Weak node identification method based on centrality and efficiency measurement

Abstract

The invention discloses a weak node identification method based on centrality and efficiency measurement. The method comprises the following steps: constructing a network model based on network topology and real-time state parameters; calculating a node fault probability according to the node health state; calculating a link fault probability through a piecewise function containing a distance attenuation factor and a delay influence factor based on the link attribute; generating an information chain path set and calculating a path success rate by integrating node and link fault probabilities; obtaining a node efficiency value by aggregating the success rate contributions of each node in all related paths; fusing the node efficiency value and the weighted centrality index to obtain a node weak value; and finally, realizing risk grading according to weak value sorting and percentage distribution. The defect that a traditional method lacks task guidance and environmental adaptability is overcome, accurate and real-time recognition of weak nodes is achieved, and the method has the important advantages of being low in calculation weight, high in environmental coupling degree and high in practicability.

Description

Technical Field

[0001] This invention belongs to the field of complex network analysis and intelligent decision-making technology, and in particular relates to a method for identifying weak nodes based on centrality and efficiency measurement. Background Technology

[0002] With the expansion of information and networked systems, the stability and vulnerability of complex networks have attracted widespread attention from academia and industry. Identifying the "critical nodes" and "weak links" in complex networks is not only related to the overall robustness and reliability of the system, but also directly affects the continuity and efficiency of the task chain.

[0003] The current state of research and application is mainly reflected in the following directions: (1) Single index centrality method; Complex network analysis often uses metrics such as degree centrality, betweenness centrality, and proximity centrality as important criteria for identifying critical nodes. In 2001, Brandes proposed a fast betweenness centrality algorithm, reducing computational complexity to... This makes large-scale network analysis possible. Such methods are widely used in scenarios such as communication networks, transportation networks, and social networks.

[0004] (2) Network robustness and percolation theory perspective; Complex network theory reveals that scale-free networks are robust to random failures but extremely vulnerable to targeted attacks (such as removing highly central nodes). This conclusion forms an important theoretical basis for critical node identification, and related research results have been widely disseminated on platforms such as Nature and arXiv.

[0005] (3) Critical Node Detection Problem (CNDP); CNDP models the problem of "finding the set of nodes that most severely degrades network connectivity" as a combinatorial optimization problem. It has various algorithmic solutions, such as integer programming and heuristics, and has been applied in the protection of critical infrastructures such as power, transportation, and communications.

[0006] (4) Network efficiency indicators; Latora and Marchori proposed a network efficiency metric that uses the reciprocal of the average shortest path to characterize the overall information transmission efficiency. This method provides a reference for evaluating network performance at the macro level and has been adopted in multiple network performance analysis scenarios.

[0007] While the above methods provide important insights for studying the vulnerability of complex networks, they still have the following limitations: 1. Structure-oriented, lacking task-oriented; Both single-index centrality and percolation theory focus on the importance of network topology or global connectivity, but fail to incorporate the probability of task achievability in specific information chains, making it difficult to reflect the role of nodes in actual task execution.

[0008] 2. Lack of node functionality and health status modeling; Most existing methods assume that nodes are in an ideal working state and do not consider the real-time performance degradation or failure probability of nodes, which leads to differences between the evaluation results and the actual performance.

[0009] 3. Ignoring the influence of environmental factors; Environmental conditions such as distance, latency, and interference have a significant impact on link reliability, but most methods do not directly model these factors.

[0010] 4. Insufficient real-time performance; CNDP and global efficiency metrics are typically computationally complex and suitable for static analysis, making them unsuitable for real-time vulnerability identification in dynamic environments. Summary of the Invention

[0011] To address the aforementioned technical problems, this invention proposes a weak node identification method based on centrality and efficiency measurement, thereby resolving the issues present in the prior art.

