Complex network disintegration method, system and device based on centrality measurement and medium

Abstract

The invention discloses a complex network disintegration method, system and device based on centrality measurement and a medium. The method comprises the following steps: constructing a complex network comprising a geometric structure and a topological structure; constructing geometric feature items used for calculating geometric structure feature values of all nodes in the geometric structure; constructing topological feature items used for calculating topological structure feature values of all nodes in the topological structure; constructing a target differential equation according to the geometric feature items and the topological feature items; calculating the importance score of each node in the complex network through the target differential equation; and sorting each node according to the importance score, and collapsing the complex network according to a sorting result. According to the invention, the effect and efficiency of complex network disintegration can be improved.

Description

Technical Field

[0001] The present application relates to the field of network disintegration technology, and in particular to a complex network disintegration method, system, device and medium based on centrality measurement. Background Art

[0002] Complex networks are models of complex systems and are widely used to describe the connections and interactions within them, such as biological networks, neural networks, and power grids. Existing centrality metrics are primarily based on topological design, such as degree centrality, betweenness centrality, closeness centrality, K-core centrality, Katz centrality, and eigenvector centrality. Degree centrality only considers the number of connected nodes, ignoring global structure. This makes it difficult to focus on nodes that act as bridges for global connectivity in neural networks. While betweenness centrality assesses influence by examining the strength of connections between adjacent nodes, it is essentially a recursive calculation of local features, making it difficult to capture hub nodes in deep network propagation paths. Closeness centrality identifies "bridge" nodes by calculating the frequency of a node's appearance in all shortest paths, but its computational complexity is high and faces serious scalability issues in large-scale networks. K-core centrality reveals the core-periphery structure of a network by iteratively removing low-degree nodes. However, this method overly discretizes node importance and cannot 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 global-local balance, determining the optimal decay coefficient is difficult in practical neural networks. Eigenvector centrality defines node importance as the weighted sum of its neighboring nodes, which theoretically reflects global connectivity patterns. However, its linear superposition assumption is fundamentally inconsistent with the nonlinear activation mechanisms prevalent in neural networks.

[0003] Complex networks often combine geometric and topological structures, and the network's structure changes as nodes are removed. Existing methods focus on a single structural type or employ static fusion strategies, making them ill-suited to the dynamic nature of complex networks. While existing methods improve node importance metrics by integrating local and global topological features, the crucial role of network structure in system collapse remains under-quantified. Consequently, existing network collapse methods exhibit poor collapse effectiveness and low efficiency. Summary of the Invention

[0004] This application aims to propose a complex network disintegration method, system, device and medium based on centrality measurement, which can improve the effect and efficiency of complex network disintegration.

[0005] In a first aspect, an embodiment of the present application provides a complex network disintegration method based on centrality measurement, the method comprising: Construct complex networks that include geometric and topological structures; Constructing geometric feature items for calculating geometric structure feature values of all nodes in the geometric structure; Constructing a topological feature item for calculating topological structure feature values of all nodes in the topological structure; Constructing a target differential equation according to the geometric characteristic term and the topological characteristic term; Calculating the importance score of each node in the complex network by using the target differential equation; Each node is sorted according to the importance score, and the complex network is collapsed according to the sorting result.

[0006] Compared with the prior art, the first aspect of the present application has the following beneficial effects: This method constructs a complex network containing both geometric and topological structures; constructs geometric characteristic terms for calculating the geometric eigenvalues of all nodes in the geometric structure; constructs topological characteristic terms for calculating the topological eigenvalues of all nodes in the topological structure; constructs a target differential equation based on the geometric and topological characteristic terms; calculates the importance score of each node in the complex network using the target differential equation; ranks each node according to the importance score, and collapses the complex network based on the ranking results. By quantifying the characteristics of the geometric and topological structures and constructing a target differential equation based on the geometric and topological characteristic terms, the method is adaptable to different types of complex networks. Using the target differential equation to calculate the importance score of each node in the complex network, and then collapsing the complex network based on the importance score, the method can improve the effectiveness and efficiency of complex network collapse.

[0007] In some embodiments, constructing geometric feature items for calculating geometric structure feature values of all nodes in the geometric structure includes: ; in, Representation node The ratio of the number of triangles participating in the construction to the largest number of triangles participating in the construction of the entire network, Representation node The neighbor set of Representation node The neighbor set of Representation node and nodes The number of neighbors in common, Representation node The neighbor set of Representation node and nodes The number of neighbors in common, Represents the set of all nodes in a complex network.

[0008] In some embodiments, constructing a topological feature item for calculating topological structure feature values of all nodes in the topological structure includes: ; in, The first node represents a high topological structure feature value that connects core neighbor nodes and is at the intersection of redundant paths. Node, wherein the core neighbor node is a neighbor node whose k-shell value is greater than a preset value, Representation node The neighbor set of represents the direct connection degree of neighbor nodes, Representation node The k-shell value of Represents the set of all nodes in a complex network.

[0009] In some embodiments, constructing a target differential equation based on the geometric characteristic term and the topological characteristic term includes: Calculating geometric structure eigenvalues of all nodes in the complex network according to the geometric characteristic items; Constructing a geometric eigenvalue matrix according to the geometric structure eigenvalues of all nodes in the complex network; Calculating topological structure characteristic values of all nodes in the complex network according to the topological characteristic items; Constructing a topological eigenvalue matrix according to the topological structure eigenvalues of all nodes in the complex network; A target differential equation is constructed according to the geometric eigenvalue matrix and the topological eigenvalue matrix.

