A method for identifying key nodes in a network based on cascading failures

Abstract

The present invention discloses a method for identifying key nodes in a network based on cascading failure, including: obtaining the network topology structure; determining an initial set of key nodes in the network according to the network topology structure and the position information of each node; expanding the initial set of key nodes to obtain an alternative set of key nodes; calculating the down-link potential of each node in the initial set of key nodes and selecting the node with the largest down-link potential value as the first key node in the final set of key nodes; removing the first key node, and obtaining the node with the largest down-link potential among the remaining nodes in the alternative set of key nodes and adding it to the final set of key nodes; successively obtaining the node with the largest down-link potential in the current iteration and adding it to the final set of key nodes until all key points in the final set of key nodes are selected. The present invention uses the down-link potential as an evaluation index for node criticality to obtain key nodes in the network for focused monitoring and protection, improving the robustness of the network under cascading failure conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of network key node identification, and particularly relates to a method for identifying network key nodes based on cascading failure. Background Art

[0002] A Mobile Ad Hoc Network (MANET) is a network that combines mobile communication and computer networks. It is an instant network system composed of a group of autonomous devices or nodes, and has the following main characteristics in terms of structure: Dynamic topology: that is, the nodes in the network can move arbitrarily, so the topology of the network may also change; Link bandwidth is limited and capacity is time-varying: Since the topology changes dynamically, the traffic forwarded by each node that is not itself the destination also changes over time. Therefore, different from wired networks, its link capacity shows time-varying characteristics; Power is limited: Due to the mobile characteristics of network nodes, most of them are powered by batteries. Therefore, when designing the system, energy conservation becomes a very important indicator; Physical security is limited: Mobile networks are more vulnerable to security threats than fixed networks (wired and wireless). In addition to overcoming the security weaknesses of wireless links, new security risks brought by mobile topologies also need to be overcome.

[0003] MANET has the characteristics of not relying on infrastructure, being easy to deploy, having no center, being self-organizing, and being highly dynamic. It can provide effective communication services for users without being restricted by factors such as time, space, and environment. It is widely used in military, daily life, disaster relief and other fields. It can either form an independent network or be connected to networks such as the Internet and the Internet of Things (IoT) to build a large network with wide coverage, and has broad application prospects.

[0004] At the same time, characteristics such as the openness, broadcast nature, and dynamic vulnerability of wireless media also pose security risks to MANET itself and other networks connected to it. The network usually carries a certain load, including substances, energy, or information, etc. Since the storage and processing capabilities of each node itself are limited, when the load increases to a certain extent, some nodes in the network will fail due to overload. After some nodes fail, the load transmitted through them will be redistributed, which in turn causes other nodes to fail because the load exceeds the node capacity, resulting in a chain reaction. This phenomenon is called cascading failure. The cascading failure caused by node failure seriously affects the performance of the entire network. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a method for identifying network key nodes based on cascading failure scenarios. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0006] One aspect of the present invention provides a method for identifying key nodes in a network based on cascading failures, including:

[0007] S1: Obtain the network topology according to the position information of each node in the network and the link relationship between nodes;

[0008] S2: Determine the initial set of key nodes in the network according to the network topology and the position information of each node;

[0009] S3: Expand the initial set of key nodes to obtain an alternative set of key nodes;

[0010] S4: Calculate the down-link potential of each node in the initial set of key nodes and select the node with the largest down-link potential value as the first key node in the final set of key nodes, where the down-link potential is the sum of the influence result on the network connectivity rate and the influence result on the overall network load when the current node fails;

[0011] S5: Remove the first key node, and obtain the node with the largest down-link potential among the remaining nodes in the alternative set of key nodes as the second key node and add it to the final set of key nodes;

[0012] S6: Sequentially obtain the nodes with the largest down-link potential in the current iteration and add them to the final set of key nodes until all the key points in the final set of key nodes are selected.

[0013] In an embodiment of the present invention, the S1 includes:

[0014] S11: Obtain the position coordinates of each node in the network;

[0015] S12: Obtain the routing table of each node in the network, and establish the adjacency matrix A of the network, A = [a ij , where a ij represents the link connection situation between node v i and node v j ;

[0016] S13: Obtain the network topology according to the position coordinates of each node and the adjacency matrix A.

