Network key node identification method fusing improved measurement and propagation influence

Abstract

The invention relates to the technical field of node identification, in particular to a network key node identification method fusing improved measurement and propagation influence, which comprises the following steps: setting an edge weight and a cross-layer dependency relationship of an infrastructure network; constructing weighted cross-layer local contact centrality, attenuation cross-layer path centrality and random walk centrality indexes; taking the maximum value of the three adaptive scores as an improved measure of the node; defining metric value standardization; calculating a propagation influence value, standardizing the measurement value, and carrying out weighted fusion on the measurement value and the propagation influence value to obtain a fusion score; carrying out propagation influence value convergence judgment by utilizing an LT linear threshold model; and arranging the nodes based on the fusion score value, and outputting a key node identification result. The method solves the problems that a traditional key node identification method only regards a multi-layer network as a plurality of isolated single-layer networks, lacks measurement of node heterogeneity in the multi-layer network, ignores a coupling relation between network layers and is difficult to be accurately applied to an urban multi-layer infrastructure network.

Description

Technical Field

[0001] This invention relates to the field of node identification technology, and in particular to a method for identifying key network nodes that integrates improved measurement and propagation influence. Background Technology

[0002] With the continuous acceleration of urbanization, my country has formed a super-large-scale infrastructure network. Urban infrastructure networks are characterized by multiple layers, high node heterogeneity, and high cross-layer coupling. They are prone to cascading failures when facing extreme weather events, leading to large-scale node failures within the system, which seriously affects the normal operation of infrastructure and poses a threat to urban safety. Optimizing network topology through key node identification technology in multi-layer complex networks has important theoretical value and practical significance for improving the stability and resilience of urban infrastructure systems.

[0003] In the analysis and research of complex networks, the importance of a node is usually referred to as centrality; the higher the centrality value of a node, the more important it is in the network. Researchers at home and abroad have proposed different centrality methods to achieve more efficient and accurate identification of critical nodes; however, existing methods are mostly used for critical node identification in single-layer infrastructure networks, and there are few methods for critical node identification in multi-layer infrastructure networks that comprehensively consider node heterogeneity and functional coupling relationships. Summary of the Invention

[0004] To address the shortcomings of existing methods, this invention solves the problem that traditional key node identification methods merely treat multi-layer networks as multiple isolated single-layer networks, lack the ability to measure the heterogeneity of nodes in multi-layer networks, ignore the coupling relationship between network layers, and are difficult to accurately apply to urban multi-layer infrastructure networks.

[0005] The technical solution adopted in this invention is: a method for identifying key network nodes that integrates improved measurement and propagation influence, comprising the following steps: Step 1: Design a multi-layer infrastructure network, setting edge weights and cross-layer dependencies. Furthermore, step one specifically includes: Step 11: Calculate the traffic layer network The probability of a newly added node connecting to an existing node. Boundary weights of the traffic layer network ; Step 12: Calculate the power layer network The probability of a newly added node connecting to an existing node. Boundary weights of power layer network ; Step 13: Calculate the communication layer network The probability of a newly added node connecting to an existing node. Boundary weights of communication layer networks ; Step 14: Design the dependency sets between traffic nodes and power nodes respectively. Boundary weights for cross-layer dependence of transportation and electricity Dependency set between power nodes and communication nodes Boundary weights for cross-layer dependencies between power and communication Dependency set between communication nodes and power nodes Boundary weights for cross-layer dependencies between communication and power .

[0006] Step 2: Construct weighted cross-layer local contact centrality, decaying cross-layer path centrality, and random walk centrality indices based on the attribute vector set of multi-layer network nodes; Furthermore, the formula for weighted cross-layer local contact centrality is: (18) in, This is the influence coefficient; Participation coefficient; This represents the layer weight coefficient.

[0007] Furthermore, the formula for attenuating cross-layer path centrality is: (19) in, The set of all paths to a node. This is the cross-layer path attenuation factor. Interlayer coupling strength, For path weights, For path length, This is the attenuation factor.

[0008] Furthermore, the formula for the centrality of random walks is: (20) in, The random walk probability of the transition tensor. As the cross-level jump factor, The total number of network nodes. is the in-layer damping factor.

