topological feature value matrix.

3. The centrality metric based complex network disintegration method according to claim 1, wherein, The method comprises: constructing the target differential equation as a node importance equation for calculating the importance score of each node in the complex network; solving the steady-state solution of the node importance equation by an iterative method, and taking the steady-state solution as the importance score of the node.

4. The centrality measure based complex network disintegration method according to claim 3, wherein, The method comprises: ； wherein, denotes an importance score of a node , denotes a threshold time for a target differential equation to reach a steady state setting, and denotes a dynamic parameter, denotes a geometric structure eigenvalue of a node , denotes a number of neighbors of a node , denotes a neighbor set of a node , denotes an importance score of a neighbor node of a node , denotes a topological structure eigenvalue of a node .

5. The centrality measure based complex network disintegration method according to claim 4, wherein, after constructing the target differential equation as a node importance equation for calculating the importance score of each node in the complex network, the method further comprises: If the characteristics of the geometric structure are more obvious than the characteristics of the topological structure in the complex network, the value of the parameter is larger. If the characteristic of the topology is more obvious than the characteristic of the geometry in the complex network, the value of the parameter is larger. for said parameter and said parameter The grid search is used for selection.

6. A system for complex network disintegration based on centrality measures, comprising: The system comprises: a complex network construction unit configured to construct a complex network comprising a geometric structure and a topological structure, wherein the complex network is any one of a biological network for describing the dominance relationship between species and a power network for describing a power supply system, each node in the complex network constructed by the biological network represents a biological organism, and each node in the complex network constructed by the power network represents a transformer; a first feature item construction unit configured to construct a geometric feature item for calculating geometric feature values of all nodes in the geometric structure, comprising: ； wherein, denotes a node participates in the most triangles, denotes a node of the neighbor set, denotes a node of the neighbor set, denotes a node and the number of neighbors common to the node , denotes a node of the neighbor set, denotes a node and the number of neighbors common to the node , denotes the set of all nodes in the complex network; a second feature item construction unit configured to construct a topological feature item for calculating topological feature values of all nodes in the topological structure, comprising: ； in, The first high-topology eigenvalue represents the value of the node that connects core neighbor nodes and is located at the intersection of redundant paths. Nodes, wherein the core neighbor nodes are neighbor nodes whose k-shell values ​​are greater than a preset value. Represents a node The neighborhood group, This represents the direct connectivity degree of neighboring nodes. Represents a node k-shell value, Represents the set of all nodes in a complex network; a differential equation construction unit configured to construct a target differential equation according to the geometric feature item and the topological feature item; an importance score calculation unit configured to calculate an importance score of each node in the complex network through the target differential equation; and an importance score calculation unit configured to calculate an importance score of each node in the complex network through the target differential equation. A complex network disintegration unit for ranking each node according to the importance score and disintegrating the complex network according to the ranking result to destroy the connectivity of the network.

7. An electronic device, comprising: A computer program product comprising at least one control processor and a memory communicatively connected to the at least one control processor; the memory storing instructions executable by the at least one control processor, the instructions being executed by the at least one control processor to enable the at least one control processor to perform the method of disintegrating a complex network based on a centrality measure according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, The computer readable storage medium stores computer executable instructions for causing a computer to perform the method of disintegrating a complex network based on a centrality measure according to any one of claims 1 to 5.

Images