[0017] In an embodiment of the present invention, the S2 includes:

[0018] S21: Calculate the betweenness value of each node in the network according to the network topology;

[0019] S22: Select a predetermined number or a predetermined proportion of nodes in descending order of the betweenness values of all nodes to form the initial set of key nodes.

[0020] In an embodiment of the present invention, S3 includes:

[0021] S31: Obtain the minimum value x of the abscissas of the nodes in the initial set of key nodes min and the maximum value x max , the minimum value y of the ordinates min and the maximum value y max , and form a coordinate interval [x min , x max and [y min , y max ;

[0022] S32: Add the nodes in the network whose remaining node coordinates belong to any one of the coordinate range intervals [x min , x max or [y min , y max to the initial set of key nodes V C , and form an alternative set of key nodes V C '.

[0023] In an embodiment of the present invention, S4 includes:

[0024] S41: Obtain the degree of decrease in network connectivity caused by the failure of the node v C in the initial set of key nodes V i ;

[0025] S42: Obtain the total increase in network load caused by the failure of the node v C in the initial set of key nodes V i ;

[0026] S43: Obtain the downlink potential of the node v i according to the degree of decrease in network connectivity and the total increase in network load caused by the failure of the node v i ;

[0027] S44: Obtain the downlink potential of each node in the initial set of key nodes V C , and obtain the node with the largest downlink potential value as the first key node in the final set of key nodes V F , where the set of key nodes V F is the set of key nodes to be finally obtained.

[0028] In an embodiment of the present invention, the calculation formula for the downlink potential of the node v i is:

[0029]

[0030] where Con(vi ) represents node v i The connectivity rate of the network after failure, Con represents node v i The connectivity rate of the network before failure represents node v i The total increase in load in the network after failure represents the remaining total capacity in the network

[0031] In one embodiment of the present invention, S6 includes:

[0032] S61: Repeat step S5, delete the key node selected in one iteration from network G. After network G undergoes cascading failure, it becomes the remaining network G'. Determine whether some or all of the nodes in the current node failure in the key node candidate set V C ' fail. If the nodes in V C ' do not completely fail, calculate the down-link potential of the non-failed nodes in the key node candidate set V C '. If all the nodes in V C ' fail, then calculate the down-link potential of the remaining non-failed nodes in the entire network G', and select the node with the largest down-link potential to join the key node set V F ;

[0033] S62: Repeat step S61 until the number of nodes in the key node set reaches the predetermined requirement or the nodes in the network completely fail in the current iteration

[0034] Another aspect of the present invention provides a storage medium, in which a computer program is stored, and the computer program is used to execute the steps of the method for identifying key nodes of a network based on cascading failure described in any one of the above embodiments

[0035] Another aspect of the present invention provides an electronic device, including a memory and a processor. A computer program is stored in the memory, and when the processor calls the computer program in the memory, the steps of the method for identifying key nodes of a network based on cascading failure described in any one of the above embodiments are implemented

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] 1. The method for identifying key nodes of a network based on cascading failure of the present invention uses the down-link potential as a new node criticality evaluation index to obtain key nodes of the network and focuses on monitoring and protecting these key nodes, which can better improve the robustness of the network under cascading failure

[0038] 2. The network key node identification method of the present invention combines the physical location information of nodes and uses betweenness to select the initial set of key nodes. How to select the first key node is crucial for the selection of key nodes in the cascading failure scenario. Selecting the first key node from the initial set of key nodes is more likely to protect the key nodes at the topological center and the physical location center, can effectively prevent the network from being fragmented, can improve the importance of relevant nodes, and thus improve the robustness of the entire network.

[0039] 3. The present invention uses the connectivity rate as a measure of network robustness, which is more reasonable than the number of non-failed nodes in the network.

[0040] The following will further elaborate on the present invention in detail with reference to the drawings and embodiments. Description of the Drawings

[0041] Figure 1 is a flowchart of a network key node identification method based on cascading failure provided by an embodiment of the present invention;

[0042] Figure 2 is a distribution diagram of an initial set of key nodes provided by an embodiment of the present invention;

[0043] Figure 3 is a distribution diagram of an alternative set of key nodes provided by an embodiment of the present invention;

[0044] Figure 4 is a flowchart of calculating the network connectivity rate provided by an embodiment of the present invention;

[0045] Figure 5 is a comparison diagram of the decline in network connectivity rate after deleting the key nodes identified by the network key node identification method of the embodiment of the present invention and the traditional method. Detailed Embodiments

[0046] In order to further elaborate on the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following will detail a network key node identification method based on a cascading failure scenario proposed according to the present invention with reference to the drawings and specific embodiments.