[0009] Step 3: Construct fitness scores for weighted cross-layer local contact centrality, decaying cross-layer path centrality, and random walk centrality, and use the maximum value of the three fitness scores as the improvement metric for the node; define and standardize the metric values ​​based on the weighted cross-layer local contact centrality, decaying cross-layer path centrality, and random walk centrality indices. Furthermore, the formula for the improved metric is: (twenty four) in, Representing nodes respectively i The weighted cross-layer local contact centrality, attenuated cross-layer path centrality, and random walk centrality fitness scores.

[0010] Furthermore, the formula for standardizing the metric is: (25) in, For nodes exist Rank under the selected metric This represents the total number of nodes.

[0011] Step 4: Calculate the propagation impact value, standardize the measurement value and weight and fuse it with the propagation impact value to obtain a fusion score; and use the LT linear threshold model to judge the convergence of the propagation impact value. Furthermore, the formula for the fusion score is: (28) in, For adjustment coefficients, To determine the propagation impact value, For nodes The measurement type.

[0012] Step 5: Arrange the nodes based on the fusion score and output the key node identification results.

[0013] Furthermore, the network key node identification system that integrates improved measurement and dissemination influence includes: a memory for storing instructions executable by a processor; and a processor for executing the instructions to implement the network key node identification method that integrates improved measurement and dissemination influence.

[0014] Furthermore, a computer-readable medium storing computer program code, which, when executed by a processor, implements a method for identifying key network nodes that integrates improved measurement and propagation influence.

[0015] The beneficial effects of this invention are: 1. This invention provides a method for identifying key network nodes by integrating improved measurement and propagation influence. First, considering the characteristics of multi-layer infrastructure networks, the traditional degree centrality and eigenvector centrality measures are improved to obtain weighted cross-layer local contact, attenuated cross-layer path, and multi-layer random walk centrality measurement methods. A rule is designed to assign an improved centrality measure to each node. Then, the propagation influence value is weighted and fused, and the fusion scoring function is reconstructed to form a key node identification method that is easy to implement, has good identification effect, and fully considers the characteristics of multi-layer infrastructure networks. 2. This invention optimizes the traditional centrality metric into three improved metric methods, which consider the heterogeneity of nodes in a single-layer network, the coupling relationship between multi-layer networks, and the weighted fusion with propagation influence, which can effectively improve the accuracy of key node identification. By designing a rule to assign an improved centrality metric to each node, the noise and redundancy that may be caused by multiple index weighting are avoided, thereby improving the effectiveness of key node identification. Attached Figure Description

[0016] Figure 1 This is a logical block diagram of the network key node identification method based on the fusion improvement of measurement and propagation influence of the present invention; Figure 2 This is a schematic diagram of the transportation layer infrastructure network of the present invention; Figure 3 This is a schematic diagram of the power layer infrastructure network structure of the present invention; Figure 4 This is a schematic diagram of the communication layer infrastructure network of the present invention; Figure 5 This is a schematic diagram of the cross-layer dependency relationships in the multi-layer infrastructure network of the present invention; Figure 6 This invention's method, compared to traditional methods, is obtained on six multilayer networks. Comparison chart of the number of activated nodes for key nodes; Figure 7 This is a comparison diagram of the similarity between the node sequences obtained by the method of this invention and the traditional method on six multi-layer networks and the sequences obtained by the LT model; Figure 8 The method of this invention, compared with traditional methods, yields the node importance sequence in a six-layer network. Comparison chart of the differences in the influence of each node; Figure 9 This is a comparison chart showing the differences in network efficiency and network connectivity between the method of this invention and the traditional method on the constructed multi-layer infrastructure network; Figure 10 This invention's method, combined with the method after removing the propagation influence weighted fusion module, is applied to a multi-layered infrastructure network. A comparison chart showing the differences in the number of activated nodes and network efficiency at key nodes. Detailed Implementation

