Multi-layer network anti-attack evaluation method

Abstract

The embodiment of the invention provides a method for evaluating the attack resistance of a multilayer network. The method comprises the following steps of: performing repeated attacks on a physical network layer of the multilayer network by adopting a target attack mode; the multi-layer network comprises a physical network layer and a logic network layer; for each attack of the target attack mode, calculating the maximum connected slice ratio of the logic network layer after the corresponding attack; and calculating a damage degree index of the multi-layer network corresponding to the target attack mode according to the maximum connected slice ratio corresponding to all attacks of the target attack mode.

Description

Technical Field

[0001] The present invention relates to the field of network attacks, and in particular to a multi-layer network anti-attack evaluation method. Background Art

[0002] Traditional methods of damaging coupled networks have the same attack capability against nodes at all network layers. Communication networks are crucial in modern warfare. Because the information flow between different communication nodes is non-physical and there are no physical metrics for communication nodes, communication networks can be considered abstract logical networks, making them difficult to directly damage. Research on node damage in single-layer complex networks is highly mature and in-depth. For example, using machine learning to predict node betweenness as a measure of node bridging capability and using machine learning to damage network nodes have greatly improved the efficiency of network disruption.

[0003] In the process of implementing the present invention, the applicant discovered that the prior art has at least the following problems:

[0004] Traditional network security evaluation methods do not take into account the impact of damage to the physical network layer on the abstract logical network layer communication nodes, nor the impact of damaged logical network layer nodes on the physical network layer, which leads to incomplete and inaccurate network security evaluation. Summary of the Invention

[0005] An embodiment of the present invention provides a multi-layer network anti-attack evaluation method to address the problem that traditional network security evaluation methods do not consider the impact of damage to the physical network layer on the abstract logical network layer communication nodes, and the impact of damaged logical network layer nodes on the physical network layer, thereby resulting in incomplete and inaccurate network security evaluation.

[0006] To achieve the above objectives, on the one hand, an embodiment of the present invention provides a multi-layer network attack resistance evaluation method, comprising:

[0007] Conducting multiple repeated attacks on the physical network layer of a multi-layer network using a targeted attack method; the multi-layer network includes a physical network layer and a logical network layer;

[0008] For each attack of the target attack mode, calculating the maximum connected slice ratio of the logical network layer after the corresponding attack;

[0009] Calculating the damage degree index of the multi-layer network corresponding to the target attack mode according to the maximum connected slice ratio corresponding to all attacks of the target attack mode;

[0010] The maximum connected slice ratio is used to represent the robustness of the logical network layer; and the damage degree index is used to evaluate the anti-attack capability of the multi-layer network under the target attack mode.

[0011] Furthermore, the targeted attack method is used to repeatedly attack the physical network layer of the multi-layer network, including:

[0012] Attacking a physical layer node of a physical network layer according to the target attack mode, deleting the attacked physical layer node, and deleting the direct edge corresponding to the attacked physical layer node;

[0013] Delete the logical layer nodes in the logical network layer according to the type of the deleted attacked physical layer nodes.

[0014] Furthermore, for each attack of the target attack mode, calculating the maximum connected slice ratio of the logical network layer after the corresponding attack includes:

[0015] For each attack of the target attack mode, selecting a subnetwork with the largest number of nodes from the multiple subnetworks composed of the remaining logical layer nodes in the logical network layer after the attack as the largest connected slice after the attack;

[0016] The maximum connected slice ratio after the attack is calculated according to the following formula:

[0017]

[0018] Where M is the maximum connected slice ratio of the logical network layer after the attack; N' All is the number of logical layer nodes in the largest connected slice of the logical network layer after the attack; N is the total number of logical layer nodes in the logical network layer before the attack.

[0019] Furthermore, calculating the damage degree index of the multi-layer network corresponding to the target attack mode according to the maximum connected slice ratio corresponding to all attacks of the target attack mode includes:

[0020] The vulnerability index of the multi-layer network corresponding to the target attack method is calculated according to the following formula:

[0021]

[0022] Where F(j) represents the vulnerability index of the multi-layer network after n attacks with the jth target attack method; i = 1, 2...n represents the number of attacks under each target attack method; M j (i) represents the maximum connected slice ratio of the logical network layer during the i-th attack of the j-th target attack method; (1-M j (i)) represents the collapse degree of the multi-layer network during the i-th attack of the j-th target attack method;

[0023] The calculated vulnerability index of the multi-layer network corresponding to the target attack mode is used as the damage degree index of the multi-layer network corresponding to the target attack mode.