[0047] The foregoing and other technical contents, features, and effects of the present invention can be clearly presented in the following detailed description in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and specific understanding of the technical means and effects adopted by the present invention to achieve the predetermined purpose can be obtained. However, the accompanying drawings are only for reference and illustration, and are not used to limit the technical solution of the present invention.

[0048] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variant are intended to cover non-exclusive inclusion, so that an article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of additional identical elements in the article or device including the said element.

[0049] This embodiment proposes a method for identifying key nodes in a network based on cascading failure. By combining the topological information of the network and the spatial location information of network nodes, it analyzes the criticality of nodes in the network, and can screen out key nodes that may cause a significant decline in network performance after failure, so as to facilitate focused monitoring of these key nodes.

[0050] The idea of this embodiment is as follows: Through the network node position information and topological structure, a corresponding network model is established. Using betweenness as an importance index, relatively important nodes in the network topological structure are selected as the initial set of key nodes. Subsequently, according to the position information of these important nodes in the initial set of key nodes, that is, the maximum and minimum values of the two-dimensional coordinates, the horizontal and vertical coordinate intervals are divided. The set of nodes with abscissa or ordinate within this area is called the alternative set of key nodes. According to the reduction of network connectivity rate caused by node failure and the ability to make other nodes vulnerable, the importance of nodes is sorted to obtain the final key nodes.

[0051] Please refer to Figure 1 , the method for identifying key nodes in a network based on cascading failure in this embodiment includes:

[0052] S1: According to the position information of each node in the network and the link relationship between nodes, obtain the network topological structure.

[0053] Specifically, step S1 includes:

[0054] S11: Obtain the position coordinates of each node in the network;

[0055] Taking the MANET network as an example in this embodiment, each node in the MANET forms stable communication links with nodes within the communication range, and then forms a complete ad-hoc network. In the actual process, each node in the MANET network uploads its own physical position and the routing table information of the node to the network platform control terminal. The network platform control terminal can obtain the topological structure of the network according to the position coordinates and routing table information of the nodes.

[0056] Specifically, in this embodiment, the MANET network is represented by G=(V, E), where V represents the set of all nodes in the network, and E represents the set of all communication links in the network. Assume that there are N nodes and M communication links in the network, then V={v i |i = 1, 2, …, N}, E={e k |e k =(v i , v j ), k = 1, 2, …, M}, v i , v j represents the two nodes at both ends of the communication link e k . After the network platform control terminal collects information, it obtains the physical coordinates P of the nodes, where P={p i}, p i =(x i , y i ), p i is the coordinate of the i-th node in the MANET network, i = 1, 2, ..., N.

[0057] Subsequently, the network platform control terminal collects the routing tables of each node and establishes the adjacency matrix A of the network, where:

[0058]

[0059] a ij represents the link connection situation between node v i and node v j . a ij = 0 indicates that there is no communication link between node v i and node v j . a ij = 1 indicates that there is a communication link between node v i and node v j .

[0060] Subsequently, the topological structure of the network, that is, the link connection relationship of the network, is obtained according to the adjacency matrix A.

[0061] S2: Determine in the network according to the network topological structure and the position information of each node.

[0062] Further, the S2 includes:

[0063] S21: Calculate the betweenness value C B (v i ) of each node in the network according to the network topological structure:

[0064]

[0065] Among them, C B (v i ) represents the betweenness value of the v i -th node, v i ∈ V, i = 1, 2, 3…, N, σ st (v i ) represents the number of paths passing through the node v s in the shortest path from the node v t to the node v i , and σ st represents the number of shortest paths from the node s to the node t. The betweenness value of each node in the MANET network can be obtained according to the above formula.

[0066] S22: Select a predetermined number or a predetermined proportion of nodes in descending order of the betweenness values of all nodes to form an initial set of key nodes.