[0010] In some embodiments, calculating the importance score of each node in the complex network using the target differential equation includes: constructing the target differential equation as a node importance equation for calculating the importance score of each node in the complex network; The steady-state solution of the node importance equation is solved by an iterative method, and the steady-state solution is used as the importance score of the node.

[0011] In some embodiments, constructing the target differential equation as a node importance equation for calculating the importance score of each node in the complex network includes: ; in, Representation node The importance score of It represents the threshold time for the target differential equation to reach the steady state. and Represents dynamic parameters, Representation node The geometric structure eigenvalues of Representation node The number of neighbors, Representation node The neighbor set of Representation node Neighbor nodes The importance score of Representation node The topological structure eigenvalues of .

[0012] In some embodiments, 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 includes: If the geometric structure features are more obvious than the topological structure features in a complex network, the parameter The larger the value of ; If the topological structure is more prominent than the geometric structure in a complex network, the parameter The larger the value of ; For the parameters and the parameters Grid search is used for selection.

[0013] In a second aspect, an embodiment of the present application further provides a complex network disintegration system based on centrality measurement, the system comprising: Complex network construction unit, used to construct complex networks containing geometric and topological structures; A first feature item construction unit is used to construct geometric feature items for calculating geometric structure feature values of all nodes in the geometric structure; A second feature item construction unit is used to construct a topology feature item for calculating the topology structure feature values of all nodes in the topology structure; A differential equation construction unit, configured to construct a target differential equation based on the geometric characteristic term and the topological characteristic term; an importance score calculation unit, configured to calculate the importance score of each node in the complex network by using the target differential equation; The complex network collapse unit is used to sort each node according to the importance score and collapse the complex network according to the sorting result.

[0014] In a third aspect, an embodiment of the present application also provides an electronic device comprising at least one control processor and a memory for communicating with the at least one control processor; the memory stores instructions that can be executed by the at least one control processor, and the instructions are executed by the at least one control processor so that the at least one control processor can execute a complex network disintegration method based on centrality measurement as described above.

[0015] In a fourth aspect, an embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the complex network disintegration method based on centrality measurement as described above.

[0016] It can be understood that the beneficial effects of the above-mentioned second to fourth aspects compared with the relevant technologies are the same as the beneficial effects of the above-mentioned first aspect compared with the relevant technologies. Please refer to the relevant description in the above-mentioned first aspect and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which: Figure 1 1 is a flow chart of an embodiment of a complex network disintegration method based on centrality measurement provided by the present application; Figure 2 This is a schematic diagram of network structure competition in a preferred embodiment of the complex network disintegration method based on centrality measurement provided by the present application; Figure 3 This is a schematic diagram of removing high G values in the best embodiment of the complex network disintegration method based on centrality measurement provided by this application; Figure 4 This is a schematic diagram of removing high T values in the best embodiment of the complex network disintegration method based on centrality measurement provided by this application; Figure 5 1 is a schematic diagram of an artificial network in a preferred embodiment of the complex network disintegration method based on centrality measurement provided by the present application; Figure 6 1. It is a schematic diagram comparing network disintegration in a preferred embodiment of the complex network disintegration method based on centrality measurement provided by the present application; Figure 7 1 is a schematic diagram of parameter sensitivity analysis in a preferred embodiment of the complex network disintegration method based on centrality measurement provided by the present application; Figure 8 1 is a schematic structural diagram of an embodiment of a complex network disintegration system based on centrality measurement provided by the present application; Figure 9It is a structural diagram of an embodiment of the electronic device provided by this application. DETAILED DESCRIPTION

[0018] The following describes in detail embodiments of the present application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application and are not to be construed as limiting the present application.

[0019] In the description of this application, if there is a description of first, second, etc., it is only for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0020] In the description of this application, it should be understood that descriptions involving orientation, such as the orientation or positional relationship indicated by 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, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on this application.

[0021] In the description of this application, it should be noted that, unless otherwise clearly defined, terms such as setting, installing, and connecting should be understood in a broad sense, and technical personnel in the relevant technical field can reasonably determine the specific meaning of the above terms in this application based on the specific content of the technical solution.

[0022] Complex networks often combine geometric and topological structures, and the network's structure changes as nodes are removed. Existing methods focus on a single structural type or employ static fusion strategies, making them ill-suited to the dynamic nature of complex networks. While existing methods improve node importance metrics by integrating local and global topological features, the crucial role of network structure in system collapse remains under-quantified. Consequently, existing network collapse methods exhibit poor collapse effectiveness and low efficiency.

[0023] In order to solve the problem that the existing technology has a relatively poor effect on network disintegration and a relatively low disintegration efficiency, the present application proposes a complex network disintegration method, system, device and medium based on centrality measurement.

[0024] Reference Figure 1 , a flow chart of a complex network disintegration method based on centrality measurement provided by an embodiment of the present application. The complex network disintegration method based on centrality measurement is applied to an electronic device, which may be a server or a mobile terminal. Figure 1 As shown, the complex network disintegration method based on centrality measurement may include the following steps: Step S101: constructing a complex network including geometric structure and topological structure; Step S102: constructing geometric feature items for calculating geometric structure feature values of all nodes in the geometric structure; Step S103: constructing a topology feature item for calculating the topology structure feature values of all nodes in the topology structure; Step S104: constructing a target differential equation based on the geometric characteristic terms and the topological characteristic terms; Step S105: Calculate the importance score of each node in the complex network through the target differential equation; Step S106: sort each node according to the importance score, and collapse the complex network according to the sorting result.