[0024] Furthermore, deleting the logical layer nodes in the logical network layer according to the type of the attacked physical layer nodes to be deleted includes:

[0025] In the case where the type of the attacked physical layer node to be deleted is a key node, after deleting the attacked physical layer node and all direct edges of the attacked physical layer node from the physical network layer, simultaneously delete the logical layer node in the logical network layer corresponding to the attacked physical layer node and all direct edges of the logical layer node;

[0026] The key node indicates that the corresponding physical layer node is directly connected to the logical layer node in the logical network layer.

[0027] Furthermore, deleting the logical layer nodes in the logical network layer according to the type of the attacked physical layer nodes to be deleted includes:

[0028] In a case where the type of the deleted attacked physical layer node is a transition node, identifying physical layer node pairs that are no longer interoperable in the physical network layer due to the deletion of the attacked physical layer node and the corresponding direct connection edge, and deleting the direct connection edge between the corresponding logical layer nodes of the identified physical layer node pairs in the logical network layer;

[0029] The transition node indicates that the corresponding physical layer node does not directly provide physical support for the logical network layer.

[0030] Furthermore, the edges of the multi-layer network have weights; and the damage degree index of the multi-layer network corresponding to the target attack method is calculated based on the maximum connected piece ratio corresponding to all attacks of the target attack method, including:

[0031] The robustness index of the multi-layer network corresponding to the target attack method is calculated according to the following formula:

[0032] Rank=F(j)-richness(j) (3)

[0033]

[0034] Wherein, Rank represents the robustness index of the multi-layer network corresponding to the target attack mode; F(j) represents the vulnerability index of the multi-layer network corresponding to n attacks with the j-th target attack mode; NP is the number of paths initially existing in the physical network layer; MP is the total path capacity obtained by summing the weights corresponding to NP paths; NP1 is the number of paths existing in the physical network layer after the attack of the multi-layer network corresponding to the j-th target attack mode ends; MP1 is the total remaining path capacity obtained by summing the weights corresponding to NP1 paths existing in the physical network layer after the attack of the multi-layer network corresponding to the j-th target attack mode ends; richness is the richness; α and β are weight parameters greater than 0, α+β=1;

[0035] The calculated robustness index of the multi-layer network corresponding to the target attack mode is used as the damage degree index of the multi-layer network corresponding to the target attack mode.

[0036] The above technical solution has the following beneficial effects: after repeatedly attacking the physical network of the multi-layer network under the target attack mode, the maximum connected piece ratio of the logical network layer after each attack is calculated, and then the damage degree index of the multi-layer network corresponding to the target attack mode is determined according to the maximum connected piece ratio after all attacks. The maximum connected piece ratio measures the integrity of the logical network layer after each physical network layer is attacked, reflects the robustness of the logical network layer, and also reflects the damage degree of the logical network from the opposite direction. The damage degree index of the multi-layer network reflects the anti-attack ability of the multi-layer network under the target attack, thereby providing a damage degree evaluation method for the multi-layer network under the target attack based on the combination of the damage degree of the logical network layer caused by the physical network attack, so as to more reasonably determine the network architecture of the multi-layer network in the real scenario, and more accurately and effectively determine the efficient attack method for the existing multi-layer network. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0038] Figure 1 This is a flow chart of a multi-layer network anti-attack evaluation method according to one embodiment of the present invention;

[0039] Figure 2 It is a diagram of the physical-logical interdependence network;

[0040] Figure 3This is a schematic diagram of changes in a physical layer node after being attacked according to one embodiment of the present invention;

[0041] Figure 4 This is a schematic diagram of changes in a logic layer node after being attacked according to one embodiment of the present invention;

[0042] Figure 5 This is a comparison curve of vulnerability indicators of an ER random network, a BA scale-free network, and a Power-Law scale-free network after a two-layer network with 20 logical network layer nodes according to one embodiment of the present invention is attacked;