[0067] In this embodiment, the betweenness values of all nodes are sorted in descending order, and the first 10 - 20% of the nodes are selected to form an initial set of key nodes V C . Preferably, the first 10% of the nodes are selected to form an initial set of key nodes V C . Please refer to Figure 2 , Figure 2 is a schematic diagram of the distribution of an initial set of key nodes provided by an embodiment of the present invention. Among them, all the spheres are all the nodes in the current network, the connections between the nodes are the links between the nodes, and the hollow spheres 26, 28, 19, 37, 38 are the nodes in the initial set of key nodes selected according to the betweenness values, that is, the five nodes with the largest betweenness values among all the nodes.

[0068] S3: Expand the initial set of key nodes to obtain an alternative set of key nodes.

[0069] Specifically, step S3 of this embodiment includes: S31: Obtain the minimum value x min and the maximum value x max of the abscissas of the nodes in the initial set of key nodes, and the minimum value y min and the maximum value y max of the ordinates, and form a coordinate interval [x min , x max and [y min , y max .

[0070] Specifically, according to the coordinates of the nodes in the initial set of key nodes V C , obtain the minimum value x min and the maximum value x max of the abscissas of the nodes, and the minimum value y min and the maximum value y max, form the coordinate range intervals [x min , x max and [y min , y max , as Figure 3 shown.

[0071] S32: Add the nodes in the MANET whose remaining node coordinates belong to any of the coordinate range intervals [x min , x max or [y min , y max to the initial set V C of key nodes to form the alternative set V C ' of key nodes.

[0072] Specifically, obtain the position coordinates of all nodes in the MANET except the initial set V C of key nodes. Add the nodes in the MANET whose coordinates belong to any of the coordinate range intervals [x min , x max and [y min , y max to the initial set V C of key nodes. That is, judge whether the abscissa of any node in the MANET is within the interval [x min , x max and whether the ordinate is within the interval [y min , y max . If one interval is satisfied, add the current node to the initial set V C of key nodes, thereby expanding the initial set V C of key nodes to the alternative set V C ' of key nodes. As Figure 3 shown, the hollow spheres 26, 28, 19, 37, 38 are the nodes in the initial set of key nodes selected according to the intermediate values. The minimum value x min and the maximum value x max of the abscissas of the nodes in the initial set of key nodes, the minimum value y min and the maximum value y max of the ordinates form the coordinate intervals [x min , x max and [y min , y max , that is, Figure 3 the tic-tac-toe area in, then add all the nodes in this tic-tac-toe area to the initial set V C of key nodes to form the alternative set V C ' of key nodes.

[0073] S4: Calculate the descending connection potential of each node in the initial critical node set and select the node with the maximum descending connection potential value as the first node in the final critical node set, where the descending connection potential is the sum of the influence result on the network connectivity rate and the influence result on the overall network load when the current node fails.

[0074] Specifically, the S4 includes:

[0075] S41: Obtain the initial critical node set V C The degree of network connectivity rate decrease caused by the failure of node v i in it.

[0076] First of all, it should be noted that for the neighbor node v of node u, there are two possible impacts that the failure of node u may have on its neighbor node v. The first is that the load redistribution causes the load of node v to exceed the capacity and fail, thereby leading to a decrease in the network connectivity rate. The second is that the failure of node u causes the load of node v to increase. In other words, if node u fails, the load of its neighbor node v will increase. One situation is that the load increases but does not exceed the load capacity, and the other is that it exceeds the load capacity of neighbor node v, resulting in a decrease in the connectivity rate of the entire network.

[0077] Please refer to Figure 4 , Figure 4 which is a flowchart for calculating the network connectivity rate provided by an embodiment of the present invention. The calculation process of the network connectivity rate includes the following steps: Obtain the total number of nodes in the network x, the total number of node pairs with paths in the network; Obtain the number of subnets into which the network is divided when node v i fails. Here, the subnet refers to multiple connected networks divided when node v i in the network fails; Obtain the sum y of the number of node pairs with paths in all subnets; Calculate the network connectivity rate of node v i according to the ratio of y / x.

[0078] Specifically, the network connectivity rate is the ratio of the number of connected node pairs in the network to the total number of node pairs in the network. Set Con as the network connectivity rate function, and its calculation formula is:

[0079]

[0080] where w is the number of subnets in the network, n is the total number of nodes in the network, and n i is the number of nodes in the i-th subnet.