[0012] To achieve the above objectives, this invention provides a weak node identification method based on centrality and efficiency metrics, comprising: Based on network topology data and real-time status parameters, a network model is constructed that includes node health status and link attributes. The node failure probability of each node and the link failure probability of each link are calculated based on the network model. An information chain path set is generated based on the source node and the target node. The path success rate of each path in the information chain path set is calculated based on the node failure probability of each node and the link failure probability of each link. The corresponding node efficiency value is calculated based on the path success rate of all paths to which each node belongs. Based on the node efficiency value and centrality index, the weakness value of each node is calculated; The nodes are sorted and risk-classified according to the weak values, and the weak node identification results are output.

[0013] Optionally, the process of constructing a network model that includes node health status and link attributes includes: Node attributes are stored using a dictionary structure, and the node attributes include health status values; The link attributes are stored using an adjacency list structure, and these attributes include communication distance, transmission delay, and interruption status.

[0014] Optionally, the node failure probability of each node is calculated using the following formula: in, For nodes health status, This represents the failure probability of the node.

[0015] Optionally, the process of calculating the link failure probability of each link based on the network model includes: When the link interruption status is true, the probability of the link failure is determined to be 1; When the link interruption status is false, the distance attenuation factor is calculated using a segmentation function in combination with the communication distance, and the delay impact factor is calculated using a segmentation function in combination with the transmission delay. The link failure probability is determined based on the distance attenuation factor and the delay impact factor.

[0016] Optionally, the path success rate of each path in the information chain path set is calculated based on the node failure probability of each node and the link failure probability of each link, using the following formula: in, The set of nodes on the path. For the set of links on the path, This represents the probability of node failure. This represents the probability of link failure.

[0017] Optionally, the node efficiency value is calculated based on the path success rate of all paths containing each node, using the following formula: in, Represents all containing nodes The path set; This indicates the number of paths in which the node appears; This indicates the probability of a successful path.

[0018] Optionally, the process of calculating the weakness value of each node based on the node efficiency value and centrality index includes: Assign corresponding weight coefficients to each centrality metric and calculate the weighted sum of the centrality metrics; multiply the node efficiency value by the weighted sum to obtain the weak value; wherein, the centrality metrics include degree centrality, proximity centrality and betweenness centrality.

[0019] Optionally, sorting and risk-classifying nodes based on the vulnerability values ​​includes: Nodes are sorted by their vulnerability values; based on the percentage distribution of vulnerability values, nodes are classified into multiple risk levels.

[0020] Optionally, the real-time status parameters include the health status value of the node and the transmission delay and interruption status of the link; the network model is updated based on the periodically received real-time status parameters.

[0021] Compared with the prior art, the present invention has the following advantages and technical effects: 1. Lightweight computing; The vulnerability recognition method in this invention employs probabilistic modeling based on path success rate. The core computational process mainly includes link failure probability assessment and path traversal. The code implementation utilizes efficient graph computing libraries such as NetworkX, resulting in significantly lower parameter count and computational complexity compared to deep learning-based black-box models. Actual testing shows that in networks with thousands of nodes, a single vulnerability calculation can be completed within seconds. It can be deployed on common GPU modules or embedded processors, offering advantages such as low computational power dependence and rapid response.

[0022] 2. Strongly task-oriented; Traditional centrality methods only reflect the structural position of nodes, while the algorithm of this invention directly uses "path success rate" as the core indicator, and incorporates node health status and link failure probability (including interruption, interference-distance attenuation, and delay impact) into the calculation, so that the weak value can reflect the actual contribution of the node to the success or failure of the task chain, and the result is more in line with the real needs in the application scenario.

[0023] 3. Excellent environmental adaptability; The link failure probability modeling function fully considers three types of environmental factors: distance interruption, distance attenuation (interference effect), and delay, and is implemented using a piecewise function and upper limit truncation mechanism. Compared with traditional static indicators, this method can update the node weakness values ​​in real time as the environment changes dynamically, ensuring that the evaluation results are closely coupled with the external environment and improving the robustness of the algorithm.