[0017] The present invention will be further described below with reference to the accompanying drawings and embodiments. The drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0018] like Figure 1 As shown, the method for identifying key network nodes that integrates improved measurement and propagation influence includes the following steps: Step 1: Design a multi-layer infrastructure network, setting edge weights and cross-layer dependencies; like Figures 2-4 As shown, this multi-layered infrastructure network includes a transportation layer network, a power layer network, and a communication layer network. like Figure 5 Configure cross-layer dependencies in a multi-layer infrastructure network; Step 11: Design the traffic layer network In this embodiment, the traffic layer network is a Watts-Strogatz small-world network. The main characteristics of the network are local high clustering, short average path length, and nodes including traffic hubs, intersections, bridges, tunnels, elevated entrances and exits, highway entrances and exits, etc. New nodes connect to neighboring nodes, with a preference for connecting to nodes with higher traffic volume. The probability of a newly added node connecting to an existing node is: (1) in, For traffic nodes The degree, Geographical distance, To iterate over variables, This is for newly added nodes.

[0019] The edge weights of the traffic layer network are designed based on the load / capacity ratio, and the formula is as follows: (2) in, Passenger flow per unit time For design capacity.

[0020] Step 12: Design the power layer network In this embodiment, the power layer network is a Barabási-Albert scale-free network. The main characteristics of the network are sparse layout, power-law distribution of node degree, and nodes include substations, distribution stations, etc. New nodes tend to connect to substations with high density or nodes with large capacity. Newly added nodes typically connect to 2-3 upstream nodes, with the following probability: (3) in, For power nodes The degree.

[0021] The edge weights of a power layer network are designed based on the power flow / capacity ratio, as shown in the formula: (4) in, For a unit of time current, For line admittance, This represents the tolerance coefficient.

[0022] Step 13: Design the communication layer network The communication layer network is a Barabási-Albert scale-free network type. The network is mainly formed through growth mechanism and priority connection mechanism, and the nodes include communication base stations, data centers, etc. New nodes connect to neighboring nodes, and are more likely to connect to data centers or large communication nodes. The probability of a newly added node connecting to an existing node is: (5) in, For communication nodes The degree.

[0023] The edge weights of a communication layer network are designed based on the data traffic / capacity ratio of the link. The formula is as follows: (6) in, Data flow per unit time This refers to the link capacity.

[0024] Step 14: Design cross-layer dependencies and edge weights for each traffic node. It depends on at least one nearby power node in the power layer, and its dependency set is as follows: (7) in, For the number of multiple power sources; The formula for edge weights is: (8) in, For traffic nodes The share of electricity supply; For each power node It depends on one nearby data center node or base station node in the communication layer, and its dependency set is as follows: (9) in, For nodes With nodes The distance between them.

[0025] The formula for edge weights is: (10) in, An identifier representing a dependency.

[0026] For each communication node It depends on several nearby and large-capacity power nodes in the power layer, and its dependency set is as follows: (11) in, The number of nearby and high-capacity power nodes. For communication nodes The share of electricity supply; The formula for edge weights is: (12) Among them, weight , All return to one Interval.

[0027] Step 2: Define a set of node attribute vectors, optimize traditional metrics, and obtain three improved metrics; Define the set of attribute vectors for each node in a multi-layer infrastructure network, optimize the traditional centrality measure, and obtain three improved centrality measures; Step 21: Define the attribute vector set of multi-layer network nodes. Each node Each contains 5 attribute vectors, including: in-layer degree. Cross-layer degree Cross-layer betweenness ratio Average shortest path and participation coefficient The calculation formulas are as follows: (13) (14) (15) (16) (17) in, For nodes In the layer The set of neighboring nodes in the middle, The adjacency matrix elements represent the connections between nodes. This represents the number of shortest paths between nodes. This is the set of shortest paths between nodes. The shortest path distance. The degree within the node layer. For nodes In the layer The set of neighboring nodes in the middle, For layer and Adjacency matrix elements of inter-connected nodes.

[0028] Step 22: Traditional degree centrality simply adds the degree within a layer to the degree of the cross-layer connection. By introducing parameters that can characterize heterogeneity and layer weights, a new approach is needed. This invention emphasizes intra-layer connectivity strength while weighing cross-layer connectivity strength to obtain an improved first type of centrality. The weighted cross-layer local contact centrality of nodes in a multi-layer infrastructure network is defined as follows: (18) in, This is the influence coefficient; Participation coefficient; The layer weight coefficient represents the layer weight. The relative importance of an infrastructure is determined based on factors such as its criticality and probability of failure.