[0081] In this embodiment, according to the network connectivity rate function, the network connectivity rate Con before the failure of node v i and the network connectivity rate Con(v i after the failure of node v i), and obtain node v i Degree of network connectivity decline caused by failure

[0082] S42: Obtain the initial set V of critical nodes C Node v in i Total increase in network load caused by the failure of

[0083] When a node fails, the traffic load transmitted through this node is proportionally allocated, mainly according to the ratio of the remaining carrying capacity of the surrounding neighbor nodes of the failed node to the capacity. Specifically, during the redistribution of the load, the load of the failed node will be redistributed according to the remaining capacity of the surrounding neighbor nodes. Assume node v t Among its neighbor nodes v i After failure, at time t, the load received from node v i Is Then The expression of is:

[0084]

[0085] Among them, Is the total load allocated to all neighbor nodes after the failure of node v i , v t ∈N(v i ), N(v i ) represents the set of neighbor nodes of node v i , Is the node capacity of node v t At time t, Is the node load of node v t At time t, Is the remaining capacity of node v t At time t.

[0086] Then the load of node v t At (t + 1) time is:

[0087]

[0088] Among them, Is the original load of node v t At time t, that is, the original load of node v i When its neighbor node v t Was not failed, node v Represents node v t Among its neighbor nodes v i The load received at time t after failure, if Then node v twill also fail, thus triggering a new round of cascading failures.

[0089] In summary, the initial set of critical nodes V can be obtained C in which the node v i after failure, the total increase in network load caused:

[0090]

[0091] where represents the total increase in load in the network after the failure of node v i , and represents the remaining total capacity in the network.

[0092] S43: Obtain the down - connection potential of node v i according to the degree of decrease in network connectivity rate and the total increase in network load caused by the failure of node v i .

[0093] It should be noted that the down - connection potential of a node is defined as the comprehensive calculation result of all possible impacts on the network under the cascading effect after the node fails, mainly including the impact result on the network connectivity rate and the impact result on the overall network load when the node fails. In this embodiment, the down - connection potential of node v i is a linear combination of two factors, including the impact on network connectivity rate and the impact on overall network load. The calculation formula for the down - connection potential of node v i is:

[0094]

[0095] The overall failure impact and load impact of node v i in the network are respectively defined as the degree of decrease in network connectivity and the total increase in load of the non - failed nodes in the network where Con(v i ) represents the connectivity rate of the network after the failure of node v i , Con represents the connectivity rate of the network before the failure of node v i , represents the total increase in load in the network after the failure of node v i , and represents the remaining total capacity in the network.

[0096] S44: Obtain the down - connection potential of each node in the initial set of critical nodes V C and obtain the node with the maximum down - connection potential value.

[0097] Specifically, calculate the initial set of critical nodes V CThe descending connection potential of each node in, calculate the initial set V of key nodes C The descending connection potential of the nodes in, select the node with the largest descending connection potential value and add it to the key node set V F , this key node set V F is the set of key nodes that ultimately need to be obtained.

[0098] S5: Remove the first key node, and obtain the node with the largest descending connection potential among the remaining nodes in the key node alternative set as the second key node and add it to the final key node set.

[0099] Specifically, remove the first key node selected in step S4 from the network, that is, make this node fail, calculate the connectivity of the remaining network after cascade failure, and calculate the key node alternative set V C ' of all nodes in, select the node with the largest descending connection potential as the second key node and add it as a key node to V F .

[0100] S6: Successively obtain the nodes with the largest descending connection potential in the current iteration and add them to the final key node set until all the key points in the final key node set are selected.

[0101] Step S6 of this embodiment includes:

[0102] S61: Repeat step S5, delete the key node selected in one iteration from the network G, and after the network G undergoes cascade failure, it becomes the remaining network G'. Determine whether the nodes in the current key node alternative set V C ' are partially or completely failed when the current node in the key node alternative set fails. If V C ' is not completely failed, calculate the descending connection potential of the non-failed nodes in the key node alternative set V C '. If all the nodes in V C ' are failed, then calculate the descending connection potential of the remaining non-failed nodes in the entire network G', and select the node with the largest descending connection potential and add it to the key node set V F ;

[0103] S62: Repeat step S61 until the number of nodes in the key node set reaches the predetermined requirement or all the nodes in the network under the current iteration are completely failed.