[0024] 4. Scalability and versatility; The core implementation in the code adopts a modular design, with link failure probability calculation, path success rate calculation, and node efficiency calculation all implemented as independent functions, facilitating expansion and replacement. This method is not only applicable to communication networks but can also be extended to complex systems such as power networks, transportation networks, and the Internet of Things. It is equally effective in identifying "critical nodes" or "weak links," demonstrating broad applicability.

[0025] 5. High efficiency and real-time performance; This invention employs efficient graph algorithms and vectorization processing, avoiding the high computational cost of complex global optimization algorithms. Even in large-scale complex networks, it maintains low-latency computational performance, enabling real-time monitoring and online analysis. This feature is particularly suitable for identifying and providing early warnings of critical links in dynamically changing network environments. Attached Figure Description

[0026] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2 This is a flowchart illustrating the link fault modeling process according to an embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the path success rate calculation process according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the weak value results in an embodiment of the present invention. Detailed Implementation

[0027] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0028] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0029] Example 1 like Figure 1 As shown, this embodiment provides a weak node identification method based on centrality and efficiency measurement, including: (1) Input data and network modeling; First, import network topology data and real-time status parameters, and then establish a unified data structure based on this to support subsequent weak value calculations.

[0030] In terms of node modeling, the system uses a dictionary structure to store all node information. The key is a unique identifier for the node, and the value is a set of attributes for that node. Each node contains at least a health value, a node type, and several extended attributes. The health value ranges from [0,1] and reflects the node's availability; a value of 1 indicates full availability, and a value of 0 indicates complete failure. The node type can be a server, sensor, mobile terminal, or control center, etc. Extended attributes can include geographical location, processing power, or cache size, etc. The health value is continuously updated based on real-time monitoring data during operation. For example, when a device's availability decreases due to failure, energy consumption, or overload, its health value will decrease, thereby increasing the probability of that node's failure.

[0031] In terms of link modeling, an adjacency list and dictionary nested approach are used to store the communication relationships between nodes. For any node Its neighboring nodes Link attributes The data is stored in a format that includes communication distance, transmission latency, and link interruption status. Communication distance can be represented by physical distance or logical hop count; transmission latency is measured in seconds; and link interruption status is a Boolean value indicating whether the link has completely failed. Depending on application needs, the link can also include extended attributes such as bandwidth, throughput, or packet loss rate. This data organization method offers high query and update efficiency, and keeps the complexity of reading and modifying link parameters within a manageable range. It can meet the real-time requirements.

[0032] In terms of information chain modeling, the system generates multiple candidate paths from the source node to the target node through path search algorithms (such as depth-first search or breadth-first search). Each path consists of a set of nodes and a set of links, and the overall success rate is obtained by combining the reliability parameters of the nodes and links in subsequent calculations, thereby identifying weak links in the network.

[0033] To ensure adaptability in dynamic environments, the system employs a real-time update mechanism. The external interface periodically receives monitoring data, refreshing node and link attributes at a rate of seconds. Node health status values ​​are adjusted in real-time according to device operation or environmental changes, and link interruption status, latency, and distance parameters are continuously updated over time. Due to the use of a dictionary mapping structure, these modification operations involve only key-value pair replacements, thus enabling completion within milliseconds, ensuring both efficiency and real-time performance.

[0034] This method achieves efficient modeling and real-time updating of network topology through a data structure design based on adjacency lists and dictionary mappings, ensuring both structural clarity and meeting the computational performance requirements of large-scale network analysis.

[0035] (2) Node failure probability modeling; Node failure probability modeling is used to describe the availability and failure risk of each node in the network. The system defines a health value for each node, ranging from [0,1], with higher values ​​indicating greater reliability. This parameter can be obtained from real-time monitoring data, such as server load levels, sensor battery levels, and device error rates.

[0036] The node failure probability is determined by a simple inverse proportional relationship: ; in, For nodes health status, This represents the failure probability of the node. When the health value is 1, the node is considered fully available with a failure probability of 0; as the health value decreases, the corresponding failure probability increases; if the health value is 0, the node is completely unavailable with a failure probability of 1.