[0025] In this embodiment, a complex network including geometric and topological structures is constructed; a geometric feature term is constructed for calculating the geometric feature values of all nodes in the geometric structure; a topological feature term is constructed for calculating 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; an importance score of each node in the complex network is calculated using the target differential equation; each node is sorted according to the importance score, and the complex network is collapsed based on the sorting result. In this way, by quantifying the characteristics of the geometric and topological structures and constructing the target differential equation based on the geometric and topological feature terms, the method can adapt to different types of complex networks, calculate the importance score of each node in the complex network using the target differential equation, and then collapse the complex network based on the importance score, thereby improving the effect and efficiency of complex network collapse.

[0026] In some embodiments, constructing a geometric feature term for calculating geometric structure feature values of all nodes in the geometric structure includes: ; in, Representation node The ratio of the number of triangles participating in the construction to the largest number of triangles participating in the construction of the entire network, Representation node The neighbor set of Representation node The neighbor set of Representation node and nodes The number of neighbors in common, Representation node The neighbor set of Representation node and nodes The number of neighbors in common, Represents the set of all nodes in a complex network.

[0027] In this embodiment, a geometric feature term is constructed to calculate the geometric structure eigenvalues of all nodes in the geometric structure. The result of this geometric feature term can be used to measure whether the node is located in a dense triangle area. The larger the value, the more obvious the node's geometric characteristics are. Removing such nodes will disrupt information transmission among local nodes and significantly reduce local network connectivity. This design ensures that the algorithm prioritizes attacking nodes with greater influence in the local structure.

[0028] In some embodiments, constructing a topology feature item for calculating topology structure feature values of all nodes in a topology structure includes: ; in, The first node represents a high topological structure feature value that connects core neighbor nodes and is at the intersection of redundant paths. Nodes, where core neighbor nodes are neighbor nodes whose k-shell value is greater than the preset value. Representation node The neighbor set of represents the direct connection degree of neighbor nodes, Representation node The k-shell value of Represents the set of all nodes in a complex network.

[0029] In this embodiment, a topological feature item is constructed to calculate the topological structure eigenvalues of all nodes in the topological structure. The result of the topological feature item indicates that nodes with high topological structure eigenvalues are connected to core neighbors and are 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.

[0030] In some embodiments, constructing a target differential equation based on geometric characteristic terms and topological characteristic terms includes: Calculate the geometric structure eigenvalues of all nodes in the complex network based on the geometric characteristic items; According to the geometric structure eigenvalues of all nodes in the complex network, a geometric eigenvalue matrix is constructed; Calculate the topological structure eigenvalues of all nodes in the complex network based on the topological characteristic items; According to the topological structure eigenvalues of all nodes in the complex network, a topological eigenvalue matrix is constructed; The target differential equation is constructed based on the geometric eigenvalue matrix and the topological eigenvalue matrix.

[0031] In this embodiment, the target differential equation is constructed based on the geometric eigenvalue matrix and the topological eigenvalue matrix. In this way, the target differential equation can adapt to different types of complex networks, laying a good data foundation for subsequent network collapse.

[0032] In some embodiments, calculating the importance score of each node in a complex network by a target differential equation includes: The target differential equation is constructed as a node importance equation for calculating the importance score of each node in the complex network; The steady-state solution of the node importance equation is solved by an iterative method, and the steady-state solution is used as the importance score of the node.

[0033] In this example, the steady-state solution serves as a node importance score, representing the node's priority for dismantling during network dismantling, balancing the contributions of geometry and topology. During network dismantling, this stable ranking guides us to prioritize the removal of nodes that have the greatest impact on network structure and functionality, thereby achieving efficient network dismantling. Furthermore, proof of the existence of the steady-state solution ensures that the algorithm can produce reliable results within a limited number of iterations in practical applications, without infinite loops or unstable results.

[0034] In some embodiments, the target differential equation is constructed as a node importance equation for calculating the importance score of each node in a complex network, including: ; in, Representation node The importance score of It represents the threshold time for the target differential equation to reach the steady state. and Represents dynamic parameters, Representation node The geometric structure eigenvalues of Representation node The number of neighbors, Representation node The neighbor set of Representation node Neighbor nodes The importance score of Representation node The topological structure eigenvalues of .

[0035] In this embodiment, the target differential equation is constructed as a node importance equation for calculating the importance score of each node in the complex network, and the dynamic parameters are adjusted. and , which can dynamically adjust the competition intensity between geometric features and topological features in the network. The introduction of these two parameters makes the target differential equation more adaptable to different types of networks, laying a good data foundation for the subsequent network disintegration.

[0036] In some embodiments, 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 includes: If the geometric structure features are more obvious than the topological structure features in a complex network, the parameter The larger the value of ; If the topological structure is more prominent than the geometric structure in a complex network, the parameter The larger the value of ; For parameters and parameters Grid search is used for selection.

[0037] In this embodiment, the parameters are searched by grid. and parameters By making the selection, the target differential equation can automatically adapt to the structural characteristics of the complex network and select the best collapse parameters, thereby achieving a better collapse effect.