[0043] Figure 6 This is a comparison curve of vulnerability indicators of an ER random network, a BA scale-free network, and a Power-Law scale-free network after a two-layer network with 30 logical network layer nodes according to one embodiment of the present invention is attacked;

[0044] Figure 7 This is a comparison curve of vulnerability indicators of an ER random network, a BA scale-free network, and a Power-Law scale-free network after a two-layer network with 40 logical network layer nodes according to one embodiment of the present invention is attacked;

[0045] Figure 8 This is a comparison curve of vulnerability indicators of an ER random network, a BA scale-free network, and a Power-Law scale-free network after a two-layer network with 50 logical network layer nodes according to one embodiment of the present invention is attacked;

[0046] Figure 9 This is a comparison curve diagram of the vulnerability indicators of an ER random network, a BA scale-free network, and a Power-Law scale-free network after a two-layer network with 60 logical network layer nodes according to one embodiment of the present invention is attacked. DETAILED DESCRIPTION

[0047] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0048] The inventors discovered that in the physical power station-command relationship network, command relationship nodes are abstract logical definitions that cannot be directly addressed using physical destruction. However, destruction is interdependent with the communication network. Once the physical nodes in the physical infrastructure network layer are destroyed, communication effectiveness is directly affected. Taking the power-communication coupled network structure as an example, the interdependence between the power system and the communication network means that a power grid outage can have a serious negative impact on the communication network, and vice versa. Failure of information infrastructure is a key factor leading to power system collapse. In some networks, each node has multiple interconnected links, and the number of interconnections per node remains consistent. In other networks, nodes have different numbers of interconnections, and the internal link distribution follows a Poisson distribution. Still other networks use a "conventional allocation" method based on internal links to demonstrate its improved robustness compared to random allocation techniques. Traditional research has explored these network models by simulating cascading failures in smart grids. The damage effect of communication node and power node failure on heterogeneous layer nodes is believed to be achievable through physical methods. The currently widely used multi-layer network anti-attack evaluation methods, although they are systematic and comprehensive in theory, have obvious shortcomings in practical applications: they often focus on the analysis of network architecture and ignore the actual characteristics of the target object, especially the in-depth consideration of its attackability in actual operation. This limitation makes it difficult to accurately predict the effect of the attack. The inventor found that the loss of communication network nodes may not directly lead to the loss of control of the corresponding power grid components. At the same time, communication nodes at the abstract logical level are difficult to physically damage at the real level. Traditional technologies lack consideration of these issues, making it difficult to effectively evaluate the degree of damage to interdependent multi-layer networks such as power-communication networks when they are attacked.

[0049] On the one hand, if Figure 1 As shown, an embodiment of the present invention provides a multi-layer network anti-attack evaluation method, including:

[0050] Step S10, repeatedly attacking the physical network layer of the multi-layer network using a targeted attack method; the multi-layer network includes a physical network layer and a logical network layer;

[0051] Step S11, for each attack of the target attack mode, calculating the maximum connected slice ratio of the logical network layer after the corresponding attack;

[0052] Step S12, calculating a damage degree index of the multi-layer network corresponding to the target attack mode according to the maximum connected slice ratios corresponding to all attacks of the target attack mode;

[0053] The maximum connected slice ratio is used to represent the robustness of the logical network layer; and the damage degree index is used to evaluate the anti-attack capability of the multi-layer network under the target attack mode.

[0054] In some embodiments, preferably, the multi-layer network is a dependent network, which refers to a network system composed of multiple interdependent networks. For example, the power network and the communication network may be interdependent, with the power network supplying power to the equipment in the communication network, and the communication network being used for monitoring and scheduling of the power network. Preferably, the multi-layer network includes a physical network layer and a logical network layer, and there is an interdependent relationship between the physical network layer and the logical network layer. For example, the logical network layer exists based on the physical network layer, and the physical network layer is monitored by the logical network layer. Preferably, any logical layer node in the logical network layer has a corresponding interdependent physical layer node in the physical network layer, and a physical layer node in the physical network layer may not have a corresponding logical layer node in the logical network layer.