[0029] Step 23: Traditional eigenvector centrality lacks a measure of cross-layer skipping decay and inter-layer differences; This invention further reflects the node propagation potential by introducing cross-layer path attenuation and inter-layer coupling related parameters, obtaining an improved second type of centrality. The attenuation cross-layer path centrality of nodes in a multi-layer infrastructure network is defined as follows: (19) in, The set of all paths to a node. This is the cross-layer path attenuation factor. Interlayer coupling strength, For path weights, For path length, The attenuation factor is determined based on factors such as the inter-layer interconnectivity of the infrastructure and the quality of signal transmission. Step 24: Traditional eigenvector centrality is based on a random walk model constructed from a single-layer adjacency matrix. In multi-layer networks, the difference between intra-layer walks and cross-layer jumps needs to be considered. This invention calculates the transition probability of nodes between different layers by introducing an inter-layer jump matrix, and reconstructs the random walk model using a three-dimensional transition tensor to obtain an improved third type of centrality. The multi-layer random walk centrality of nodes in a multi-layer infrastructure network is defined as follows: (20) in, The random walk probability of the transition tensor. As the cross-level jump factor, For indicator variables, For layer Middle node The importance of The total number of network nodes. It is the damping factor within the layer, determined based on factors such as inter-layer dependencies, flow rate, and carrying capacity of the infrastructure.

[0030] Step 3: Design a metric allocation rule, allocate the most suitable improvement metric, and calculate the metric value; Design a metric allocation rule to assign an optimal improvement metric to each node in each layer of a multi-layer infrastructure network, and calculate the metric value. Step 31, Definition Adaptation score , representing a node The appropriate degree of weighted cross-layer local contact centrality is determined by the following formula: (twenty one) in, Based on the weights set by cross-validation, This is the normalized value of the attribute vector.

[0031] Step 32, Definition Adaptation score , representing a node The appropriate formula for using decaying cross-layer path centrality is: (twenty two) Step 33, Definition Adaptation score , representing a node The appropriateness of using multi-level random walk centrality is determined by the following formula: (twenty three) Step 34: Calculate the nodes attribute vector Normalized to the maximum value ; Step 35: Calculate nodes based on attribute vector values of , , Select the largest metric as the node. The improved metric is defined by the following formula: (twenty four) Step 36, according to compute nodes The centrality value is used to construct a standardized formula for the metric based on node ranking to ensure that the centrality metric of all nodes can maintain the same scale during fusion. The standardization formula for a metric is defined as follows: (25) in, For nodes exist Rank under the selected metric This represents the total number of nodes.

[0032] Step 4: Calculate the dissemination impact value, perform a weighted fusion of the improved metric and the dissemination impact, and obtain a fusion score; Node Set up an independent information source and calculate the propagation impact value. Then, a weighted fusion of improved metrics and dissemination impact is performed to obtain a fusion score. ; Step 41: Construct a propagation matrix based on the edge weights of the multi-layer infrastructure network. The weight of each edge. Represents a node For nodes The propagation impact value, initializing the node set. and fusion coefficient Error threshold wait; Step 42: For each node When the propagation matrix spectral radius When solving this problem, the matrix geometric series formula is used, and the calculation formula is as follows: (26) in, For the first There are standard basis vectors, with length . , I for The identity matrix, The Green's function of the hyperadjacency matrix. For the propagation path length, It is a vector consisting entirely of 1s.

[0033] when When the network size is too large, the Live-Edge model should be used. The propagation impact value is obtained by sub-Monte Carlo sampling. The calculation formula is: (27) in, For the number of samples taken in Monte Carlo, For the first The impact value of the second sampling.

[0034] Step 43: Normalize the propagation impact value and record the nodes. The propagation impact value This further constitutes a standardized vector for weighted fusion. ; Step 44: Transfer the node Standardized metric With propagation impact value By performing weighted fusion, the nodes can be obtained. Fusion score The formula is: (28) in, For nodes The measurement type, The adjustment coefficient is calculated based on the principle of minimizing variance. The formula is ; Step 45: Perform convergence testing under the Linear Threshold (LT) model and calculate the Euclidean distance between the propagation impact values ​​of the two rounds. If this value is less than the error threshold If convergence is achieved, then return to step 42; otherwise, proceed to step 42.