[0038] To facilitate understanding by those skilled in the art, a set of best embodiments is provided below: Identifying key nodes in complex networks is of great significance for the robustness control, information dissemination, and structural analysis of complex systems. Although existing methods have improved the measurement of node importance by integrating local and global topological features, the key role of network structure in system collapse has not been fully quantified. To address this challenge, this embodiment proposes a centrality measurement method, TripRank, based on dynamic competition of geometric and topological structures. This method constructs a competition mechanism for node influence through differential equations, simultaneously integrates the spatial position relationship of nodes in geometric features and the local and global structural properties in topological features, and introduces dynamic parameters to adaptively adjust the structural competition intensity of different complex networks. Experimental results show that the TripRank method outperforms multiple baseline methods in the effect of complex network collapse, with a performance improvement of 10%-15%. Parameter sensitivity analysis further shows that network density is nonlinearly related to the optimal competition intensity. This finding provides a basis for the adaptability of the TripRank method in different networks.

[0039] The method of this embodiment specifically includes the following contents: In real-world scenarios, many complex systems can be described using complex networks. For example, biological networks can be used to describe the dominance relationship between species, where the nodes in the network represent an organism; 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 of this embodiment can be applied to complex networks of different types, and this embodiment does not specifically limit this. By studying the influential nodes in these networks, it is possible to map them to important people or things in these systems. For these complex networks, this embodiment can divide the structures therein into local geometric structures and global topological structures.

[0040] like Figure 2 As shown, black represents the geometric structure area in the network, and gray represents the topological structure area in the network. The structural characteristics of the network are determined by the relative size of the characteristics of these two parts of the structure, indicating that there is a competitive relationship between the geometric structure and the topological structure in the network characteristics. In this embodiment, the G value is used to represent the size of the geometric structure characteristic value in the complex network, and the T value is used to represent the size of the topological structure characteristic value in the complex network. If the T value in the complex network is greater than the G value, it means that the complex network has strong topological characteristics and is suitable for using a method based on topological structure design to identify key nodes; conversely, if the T value in the complex network is less than the G value, it means that the complex network has strong geometric characteristics and is suitable for using a method based on geometric structure design to identify key nodes. From the figure, it can be seen that the basic idea of network structure competition is to first measure the structural characteristic value of each node, then simplify the area with obvious geometric characteristics into a node, and then judge the structural characteristics of the complex network from the simplified network, and finally use a centrality measurement method suitable for the structural characteristics of the network to identify its key nodes.

[0041] 1. Design the TripRank equation (i.e., the target differential equation).

[0042] In order to realize this idea, the present embodiment designs the TripRank equation. The TripRank equation is mainly composed of the geometric characteristic terms and topological features constitute( ), where the geometric characteristic term It mainly measures the local geometric eigenvalue of the node. The specific calculation formula is shown in equation (1); the topological characteristic term It mainly measures the global topological characteristic value of the node. The specific calculation formula is shown in Equation (2).

[0043] (1); (2); In equation (1), Representation node The ratio of the number of triangles participating in the construction to the largest number of triangles participating in the construction of the entire network, represents the set of all nodes in the network, Representation node The neighbor set of Representation node The neighbor set of Representation node and nodes The number of common neighbors. This result can measure the node Is it in a dense triangle area? The larger the value, the more obvious the geometric characteristics of the node. Removing such nodes will destroy the information transmission of local nodes and greatly reduce the connectivity of the local network. This design ensures that the algorithm prioritizes attacking nodes that have a greater influence in the local structure, such as Figure 3 shown.

[0044] In equation (2), Representation node The neighbor set of Indicates the direct connection degree of neighbor nodes, which can be used to measure their propagation ability. is a node The k-shell value is calculated using the k-core decomposition algorithm. This algorithm is currently available 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; higher values indicate a node is closer to the network core. The physical meaning is high Nodes connect core neighbors and are at the intersection of redundant paths. Removing such nodes will destroy the long-range connections between modules in the network, thereby reducing global connectivity. Figure 4 shown.

[0045] The TripRank equation (i.e., the target differential equation) is obtained by comprehensive analysis of differential equations, as shown in equation (3): (3); in, Represents the TripRank score matrix of all nodes in the network, represents the geometric eigenvalue matrix of all nodes, represents the topological eigenvalue matrix of all nodes, represents the threshold time for the differential equation to reach steady state, and is a dynamic parameter ( ), can dynamically adjust the competition intensity between geometric features and topological features in complex networks. The introduction of these two parameters makes the TripRank equation more adaptable to different types of complex networks. Therefore, for each node , its node importance equation can be described as: (4); in, Representation node The TripRank score value, Representation node The geometric eigenvalues of Representation node The number of neighbors, Representation node Neighbor nodes The TripRank score (i.e., importance score) of Representation node The topological eigenvalue of . The parameters in equation (4) and Used to control the competition intensity of the geometry and topology in the network. When , the equation focuses on local geometric attack; when When , it focuses on global topology attacks. This depends on the structural characteristics of the network. Generally speaking, in a network with obvious geometric characteristics, The larger the value of , the more accurate the key nodes identified by the equation; in a network with obvious topological characteristics, The larger the value of , the more accurate the key nodes identified by the equation. It should be noted that in order to achieve a good collapse effect, in this embodiment and It is selected through grid search. Through grid search, the target differential equation can automatically adapt to the structural characteristics of the complex network, select the best collapse parameters, and thus achieve better network collapse effect.

[0046] The basic steps of using TripRank to perform network collapse in this embodiment are: (1) Setting 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.

[0047] (2) Calculate the geometric eigenvalue and topological eigenvalue of each node.

[0048] (3) Solve the steady-state solution of the target differential equation by iterative method and obtain the importance score .