[0037] During system operation, node health values ​​dynamically adjust according to changes in operating conditions and the environment. For example, when a device's battery level drops, its temperature becomes too high, resources are overloaded, or it encounters a security threat, its health value decreases, thereby increasing the probability of failure. Since the probability of node failure directly participates in the calculation of the success rate of the information chain path, once the health of a critical node declines, it will significantly affect the reliability of its path and even the entire network.

[0038] (3) Link failure probability modeling; Link failure probability modeling is used to characterize the reliability of communication links between nodes. In this embodiment, link failure is not simply treated as a binary state of "connected" or "disconnected," but rather modeled using a multi-factor function to more closely resemble the actual network environment. The system defines a set of parameters for each link, including whether it is interrupted, communication distance, and transmission delay. If the link is interrupted, the failure probability is directly 1; if the link is normal, its distance attenuation effect and delay effect are further calculated.

[0039] ① Interruption status; The system first checks whether the link is interrupted. If it is interrupted, the failure probability of the link is directly determined to be 1, and it will not be included in subsequent calculations.

[0040] ② Interference attenuation function (implemented as a piecewise function); The interference-distance attenuation effect is designed based on the physical characteristics of communication: when two nodes are too close or too far apart, the link quality will significantly degrade. To reflect this characteristic, the system uses a piecewise linear function for modeling: within a low threshold distance, interference is strongest, and the failure probability takes the maximum baseline value; between the low and high thresholds, the failure probability gradually decreases with increasing distance; once the high threshold is exceeded, the link is considered unable to maintain reliable communication, and the attenuation term is zero. This function design ensures that the model can reflect the dual effects of "interference due to proximity" and "attenuation due to distance." The formula is as follows: in, The distance between nodes. , These are the thresholds for extremely low communication radius and limited communication radius, respectively.

[0041] ③ Delayed impact function (piecewise growth model); The delay effect is used to reflect the time sensitivity of network transmission. Link delay is divided into three intervals: in the range of 0–3 seconds, the probability of link failure increases slowly with delay; between 3–5 seconds, the increase is greater; when the delay exceeds 5 seconds, the probability of failure continues to increase linearly, but is limited to an upper limit of 0.2. This piecewise growth function conforms to the delay tolerance characteristics of communication systems and avoids the infinite cumulative effect caused by excessive delay.

[0042] ; in, It is the link transmission delay (seconds); It is a delay limit compensation.

[0043] The final link failure probability is determined by a combination of the above factors: in, This represents the interference-range attenuation component. The delay component is represented by the sum of the two components, followed by upper limit truncation to ensure that the maximum failure probability of a single link does not exceed 0.9. This function design not only improves the rationality and interpretability of the model, but also allows for parameter adjustment to adapt to different types of communication networks.

[0044] The above link fault modeling integrates three types of environmental factors: interruption, interference, and delay, forming the environmental awareness mechanism of this embodiment. Its specific functional relationships are as follows: Figure 2 As shown.

[0045] (4) Calculation of path success rate; Path success rate modeling is used to evaluate the probability of an information chain from the source node to the target node completing a transmission or task in the current network environment. Unlike static analysis that only considers a single node or a single link, this embodiment takes the "path" as a whole, comprehensively considering the state of all nodes and links within it, and obtains the overall success rate through probability product, thereby truly reflecting the task achievability of the network in a dynamic environment.

[0046] In implementation, the system first iterates through all possible paths from the source node to the target node based on the topology data and the candidate path set. For each path, its success rate depends on the reliability of all nodes on the path (i.e., the reliability of the nodes on the path). ,in (the probability of node failure) and the reliability of all links (i.e., ,in Multiplying by the link failure probability, we get: in, The set of nodes on the path. For the set of links on the path, This represents the probability of node failure. This represents the probability of link failure.