[0035] Step 5: Node sorting. Sort the nodes in descending order according to the fusion score to obtain the key node identification results; The obtained nodes of the multi-layer network The scores are sorted in descending order, and the sorted results are used as a sequence. It means that among them This represents the value of the node with the highest fusion score in the network. This is the value of the node with the lowest fusion score in the network.

[0036] Performance testing and analysis of the method of this invention: To verify the accuracy and reliability of the FCSI method of this invention, extensive experiments were conducted on two manually constructed multi-layer infrastructure network datasets and four real-world public multi-layer network datasets. Six different methods were applied to comprehensively compare the performance of key node identification. The four real-world multi-layer networks were obtained from the Stanford Large Network Dataset Collection, and varied in type, size, and features. Specifically, they included: one biological neural network where different layers represent different types of neural connections; one biological gene network that simulates different types of gene interactions in an organism; and two multi-layer social networks where each individual is represented as a node, and edges represent social relationships or suggestions between individuals. All experiments were implemented in Python on a Windows 11 operating system equipped with 64GB of memory, a 16-core, 22-thread 5.1GHz Intel Ultra9-185H CPU. To ensure fairness and reliability, all experiments were run independently 100 times, and the average value was taken. The fault propagation model is used to measure the fault propagation capability of network nodes, and multi-layer infrastructure network node sequences obtained by different methods are acquired. The ranking of the top 10 key nodes on the multi-layer infrastructure network 1 using different methods is shown in Table 1; the results obtained using the method of this invention and six traditional Degree, Katz, PageRank, Betweenness, CrossLayerBet, and KCore methods on six multi-layer networks are generated. A comparison chart of the number of activated nodes for key nodes, as shown below. Figure 6 As shown; from Figure 6 As can be seen from (a) and (b), on the two multi-layer infrastructure networks, FCSI activates more nodes and activates them faster; from Figure 6 From (c), (d), (e), and (f), it can be seen that, except for Figure 6 (f) Among all networks except those in which FCSI was ultimately activated, the number of nodes activated and the activation speed were slightly higher than all other methods. This indicates that FCSI has a clear advantage in both multi-layer infrastructure networks and other types of multi-layer networks. It can more accurately identify nodes with significant influence during the propagation process in multi-layer networks and can influence more nodes on the network more quickly. The main reasons for FCSI's excellent performance are as follows: First, FCSI includes a variety of improved metrics, which can more effectively simulate the heterogeneity of nodes at each layer compared to other metrics that use the same and fixed range of influence. FCSI also discovers key propagation information contained in the multi-layer network structure more comprehensively by integrating improved metrics and propagation influence. Table 1. Ranking of the top 10 critical nodes on multi-layer infrastructure network 1 using different methods.