[0049] (4) According to the steady-state solution The importance of each node is ranked and the complex network is collapsed according to the ranking results.

[0050] 2. Prove that the equation has a solution.

[0051] As mentioned above, the steady-state solution of the TripRank equation represents the importance score of the node. From a mathematical point of view, equation (3) is a differential equation if and only if When , the equation has a steady-state solution. For the nodes In terms of, assuming , then the steady-state equation is obtained: (5); Arranged: (6); Define a diagonal matrix ( ), the adjacency matrix , , then equation (6) can be expressed as: (7); In order to prove that the equation has a solution, we need to further simplify the equation, let , then the original formula becomes: (8); make The iteration format is: (9); Assuming the network is strongly connected, the adjacency matrix Irreducible (the so-called irreducible means that the network To any node There are paths), and the corresponding normalized matrix Satisfies non-negativity and row sum is 1. According to the Perron-Frobenius theorem, the non-negative irreducible matrix The maximum eigenvalue of is 1, corresponding to the only positive eigenvector , at this time the iterative equation (9) can converge to the steady-state solution: (10); because It is reversible, so there is a unique steady-state solution. This value represents the node collapse priority during network collapse, balancing the contributions of geometric and topological structures. During the complex network collapse process, this stable sorting can guide this embodiment to prioritize the removal of nodes that have the greatest impact on network structure and function, thereby achieving efficient network collapse. At the same time, the proof of the existence of a steady-state solution can ensure that the TripRank algorithm of this embodiment can obtain reliable results within a limited number of iterations in practical applications, without infinite loops or unstable results.

[0052] 3. Time complexity analysis.

[0053] The time complexity of the TripRank algorithm is mainly composed of three parts: geometric competition, topological competition, and iterative solution of differential equations. The core of the geometric competition is to count the number of triangles involved in the node. For each node , we need to check whether all possible pairs of nodes in their neighbor sets are connected. Assuming that the average degree of the network is , then the time complexity is ; For topological competition items, it is necessary to calculate the degree of each neighbor node and k-shell values, whose time complexities are and , for the node , the time complexity of the topological term is ; Finally, the iterative calculation part of the equation, assuming that the complexity of a single iteration is , requires iteration times, then the time complexity of the equation iteration is ; Therefore, the total time complexity is ,Although the time complexity of TripRank is slightly higher, the time complexity of ,the algorithm increases linearly with the increase of the network size ,n, and is applicable to networks of various ,sizes.

[0054] 4. Case study.

[0055] To further explain the basic principle and process of TripRank collapse, this embodiment is demonstrated through a simple artificial network. The artificial network has 10 nodes and 17 edges (such as Figure 5 ), and the network contains numerous triangles, with only node 2 not participating in the triangle formation. Overall, the network can be abstracted as a network with node 4 as a bridge node, the geometric region on the left, and the topological region on the right.

[0056] The artificial network is solved by using the TripRank equation to obtain the parameters The best collapse effect is achieved when , which indicates that the geometric features in the network are slightly stronger than the topological features. In theory, 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. . It can be seen that as the number of iterations increases, the TripRank scores of nodes 1 and 4 are gradually increasing. This shows that the importance of nodes 1 and 4 is gradually increasing 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 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 process of equation iteration, this feature advantage weakens the influence of node 3, making node 4 the most influential node. This shows that under the TripRank solution, important hidden nodes in the network are gradually identified.

[0057] Table 1 Scores of each node

[0058] 5. Experiment of the method of this embodiment.

[0059] 5.1. Data introduction

[0060] In the experiment to test the effectiveness of the TripRank algorithm, this example found four real networks for the experiment: the Highschool network, which represents the friendship between boys at a small high school in Illinois; the Caenorhabditis elegans network, which represents the metabolic network of the nematode Caenorhabditis elegans; the Bitcoin OTC network, which represents the trust relationship between users; and the Chess network, which represents the results of chess games. These networks are all undirected and unweighted, and their characteristics are summarized in Table 2. Indicates the number of nodes, represents the number of connected edges, represents the average degree of the nodes, represents the maximum degree of a node, represents the average distance of the network, represents the diameter of the network, represents the number of triangles in the network, represents the number of clusters in the network, Indicates network density.

[0061] Table 2 Statistics of real network characteristics

[0062] 5.2. Network collapse experiment.

[0063] In this section, this embodiment evaluates the structural stability of different networks under sequential node attacks based on different centrality indicators, and compares the results with those obtained based on TripRank. In order to evaluate the superiority of TripRank, this embodiment uses the relative size evolution of the maximum connected component (LCC), the most basic concept in graph theory, as an evaluation indicator. The maximum connected component refers to a connected subgraph containing the largest number of nodes in a network, in which any two nodes can reach each other through a path and no other nodes can be added without destroying the connectivity. In network robustness research, the relative size evolution of the maximum connected component is often used as a key indicator to measure the overall connectivity of the network. By comparing the maximum connected component change curves obtained by removing nodes in sequence according to different algorithms, the advantages and disadvantages and performance of the network collapse algorithm can be intuitively reflected. Its collapse effect is as follows Figure 6 As shown, Figure 6 TripRank is the method of this embodiment, the Tricentrality algorithm is a triangle centrality measurement method, and the DomiRank algorithm is a DomiRank centrality measurement method. The Tricentrality algorithm and the DomiRank algorithm are algorithms in the prior art well known to those skilled in the art and are not described in detail in this embodiment. Figure 6 (a) is a schematic diagram of the collapse effect of the three methods in the Highschool network. Figure 6 (b) is a schematic diagram of the disruption effects of the three methods in the Caenorhabditis elegans network. Figure 6 (c) is a schematic diagram of the disintegration effects of the three methods in the Bitcoin OTC network. Figure 6 (d) is a schematic diagram of the collapse effects of the three methods in the Chess network.