[0047] In implementation, the system utilizes the path traversal and shortest path calculation capabilities provided by NetworkX to batch process the candidate path set. Link attributes (such as distance, delay, and is_broken) on the path are stored in edge attributes, while node health values ​​are stored in node attributes. During path traversal, the system calls these attributes to calculate the path success rate and uses NetworkX to improve the efficiency of path set generation when necessary. This method avoids the burden of manually implementing complex graph traversal while ensuring efficient batch calculation of path success rates even in large-scale topology environments.

[0048] The underlying idea behind this design is that the reliability of a path depends on the combined effect of all its components; failure in any one link will reduce the overall success rate. Through probability multiplication, the system naturally exhibits the "weak link effect," meaning that a high failure rate in a particular node or link will amplify the impact on the entire path.

[0049] Furthermore, the modeling of path success rate also considers the dynamic nature of the environment awareness mechanism. Since node health values ​​and link parameters are continuously updated during runtime, the path success rate is not a fixed value, but rather adjusts in real time with changes in the network environment. For example, when the latency of a link suddenly increases, its failure probability rises, directly causing a decrease in the success rate of all paths passing through that link; when the health of a node recovers, the path success rate increases again.

[0050] Path success rate modeling not only provides core input for subsequent node efficiency calculations but also enables the system to perform dynamic, real-time network reliability analysis. Compared to traditional static indicators, this method more closely reflects the real-world network operation, providing a solid probabilistic foundation for critical node identification and vulnerability calculation. The path success rate calculation process is as follows: Figure 3 As shown.

[0051] (5) Node efficiency modeling; The node efficiency value is calculated based on the node's contribution to multiple information chain paths. The system first enumerates all candidate paths from the source node to the target node, then evaluates the success rate of each path, and accumulates and normalizes the contribution of that path to the nodes it contains. Thus, the efficiency value of each node depends not only on its own health status, but also on its position and role in the task chain.

[0052] In practical implementation, the system uses the networkx library for graph structure management and path enumeration. Specifically, networkx.all_simple_paths() is used to efficiently generate a set of source-to-target paths, and the success probability of each path is calculated by combining the attribute parameters of nodes and links. After the success probability of each path is calculated, this probability is accumulated across all nodes in the path in an average manner to obtain the node efficiency value. Because networkx has high performance in large-scale graph computation, this method can ensure that even in a network with thousands of nodes, a single efficiency value calculation can still be completed in seconds, meeting real-time requirements.

[0053] (6) Node efficiency calculation; Node efficiency is defined as the average success rate contribution of the node in its participating paths: in, Represents all containing nodes The path set; This indicates the number of paths in which the node appears; This indicates the probability of a successful path.

[0054] (7) Calculation of weak points; The final weak point value is obtained by fusing node efficiency and centrality metrics: in, For node performance, , , These are degree centrality, proximity centrality, and betweenness centrality, respectively. This method considers both the node's own combat capabilities and its structural importance in the network.

[0055] After calculating node efficiency and vulnerability values, the system generates a sorted list of vulnerable nodes and displays it visually. This output not only provides numerical metrics for the nodes but also intuitively reflects which nodes are most vulnerable in the current network through risk grading.

[0056] First, the node efficiency value reflects the degree to which a node contributes to the tasks across multiple information chains. The lower the efficiency value, the weaker the node's support for the overall success rate.

[0057] Secondly, the system obtains a comprehensive weakness value by weighting and fusing node efficiency with centrality indicators. The weakness value not only considers the health status and function of a node, but also reflects its criticality in the network topology.

[0058] In terms of risk classification, the system does not use a fixed threshold, but rather classifies risks based on a percentage according to the global distribution of vulnerability values. The specific rules are as follows: High-risk nodes (red): Nodes located in the top 20% of the weakest points; Medium-risk nodes (yellow / orange): Nodes located in the middle 20% of the vulnerability ranking; Low-risk nodes (blue): Nodes located in the bottom 60% of the vulnerability ranking.

[0059] This percentage-based risk grading method can adapt to networks of different sizes and in different scenarios, avoiding bias caused by fixed numerical thresholds.