[0037] Using normalized intersection similarity: The similarity between node sequences obtained by different methods and sequences obtained by the LT model is compared. For sequence The former One element, For sequence The former The length of each element; generating a similarity comparison diagram between the node sequences obtained using the method of this invention and six traditional methods (Degree, Katz, PageRank, Betweenness, CrossLayerBet, and KCore) on six multi-layer networks and the sequences obtained by the LT model, such as... Figure 7 As shown; in Figure 7 In the multi-layer networks (a), (b), (c), (d), and (f), FCSI achieves the lowest intersection similarity regardless of the K value; Figure 7 In the multi-layer network of (e), as the value of K increases, FCSI can also achieve competitive performance, approaching the result of the optimal method. The above experimental results show that the node influence ranking result of FCSI is most similar to the sequence obtained by the LT model, which is better than other methods. This is mainly because weighted fusion itself is a comprehensive measure of the actual propagation effect of each node in the network, thereby capturing the importance of the node in the network structure. Using imprecise functions Analyzing the node importance sequences obtained by different methods The influence of each node varies, among which For the first method 1 Ranking the importance of each node in the sequence; generating a comparison chart of the influence differences of the top P nodes in the node importance sequences obtained using the method of this invention and eight traditional methods (Degree, Katz, PageRank, Betweenness, CrossLayerBet, and KCore) on six multi-layer networks, as shown in the figure. Figure 8 As shown; from Figure 6 As can be seen from the multilayer networks in (a), (b), (d), and (e), FCSI achieves lower imprecise function values ​​than the comparative method across almost all P-value ranges; Figure 8 In the multilayer network of (c), as the P-value increases, FCSI gradually reaches the optimal imprecise function value among all methods; furthermore, Figure 8 In the multilayer network of (f), the imprecise function value of FCSI remains competitive, approaching the result of the optimal method, and at one point achieves the best imprecise function value when P takes partial values; from Figure 8In the multilayer networks shown in (b), (c), (d), and (e), it can also be seen that the imprecise function values ​​of different methods at different P values ​​are basically negatively correlated with the number of nodes affected by the identified key nodes. The more nodes that the identified key nodes can affect, the lower the imprecise function value, which indicates that the corresponding method performs better. Overall, compared with other key node identification methods, FCSI achieved excellent imprecise function values ​​in all multilayer networks, further proving the superiority of this method. Using Kendall's rank correlation coefficient Statistical analysis was performed on the node sequences identified by the method described in this invention and the node sequences obtained by other methods, wherein... For the number of consistent pairs, To account for the number of inconsistencies, the higher the correlation coefficient between the node sequence and the sequence obtained by FCSI, the more similar the node sequence obtained by the comparison method is to the node sequence obtained by FCSI. The comparison methods with the highest, second highest, and third highest correlation coefficients on each network are indicated by double underlines, wavy lines, and italics, respectively. The Kendall rank correlation coefficients of various methods are shown in Table 2. As shown in Table 2, compared with FCSI, the key node sequences obtained by different methods are more significantly different. Degree, PageRank, and Katz have higher correlation coefficients on most datasets, especially on multilayer gene networks, multilayer neural networks, and multilayer social networks, where the key node sequences obtained are highly consistent with the sequences obtained by FCSI. The coefficient value of CrossLayer is relatively low in the same dataset, indicating that the difference between this method and FCSI is relatively large. Overall, combining Figure 6 , 7 As can be observed in Figures 8 and 9, the correlation coefficients between different methods and FCSI are generally weakly positively correlated with the performance of key node identification. The more similar the result sequences obtained by the comparison methods are to the sequences obtained by FCSI, the stronger the corresponding key node identification ability is, which further proves the effectiveness of FCSI. Table 2. Kendall's rank correlation coefficients for various methods

[0038] To verify the fault tolerance and reliability of the FCSI method of this invention, a robustness experiment was conducted on a constructed multi-layer infrastructure network 1. Infrastructure network nodes were intentionally attacked one by one according to their importance, causing structural damage and functional failure. This simulated the potential cascading failures of infrastructure network nodes under extreme weather events or sudden disasters. A comparison chart was generated showing the differences in network efficiency and connectivity obtained using the method of this invention versus six traditional methods (Degree, Katz, PageRank, Betweenness, CrossLayerBet, and KCore) on the constructed multi-layer infrastructure network. Figure 9 As shown; from Figure 9 As can be seen, in the initial stage of critical node removal, the network efficiency of most methods showed a significant downward trend, indicating that these methods can identify critical nodes that have a significant impact on network efficiency. However, as nodes continue to be removed, the degree of network efficiency decline varies significantly among different methods. The critical nodes identified by the FCSI method have the greatest impact on network efficiency. When 12% of the critical nodes are removed, the decline in network efficiency is generally greater than that of other methods. As more critical nodes fail, the network efficiency of the FCSI method remains at a low level throughout the process. In addition, the remaining connectivity after critical node removal gradually shows significant differences among the methods. When the percentage of node removal reaches 31%, the decline in network connectivity of FCSI is generally greater than that of other methods. When the percentage of node removal reaches 45%, the network connectivity begins to decline sharply. This is because there are redundant dependencies between different layers of the multilayer network, which leads to a slow decay of connectivity in the early stage, and a sudden collapse when approaching the critical point. Overall, compared with other methods, FCSI performs better in terms of functional robustness and structural robustness. Ablation experiments were conducted on a constructed multi-layer infrastructure network to compare the performance differences between the complete method of this invention and the method after removing the propagation influence weighted fusion module. This yielded results demonstrating the performance differences between the method of this invention and the method after removing the propagation influence weighted fusion module on the constructed multi-layer infrastructure network. A comparison chart showing the differences in the number of activated nodes and network efficiency at key nodes, as shown below. Figure 10 As shown; from Figure 10 As can be seen from the data, in multi-layer infrastructure network 1, the complete FCSI can activate more nodes faster than the method after removing the propagation influence, and the degree of network efficiency degradation is also more significant. This indicates that weighted fusion of improvement metric and propagation influence value can effectively improve the performance of the method in identifying key nodes in multi-layer infrastructure networks.