[0064] from Figure 6 It can be seen that TripRank performs well in the four networks. When the proportion of removed nodes reaches 40%, TripRank can reduce the maximum connectivity rate in the network to below 20%, which causes the network to collapse faster than the other two methods, highlighting the superiority of TripRank. Figure 6 Middle (a) to Figure 6As shown in (d), as the scale of the collapsed network increases, TripRank's collapse rate also accelerates, and its collapse efficiency gradually improves. This shows that TripRank is not only suitable for small-scale networks, but also has good collapse effects in large-scale networks. This reflects that compared to the other two algorithms, TripRank can more accurately and quickly identify key nodes in the network by quantifying the geometric and topological features of the network and using differential equation modeling to enable dynamic competition. Assuming that a reduction in the network's maximum connectivity rate to 20% is the sign of successful collapse, TripRank successfully collapses by removing an average of 40% of nodes, while the other two methods require an average of 50% to 55% of nodes to reduce the network's maximum connectivity rate to 20%. This shows that TripRank improves collapse efficiency by 10% to 15% compared to the other two methods in terms of collapse performance.

[0065] 5.3. Parameter sensitivity analysis.

[0066] This section mainly explores the impact of parameter values on the network collapse effect. The evaluation indicator we choose is the area under the LCC curve (AUC). Each parameter corresponds to an AUC value. By comparing the optimal parameter values of different network collapses, we try to find the connection between parameter values and network size. Figure 7 , Figure 7 TripRank AUC is the AUC curve area of the method in this embodiment, and best alpha is the optimal parameter value, Figure 7 (a) shows the AUC curve area and optimal parameters of the method in this embodiment in the Highschool network. Schematic diagram of the value, Figure 7 (b) shows the AUC curve area and optimal parameters of the method in this embodiment in the Caenorhabditis elegans network. Schematic diagram of the value, Figure 7 (c) shows the AUC curve area and optimal parameters of the method in this embodiment in the Bitcoin OTC network. Schematic diagram of the value, Figure 7 (d) is the AUC curve area and optimal parameters of the method in this embodiment in the Chess network Schematic diagram of the value.

[0067] from Figure 7 In the figure, we can see the AUC and change trend of each network under different parameter values. Figure 7 (a) and Figure 7 In (b), the optimal parameters are between Figure 7 (c) and Figure 7The optimal parameter value for (d) lies within the range [ 1 ]. Based on Table 2, this example shows that higher network density correlates with higher optimal parameter values. Conversely, lower network density correlates with lower optimal parameter values, demonstrating a positive correlation. From the perspective of the TripRank equation, a larger optimal parameter indicates a more competitive network geometry, meaning the network's geometric characteristics are more prominent. In addition, this example also shows that the collapse effect of the Bitcoin OTC network and the Chess network is most affected by the parameters, with the AUC variation range being around 0.07, while the AUC variations of the other networks are all affected by the parameters below 0.05. This shows that the intensity of network structure competition varies with different types of networks, and this method can also be used to further test the robustness of the network. In contrast, the robustness of the Highschool network and the Caenorhabditis elegans network is the strongest among these types of networks, while the robustness of the Bitcoin OTC network and the Chess network is the weakest. Combining the data in Table 2, it can be found that the network density of the network that is sensitive to the parameters is relatively small, which shows that the network with a simple topological structure without a loop is more easily affected by the parameter selection, that is, the acyclic structure is more unstable than the cyclic structure.

[0068] Compared with the prior art, the method of this embodiment has the following advantages: The TripRank algorithm proposed in this example 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 a target differential equation modeling approach, TripRank achieves a quantitative balance between local geometric and global topological features for the first time. By adjusting the competition intensity through dynamic parameters, this method adapts to the structural characteristics of different networks. Theoretical analysis demonstrates that the steady-state solution of this example is mathematically unique and stable, providing a reliable basis for ranking node importance. Experimental validation demonstrates that TripRank demonstrates significant advantages across four different networks, achieving a 10% to 15% improvement in the reduction rate of the maximum connected component (LCC) compared to other algorithms. This breakthrough not only confirms the effectiveness of the structural competition mechanism but also provides new insights for optimizing network disruption strategies.

[0069] Reference Figure 8 The embodiment of the present application further provides a complex network disintegration system based on centrality measurement, which includes a complex network construction unit 801, a first feature item construction unit 802, a second feature item construction unit 803, a differential equation construction unit 804, an importance score calculation unit 805, and a complex network disintegration unit 806, wherein: A complex network construction unit 801 is used to construct a complex network including geometric structure and topological structure; A first feature item construction unit 802 is used to construct geometric feature items for calculating geometric structure feature values of all nodes in the geometric structure; The second feature item construction unit 803 is used to construct a topology feature item for calculating the topology structure feature values of all nodes in the topology structure; A differential equation construction unit 804 is used to construct a target differential equation based on geometric characteristic terms and topological characteristic terms; The importance score calculation unit 805 is used to calculate the importance score of each node in the complex network through the target differential equation; The complex network collapse unit 806 is configured to sort each node according to the importance score and collapse the complex network according to the sorting result.