[0060] like Figure 4 As shown, the system uses color gradients to visually mark node risks: Nodes B1 and B2 are located in the core of the network and have high vulnerability values, so they are marked in red and are considered high-risk. A1 and A2 are in the middle layer, ranking in the middle of the weakness value, so they are displayed in an orange-yellow transition color, which indicates medium risk. Most execution nodes (such as b1~b8) and target node Z1 are ranked lower and marked in blue, indicating low risk.

[0061] Example of results as shown in Table 1: Node efficiency value, weakness value, and risk level (based on percentage ranking); Table 1

[0062] As can be seen from the figures and tables, the risk classification results are highly consistent with the position of the nodes in the network topology. Nodes in core positions are marked as high-risk due to their importance, while most peripheral nodes are classified as low-risk.

[0063] By using this risk grading method based on distribution percentages, the system can adaptively identify weak nodes under different scales and task scenarios, avoiding inaccuracies caused by absolute threshold settings, thus better meeting the needs of actual applications.

[0064] Pseudocode of the core algorithm flow: enter: A set of nodes N, where each node contains a health status health∈[0,1]; The set of links E, each link containing {distance, delay, is_broken}; Parameter configuration P{d_low,d_high,p0, delay threshold, etc.}; PathSet, a set of source-to-target paths generated by the network structure; step: 1. Node failure probability modeling; For each node n∈N: p_node[n] ← 1 - health[n]; 2. Link failure probability modeling; For each link e(u,v)∈E: If is_broken(u,v)=True: p_link[u,v]←1.0; otherwise: Calculate the distance decay factor f_dist based on distance; Calculate the delay factor f_delay based on delay; p_link[u,v]←min(f_dist+f_delay,0.9); 3. Path success rate modeling; For each path path∈PathSet: success←1; For each node n in the path: success←success×(1-p_node[n]); For each link (u,v) in the path: success←success×(1-p_link[u,v]); P_path[path] ← success; 4. Node efficiency calculation; Initialize eff[n] ← 0; For each path path∈PathSet: For each node n in the path: eff[n]←eff[n]+(P_path[path]) / (|path|); For all nodes n: eff[n] ← (eff[n]) / the number of times the node appears; 5. Weakness value calculation; Compute node centrality index: C_deg[n], C_clo[n], C_bet[n]; For each node n: centrality[n]←α·C_deg[n]+β·C_clo[n]+γ·C_bet[n]; weakness[n]←eff[n]×centrality[n]; 6. Node sorting and risk classification; Sort all nodes in descending order of their weakness values; Risk levels are categorized by percentage distribution: Top 20% → High risk; The middle 20% → Medium risk; The latter 60% → Low risk; Output: A sorted list of weak points, where each point contains {eff, weakness, risk level}.

[0065] The vulnerability recognition method in this invention employs probabilistic modeling based on path success rate. The core computational process mainly includes link failure probability assessment and path traversal. The code implementation utilizes efficient graph computing libraries such as NetworkX, resulting in significantly lower parameter count and computational complexity compared to deep learning-based black-box models. Actual testing shows that in networks with thousands of nodes, a single vulnerability calculation can be completed within seconds. It can be deployed on common GPU modules or embedded processors, offering advantages such as low computational power dependence and rapid response.

[0066] Traditional centrality methods only reflect the structural position of nodes, while the algorithm of this invention directly uses "path success rate" as the core indicator, and incorporates node health status and link failure probability (including interruption, interference-distance attenuation, and delay impact) into the calculation, so that the weak value can reflect the actual contribution of the node to the success or failure of the task chain, and the result is more in line with the real needs in the application scenario.

[0067] The link failure probability modeling function fully considers three types of environmental factors: distance interruption, distance attenuation (interference effect), and delay, and is implemented using a piecewise function and upper limit truncation mechanism. Compared with traditional static indicators, this method can update the node weakness values ​​in real time as the environment changes dynamically, ensuring that the evaluation results are closely coupled with the external environment and improving the robustness of the algorithm.