[0104] Specifically, remove the second key node, repeat step S5, and obtain the node with the largest descending connection potential among the remaining nodes in the key node alternative set as the third key node and add it to the final key node set; subsequently, remove the third key node from the network and repeat the above steps, and so on.

[0105] It should be noted that during a certain iteration process, when a node in the critical node candidate set fails, due to the proportional redistribution of traffic load, partial or complete failure of the remaining nodes in the critical node candidate set may occur. If the failure of a certain node causes partial failure of the nodes in the critical node candidate set V C ', that is, there are still non-failed nodes, calculate the connectivity loss potential of all non-failed nodes in the critical node candidate set V C '. If the failure of a certain node causes all nodes in the critical node candidate set V C ' to fail, that is, no remaining nodes survive, calculate the connectivity loss potential of all remaining surviving nodes in the entire network, and select the node with the largest connectivity loss potential to join the critical node set V F . Repeat the above steps until the number of nodes in the critical node set V F reaches 10% of the total number of nodes in the network or the network completely fails and there are no normally operating nodes in the current iteration. The nodes in the obtained critical node set V F are the critical nodes that need to be monitored and protected with emphasis.

[0106] The effectiveness of the network critical node identification method based on cascading failure in this embodiment is verified through experiments below. Taking Figure 2 as a MANET scenario, the nodes in the figure are distributed according to their physical coordinates, and the connections between nodes indicate the existence of communication links between nodes. Taking Figure 2 as the experimental object, a comparative experiment is conducted on the nodes in Figure 2 . Specifically, the network critical node identification method based on cascading failure in this embodiment and two existing methods are respectively used to screen the critical nodes.

[0107] To prove the effectiveness of the critical node screening method proposed in this embodiment of the invention, HL (Highest Loads, maximum load) and RIF (Risk if Failure) are selected as comparison indicators for experiments and comparisons in the scenario of Figure 2 . The same screening steps are adopted, only the screening indicators are different. The method in this embodiment of the invention is a method based on CLP (Connectivity Loss Potential), and the two existing methods are a method based on the HL indicator and a method based on the RIF indicator respectively.

[0108] HL indicator: That is, this indicator believes that the node with the largest attack load is more likely to cause the failure of the network and is beneficial to improving the attack effect.

[0109] RIF indicator: This indicator represents the ratio of the load of the attacked node to the total load of its neighbor nodes:

[0110]

[0111] L i Refers to the initial load of the attacked node Refers to the total initial load of its neighbor nodes. The larger this indicator is, the more likely it is to cause cascading failures.

[0112] Please refer to Figure 5 , Figure 5 is a comparison graph of the decline in network connectivity rate after deleting the key nodes identified by the network key node identification method of the embodiment of the present invention and the traditional method. Among them, the abscissa is the serial number of the key nodes, and the ordinate is the network connectivity rate. From Figure 5 it can be seen that deleting the key nodes screened by using CLP as an indicator causes the largest decline in the network connectivity rate, proving the importance of the nodes screened by the network key node identification method of the embodiment of the present invention, and thus proving the effectiveness of this method.

[0113] The network key node identification method based on cascading failures in this embodiment uses the downlink potential as a new node criticality evaluation indicator to obtain network key nodes and focuses on monitoring and protecting these key nodes, which can better improve the robustness of the network in the case of cascading failures. The network key node identification method of this embodiment combines the physical location information of the nodes and selects the initial key node set by betweenness. How to select the first key node is crucial for the selection of key nodes in the cascading failure scenario. Selecting the first key node from the initial key node set is more likely to protect the key nodes at the topological center and the physical location center, can effectively prevent the network from being split, can improve the importance of relevant nodes, and thus improve the robustness of the entire network.

[0114] Another embodiment of the present invention provides a storage medium storing a computer program for executing the steps of the method for identifying key nodes of a network based on cascading failure in the above embodiment. Another aspect of the present invention provides an electronic device including a memory and a processor, where the memory stores a computer program, and when the processor calls the computer program in the memory, the steps of the method for identifying key nodes of a network based on cascading failure as described in the above embodiment are implemented. Specifically, the above integrated module implemented in the form of software function modules can be stored in a computer-readable storage medium. The above software function modules stored in a storage medium include several instructions for causing an electronic device (which may be a personal computer, a server, or a network device, etc.) or a processor to execute some steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: various media 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 disc that can store program codes.