[0070] In some implementations, the first feature item constructing unit 802 may be specifically configured to: ; in, Representation node The ratio of the number of triangles participating in the construction to the largest number of triangles participating in the construction of the entire network, Representation node The neighbor set of Representation node The neighbor set of Representation node and nodes The number of neighbors in common, Representation node The neighbor set of Representation node and nodes The number of neighbors in common, Represents the set of all nodes in a complex network.

[0071] In some implementations, the second feature item constructing unit 803 may be specifically configured to: ; in, The first eigenvalue representing the high topological structure The node is connected to the core neighbor node and is at the intersection of redundant paths. The core neighbor node is the neighbor node whose k-shell value is greater than the preset value. Representation node The neighbor set of represents the direct connection degree of neighbor nodes, Representation node The k-shell value of Represents the set of all nodes in a complex network.

[0072] In some implementations, the differential equation construction unit 804 may be specifically configured to: Calculate the geometric structure eigenvalues of all nodes in the complex network based on the geometric characteristic items; According to the geometric structure eigenvalues of all nodes in the complex network, a geometric eigenvalue matrix is constructed; Calculate the topological structure eigenvalues of all nodes in the complex network based on the topological characteristic items; According to the topological structure eigenvalues of all nodes in the complex network, a topological eigenvalue matrix is constructed; The target differential equation is constructed based on the geometric eigenvalue matrix and the topological eigenvalue matrix.

[0073] In some implementations, the importance score calculation unit 805 may be specifically configured to: The target differential equation is constructed as a node importance equation for calculating the importance score of each node in the complex network; The steady-state solution of the node importance equation is solved by an iterative method, and the steady-state solution is used as the importance score of the node.

[0074] In some implementations, the importance score calculation unit 805 may be specifically configured to: ; in, Representation node The importance score of It represents the threshold time for the target differential equation to reach the steady state. and Indicates parameters, Representation node The geometric structure eigenvalues of Representation node The number of neighbors, Representation node The neighbor set of Representation node Neighbor nodes The importance score of Representation node The topological structure eigenvalues of .

[0075] In some implementations, the importance score calculation unit 805 may be specifically configured to: If the geometric structure features are more obvious than the topological structure features in a complex network, the parameter The larger the value of ; If the topological structure is more prominent than the geometric structure in a complex network, the parameter The larger the value of ; For parameters and parameters Grid search is used for selection.

[0076] It should be noted that, since the complex network disintegration system based on centrality measurement in this embodiment and the above-mentioned complex network disintegration method based on centrality measurement are based on the same inventive concept, the corresponding contents in the method embodiment are also applicable to the system embodiment and will not be described in detail here.

[0077] Reference Figure 9 , an embodiment of the present application further provides an electronic device, the electronic device comprising: at least one memory; at least one processor; at least one program; The programs are stored in the memory, and the processor executes at least one program to implement the above-mentioned complex network disintegration method based on centrality measurement in the present disclosure.

[0078] The electronic device may be any intelligent terminal including a mobile phone, a tablet computer, a personal digital assistant (PDA), a car computer, etc.

[0079] The electronic device according to the embodiment of the present application is described in detail below.

[0080] The processor 1600 may be implemented as a general-purpose central processing unit (CPU), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, and is configured to execute relevant programs to implement the technical solutions provided by the embodiments of the present disclosure. Memory 1700 can be implemented in the form of a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RAM). Memory 1700 can store an 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 memory 1700 and is called by processor 1600 to execute the complex network disintegration method based on centrality measurement in the embodiments of this disclosure.

[0081] Input / output interface 1800, used for information input and output; Communication interface 1900, used to implement communication interaction between this device and other devices, which can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WiFi, Bluetooth, etc.); Bus 2000 , which transmits information between various components of the device (e.g., processor 1600 , memory 1700 , input / output interface 1800 , and communication interface 1900 ); The processor 1600 , the memory 1700 , the input / output interface 1800 , and the communication interface 1900 are connected to each other in communication within the device via the bus 2000 .

[0082] An embodiment of the present disclosure further provides a storage medium, which is a computer-readable storage medium and stores computer-executable instructions. The computer-executable instructions are used to enable a computer to execute the above-mentioned complex network disintegration method based on centrality measurement.

[0083] The memory, as a non-transient computer-readable storage medium, can be used to store non-transient software programs and non-transient computer executable programs. In addition, the memory may include a high-speed random access memory and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory may optionally include a memory remotely arranged relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0084] The embodiments described in the embodiments of the present disclosure are intended to more clearly illustrate the technical solutions of the embodiments of the present disclosure and do not constitute a limitation on the technical solutions provided by the embodiments of the present disclosure. Those skilled in the art will appreciate that with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of the present disclosure are also applicable to similar technical problems.

[0085] Those skilled in the art will understand that the technical solutions shown in the drawings do not constitute a limitation on the embodiments of the present disclosure, and may include more or fewer steps than shown in the drawings, or a combination of certain steps, or different steps.

[0086] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, i.e., they may be located in one place or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of this embodiment.

[0087] Those skilled in the art will appreciate that all or some of the steps in the methods, systems, and functional modules / units in the devices disclosed above may be implemented as software, firmware, hardware, or appropriate combinations thereof.