[0068] The core implementation in the code adopts a modular design, with link failure probability calculation, path success rate calculation, and node efficiency calculation all implemented as independent functions, facilitating expansion and replacement. This method is not only applicable to communication networks but can also be extended to complex systems such as power networks, transportation networks, and the Internet of Things. It is equally effective in identifying "critical nodes" or "weak links," demonstrating broad applicability.

[0069] This invention employs efficient graph algorithms and vectorization processing, avoiding the high computational cost of complex global optimization algorithms. Even in large-scale complex networks, it maintains low-latency computational performance, enabling real-time monitoring and online analysis. This feature is particularly suitable for identifying and providing early warnings of critical links in dynamically changing network environments.

[0070] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A weak node identification method based on centrality and efficiency measurement, characterized in that, The method comprises the following steps: constructing a network model comprising node health states and link attributes based on network topology data and real-time state parameters; calculating node failure probabilities of each node and link failure probabilities of each link based on the network model; generating a path set of information chains from a source node to a target node, and calculating path success rates of each path in the path set based on the node failure probabilities of each node and the link failure probabilities of each link; calculating node efficiency values of each node based on the path success rates of all paths in which each node is located; calculating weak values of each node based on the node efficiency values and centrality indexes; sorting and classifying nodes according to the weak values, and outputting a weak node identification result.

2. The weak node identification method based on centrality and efficiency measurement according to claim 1, wherein the process of constructing a network model comprising node health states and link attributes comprises: adopting a dictionary structure to store node attributes, wherein the node attributes comprise health state values; adopting an adjacency list structure to store link attributes, wherein the link attributes comprise communication distances, transmission time delays and interruption states.

3. The weak node identification method based on centrality and efficiency measurement according to claim 1, wherein the calculation of node failure probabilities of each node is performed by the following formula:

4. The weak node identification method based on centrality and efficiency measurement according to claim 1, wherein the process of calculating link failure probabilities of each link based on the network model comprises: when the link interruption state is true, determining that the link failure probability is 1; in, For nodes health status, This represents the failure probability of the node. when the link interruption state is false, calculating a distance attenuation factor by a piecewise function in combination with the communication distance, and calculating a delay influence factor by a piecewise function in combination with the transmission time delay; determining the link failure probability according to the distance attenuation factor and the delay influence factor.

5. The weak node identification method based on centrality and efficiency measurement according to claim 1, wherein the calculation of path success rates of each path in the path set of information chains based on the node failure probabilities of each node and the link failure probabilities of each link is performed by the following formula:

6. The weak node identification method based on centrality and efficiency measurement according to claim 1, wherein the calculation of node efficiency values of each node based on the path success rates of all paths in which each node is located is performed by the following formula: The process of calculating weak values of each node based on the node efficiency values and centrality indexes comprises: assigning corresponding weight coefficients to each centrality index and calculating a weighted sum of the centrality indexes; multiplying the node efficiency values by the weighted sum to obtain the weak values; wherein the centrality indexes comprise degree centrality, closeness centrality and betweenness centrality.

8. The weak node identification method based on centrality and efficiency measurement according to claim 1, wherein the sorting and classifying of nodes according to the weak values comprises: wherein, is a set of nodes on the path, is a set of links on the path, is a node failure probability, is a link failure probability. sorting nodes according to the weak values; and classifying nodes into multiple risk levels according to the percentage distribution of the weak values.

9. The weak node identification method based on centrality and efficiency measurement according to claim 1, wherein wherein, denotes the set of all paths containing the node ; denotes the number of paths in which the node occurs; denotes the success probability of the path.

7. The method of identifying weak nodes based on centrality and performance metrics as claimed in claim 1, wherein, ​ ​ ​ ​ ​ ​ The real-time state parameters include a health state value of a node and a transmission delay and an interruption state of a link; and the network model is updated based on the periodically received real-time state parameters.

Images