[0039] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A method for identifying key network nodes that integrates improved measurement and propagation influence, characterized in that: Includes the following steps: Step 1: Design a multi-layer infrastructure network, setting edge weights and cross-layer dependencies. Step 2: Construct weighted cross-layer local contact centrality, decaying cross-layer path centrality, and random walk centrality indices based on the attribute vector set of multi-layer network nodes; Step 3: Construct fitness scores for weighted cross-layer local contact centrality, decaying cross-layer path centrality, and random walk centrality, and use the maximum value of the three fitness scores as the improvement metric for the node; define and standardize the metric values ​​based on the weighted cross-layer local contact centrality, decaying cross-layer path centrality, and random walk centrality indices. Step 4: Calculate the propagation impact value, standardize the measurement value and weight and fuse it with the propagation impact value to obtain a fusion score; and use the LT linear threshold model to judge the convergence of the propagation impact value. Step 5: Arrange the nodes based on the fusion score and output the key node identification results.

2. The method for identifying key network nodes that integrates improved measurement and propagation influence as described in claim 1, characterized in that, Step one specifically includes: Step 11: Calculate the traffic layer network The probability of a newly added node connecting to an existing node. Boundary weights of the traffic layer network ; Step 12: Calculate the power layer network The probability of a newly added node connecting to an existing node. Boundary weights of power layer network ; Step 13: Calculate the communication layer network The probability of a newly added node connecting to an existing node. Boundary weights of communication layer networks ; Step 14: Design the dependency sets between traffic nodes and power nodes respectively. Boundary weights for cross-layer dependence of transportation and electricity Dependency set between power nodes and communication nodes Boundary weights for cross-layer dependencies between power and communication Dependency set between communication nodes and power nodes Boundary weights for cross-layer dependencies between communication and power .

3. The method for identifying key network nodes that integrates improved measurement and propagation influence as described in claim 1, characterized in that, The formula for weighted cross-layer local contact centrality is: (18) in, This is the influence coefficient; Participation coefficient; This represents the layer weight coefficient.

4. The method for identifying key network nodes that integrates improved measurement and propagation influence as described in claim 1, characterized in that, The formula for attenuating cross-layer path centrality is: (19) in, The set of all paths to a node. This is the cross-layer path attenuation factor. Interlayer coupling strength, For path weights, For path length, This is the attenuation factor.

5. The method for identifying key network nodes that integrates improved measurement and propagation influence as described in claim 1, characterized in that, The formula for the centrality of random walk is: (20) in, The random walk probability of the transition tensor. As the cross-level jump factor, The total number of network nodes. is the in-layer damping factor.

6. The method for identifying key network nodes that integrates improved measurement and propagation influence as described in claim 1, characterized in that, The formula for improving the metric is: (24) in, Representing nodes respectively i The weighted cross-layer local contact centrality, attenuated cross-layer path centrality, and random walk centrality fitness scores.

7. The method for identifying key network nodes that integrates improved measurement and propagation influence as described in claim 1, characterized in that, The formula for standardizing a metric is: (25) in, For nodes exist Rank under the selected metric This represents the total number of nodes.

8. The method for identifying key network nodes that integrates improved measurement and propagation influence as described in claim 1, characterized in that, The formula for the fusion score is: (28) in, For adjustment coefficients, To determine the propagation impact value, For nodes The measurement type.

9. A network key node identification system that integrates improved measurement and dissemination influence, characterized in that: include: Memory is used to store instructions that can be executed by the processor; A processor for executing instructions to implement the network critical node identification method that integrates improved measurement and propagation influence as described in any one of claims 1-8.

10. A computer-readable medium storing computer program code, characterized in that, The computer program code, when executed by a processor, implements the network key node identification method that integrates improved measurement and propagation influence as described in any one of claims 1-8.

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