[0088] The terms "first", "second", "third", "fourth", etc. (if any) in the specification of the present application and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequential order. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0089] It should be understood that in this application, "at least one (item)" means one or more, and "plurality" means two or more. "And / or" is used to describe the association relationship of associated objects, indicating that three relationships may exist. For example, "A and / or B" can mean: only A exists, only B exists, and A and B exist at the same time, where A and B can be singular or plural. The character " / " generally indicates that the previous and next associated objects are in an "or" relationship. "At least one of the following items" or similar expressions refers to any combination of these items, including any combination of single items or plural items. For example, at least one of a, b or c can mean: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, c can be single or multiple.

[0090] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of units is only a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0091] Units described as separate components may or may not be physically separate, and 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 these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0092] In addition, the functional units in the various embodiments of the present application may be integrated into a single processing unit, or each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0093] If the integrated unit is implemented in the form of 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 the present application is essentially 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, and the computer software product is stored in a storage medium, including multiple instructions for enabling an electronic device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the various embodiments of the present application. The aforementioned storage medium includes various media that can store programs, 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. The embodiments of the present application are described in detail above in conjunction with the accompanying drawings, but the present application is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in the relevant technical field without departing from the purpose of the present application.

[0094] The embodiments of the present application are described in detail above in conjunction with the accompanying drawings, but the present application is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in the relevant technical field without departing from the purpose of the present application.

Claims

1. A complex network disintegration method based on centrality measurement, characterized in that: The method comprises: Construct complex networks that include geometric and topological structures; Constructing geometric feature items for calculating geometric structure feature values of all nodes in the geometric structure; Constructing a topological feature item for calculating topological structure feature values of all nodes in the topological structure; Constructing a target differential equation according to the geometric characteristic term and the topological characteristic term; Calculating the importance score of each node in the complex network by using the target differential equation; Each node is sorted according to the importance score, and the complex network is collapsed according to the sorting result.

2. The complex network disintegration method based on centrality measurement according to claim 1, characterized in that: The constructing of geometric feature items for calculating geometric structure feature values of all nodes in the geometric structure includes: ； in, Representation node The ratio of the number of triangles participating in the construction to the largest number of triangles participating in the construction of the entire network, Representation node The neighbor set of Representation node The neighbor set of Representation node and nodes The number of neighbors in common, Representation node The neighbor set of Representation node and nodes The number of neighbors in common, Represents the set of all nodes in a complex network.

3. The complex network disintegration method based on centrality measurement according to claim 1, characterized in that: The constructing of topological feature items for calculating topological structure feature values of all nodes in the topological structure includes: ； in, The first node represents a high topological structure feature value that connects core neighbor nodes and is at the intersection of redundant paths. Node, wherein the core neighbor node is a neighbor node whose k-shell value is greater than a preset value, Representation node The neighbor set of represents the direct connection degree of neighbor nodes, Representation node The k-shell value of Represents the set of all nodes in a complex network.

4. The complex network disintegration method based on centrality measurement according to claim 1, characterized in that: The constructing of a target differential equation according to the geometric characteristic term and the topological characteristic term includes: Calculating geometric structure eigenvalues of all nodes in the complex network according to the geometric characteristic items; Constructing a geometric eigenvalue matrix according to the geometric structure eigenvalues of all nodes in the complex network; Calculating topological structure characteristic values of all nodes in the complex network according to the topological characteristic items; Constructing a topological eigenvalue matrix according to the topological structure eigenvalues of all nodes in the complex network; A target differential equation is constructed according to the geometric eigenvalue matrix and the topological eigenvalue matrix.

5. The complex network disintegration method based on centrality measurement according to claim 1, characterized in that: Calculating the importance score of each node in the complex network by using the target differential equation includes: constructing the target differential equation as a node importance equation for calculating the importance score of each node in the complex network; The steady-state solution of the node importance equation is solved by an iterative method, and the steady-state solution is used as the importance score of the node.

6. The complex network disintegration method based on centrality measurement according to claim 5, characterized in that: The step of constructing the target differential equation as a node importance equation for calculating the importance score of each node in the complex network comprises: ； in, Representation node The importance score of It represents the threshold time for the target differential equation to reach the steady state. and Represents dynamic parameters, Representation node The geometric structure eigenvalues of Representation node The number of neighbors, Representation node The neighbor set of Representation node Neighbor nodes The importance score of Representation node The topological structure eigenvalues of .

7. The complex network disintegration method based on centrality measurement according to claim 6, characterized in that: 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 includes: If the geometric structure features are more obvious than the topological structure features in a complex network, the parameter The larger the value of ; If the topological structure is more prominent than the geometric structure in a complex network, the parameter The larger the value of ; For the parameters and the parameters Grid search is used for selection.

8. A complex network disintegration system based on centrality measurement, characterized in that: The system comprises: Complex network construction unit, used to construct complex networks containing geometric and topological structures; A first feature item construction unit is used to construct geometric feature items for calculating geometric structure feature values of all nodes in the geometric structure; A second feature item construction unit is used to construct a topology feature item for calculating the topology structure feature values of all nodes in the topology structure; A differential equation construction unit, configured to construct a target differential equation based on the geometric characteristic term and the topological characteristic term; an importance score calculation unit, configured to calculate the importance score of each node in the complex network by using the target differential equation; The complex network collapse unit is used to sort each node according to the importance score and collapse the complex network according to the sorting result.

9. An electronic device, characterized in that: It includes at least one control processor and a memory for communicating with the at least one control processor; the memory stores instructions that can be executed by the at least one control processor, and the instructions are executed by the at least one control processor to enable the at least one control processor to execute the complex network disintegration method based on centrality measurement as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the complex network disintegration method based on centrality measurement according to any one of claims 1 to 7.

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