[0115] The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, which should all be regarded as belonging to the protection scope of the present invention.

Claims

1. A method for identifying key nodes in a network based on cascading failures, characterized in that Including: S1: Obtain the network topology structure according to the location information of each node in the network and the link relationship between nodes; S2: Determine the initial set of critical nodes in the network according to the network topology structure and the location information of each node; S3: Expand the initial set of critical nodes to obtain an alternative set of critical nodes; S4: Calculate the descending connection potential of each node in the initial set of critical nodes and select the node with the largest descending connection potential value as the first critical node in the final set of critical nodes, where the descending connection potential is the sum of the influence result on the network connectivity rate and the influence result on the overall network load when the current node fails; S5: Remove the first critical node, and obtain the node with the largest descending connection potential among the remaining nodes in the alternative set of critical nodes as the second critical node and add it to the final set of critical nodes; S6: Sequentially obtain the node with the largest descending connection potential in the current iteration and add it to the final set of critical nodes until all the critical points in the final set of critical nodes are selected; The S2 includes: S21: Calculate the betweenness value of each node in the network according to the network topology structure; S22: Select a predetermined number or a predetermined proportion of nodes in descending order of the betweenness values of all nodes to form the initial set of critical nodes; The S3 includes: S31: Obtain the minimum value x of the abscissas of the nodes in the initial set of key nodes min and the maximum value x max , the minimum value y of the ordinates min and the maximum value y max , and form a coordinate interval [x min , x max and [y min , y max ; S32: Add the nodes in the network whose remaining node coordinates belong to any one of the coordinate intervals [x min , x max or [y min , y max to the initial key node set V C , to form an alternative key node set V C '.

2. The method for identifying key nodes in a network based on cascading failure according to claim 1, wherein The S1 includes: S11: Obtain the position coordinates of each node in the network; S12: Obtain the routing tables of each node in the network, and establish the adjacency matrix A of the network, A = [a ij , where a ij represents the link connection situation between node v i and node v j . S13: Obtain the network topology structure according to the position coordinates of each node and the adjacency matrix A.

3. The method for identifying key nodes in a network based on cascading failures according to claim 1, characterized in that The S4 includes: S41: Obtain the initial set V of key nodes C intermediate node v i the degree of decrease in the network connectivity rate caused after failure S42: Obtain the initial set V of key nodes C intermediate node v i the total increase in network load caused by the failure of S43: Obtain the down - connection potential of node v i according to the degree of decrease in network connectivity rate caused by the failure of node v i and the total increase in network load; S44: Obtain the initial set V of key nodes C The descending connection potential of each node in, and obtain the node with the largest descending connection potential value as the first key node in the final key node set V F in which the key node set V F is the set of key nodes to be finally obtained.

4. The method for identifying key nodes of a network based on cascading failure according to claim 1, characterized in that Node v i The calculation formula for the descending connection potential of Among them, Con(v i ) represents the connectivity rate of the network after node v i fails. Con represents the connectivity rate of the network before node v i fails, represents the total increase in load in the network after node v i fails, represents the remaining total capacity in the network.

5. The method for identifying key nodes in a network based on cascading failures according to claim 4, wherein The S6 includes: S61: Repeat step S5 to remove the key nodes selected in one iteration from network G. After cascading failures occur in network G, it becomes the remaining network G'. Determine whether some or all of the nodes in the current key node candidate set fail when the current node in the key node candidate set fails. If not all nodes in V C ' fail, calculate the descending connection potential of the non-failed nodes in the key node candidate set V C '. If all nodes in V C ' fail, then calculate the descending connection potential of the remaining non-failed nodes in the entire network G', and select the node with the largest descending connection potential to add to the key node set V C ; F ; S62: Repeat step S61 until the number of nodes in the set of critical nodes reaches a predetermined requirement or all the nodes in the network completely fail in the current iteration.

6. A storage medium, characterized in that, The storage medium stores a computer program, and the computer program is used to execute the steps of the method for identifying critical nodes in a network based on cascading failure according to any one of claims 1 to 5.

7. An electronic device, characterized in that, Including a memory and a processor, the memory stores a computer program, and when the processor calls the computer program in the memory, it implements the steps of the method for identifying critical nodes in a network based on cascading failure according to any one of claims 1 to 5.

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