[0055] Targeted attack methods (attack strategies) include but are not limited to hub node attacks, high-betweenness node attacks, closeness centrality attacks, and random attacks. High-degree targeting prioritizes attacking nodes with the highest degree (number of connections) (e.g., opinion leaders in social networks, substations in power grids, etc.). The rationale behind this is that hub nodes serve as core connectivity within a network, and their destruction can lead to network fragmentation or a sharp drop in performance. High-betweenness centrality targeting targets attack nodes that act as "bridges" within the network (i.e., nodes with high betweenness centrality). The rationale is that these nodes control a large number of paths, and their removal significantly increases the average path length of the network, reducing connectivity. Closeness centrality targeting targets nodes with the shortest average distance to other nodes (nodes with high closeness centrality). The rationale is that these nodes are efficient intermediaries for information dissemination, and their destruction can cause delays or interruptions in information transmission. The specific method of random attack is to randomly select nodes for destruction. Its principle is low cost but low efficiency. When it is applicable to scale-free networks, a large number of nodes must be destroyed to significantly affect the network.

[0056] Multi-layer networks include physical network layers and logical network layers. Since the logical layer nodes and edges of the logical network layer are at an abstract level, it is difficult to effectively attack and damage them directly through physical attacks.

[0057] The embodiments of the present invention have the following technical effects: the embodiments of the present invention repeatedly attacks a multi-layer network according to a target attack method, and evaluates the robustness of the logical network layer after each attack, that is, the maximum connected piece ratio, and then combines the maximum connected piece ratios of the logical network layer after all attacks under the target attack method to obtain a damage degree index of the target attack method on the multi-layer network. Based on the damage degree index, the attack resistance of the multi-layer network under the target attack method can be evaluated; based on the embodiments of the present invention, multiple target attack methods are applied to multiple selected multi-layer networks, and the corresponding damage degree index of each multi-layer network under the multiple target attack methods can be obtained. By comparing the damage degree indicators corresponding to the multiple target attack methods between different multi-layer networks, the multi-layer network with the best robustness under the multiple target attack methods can be selected from the multiple multi-layer networks, thereby improving the rationality of network structure selection. Based on the embodiments of the present invention, it is also possible to attack an existing multi-layer network using a variety of different target attack methods, and obtain a damage degree index for the multi-layer network under each attack method (attack strategy). By comparing the damage degree indexes corresponding to the target attack methods (attack strategies), it is possible to find the target attack method (attack strategy) that causes the greatest damage to the attacked multi-layer network and has the best attack effect from the multiple target attack methods (attack strategies). In this way, when conducting a network attack, it is possible to reasonably select the attack method with the strongest attack capability and the most destructive to the logical network layer, thereby achieving the effect of increasing the physical damage degree to the logical network layer in the dependent network at the actual level.

[0058] Furthermore, a targeted attack method is used to repeatedly attack the physical network layer of the multi-layer network, including:

[0059] Attacking a physical layer node of a physical network layer according to the target attack mode, deleting the attacked physical layer node, and deleting the direct edge corresponding to the attacked physical layer node;

[0060] Delete the logical layer nodes in the logical network layer according to the type of the deleted attacked physical layer nodes.

[0061] In some embodiments, the physical network layer is typically a physical network, making it easy to perform physical attacks. The logical network layer's logical layer nodes and edges are abstract and difficult to effectively destroy directly through physical attacks. Attacking the physical network layer results in the destruction of physical layer nodes, which in turn deletes the corresponding physical layer nodes from the network. Direct edges connected to the deleted physical layer nodes are also deleted, resulting in a reduction in connection paths in the physical network layer. Because the logical network layer and the physical network layer are interdependent, logical layer nodes in the logical network layer correspond to physical layer nodes in the physical network layer. When a physical layer node in the physical network layer is destroyed, if a physical layer node has a corresponding logical layer node, the corresponding logical layer node in the logical network layer will also be destroyed. However, if a physical layer node does not have a corresponding logical layer node, the destruction of the logical layer node will not result in the destruction of the logical layer node. By combining attacks on the physical network layer with an evaluation of the robustness of the logical network layer after the attack (maximum connected slice ratio), it is possible to evaluate the effect of physical attacks on the physical network layer causing damage to the logical network layer, and thus to assess the extent of damage to the entire multi-layer network. When damage to physical layer nodes leads to damage to logical layer nodes, in turn, the damaged logical network layer's ability to control the physical network layer will also be damaged, resulting in deep damage to the multi-layer network.

[0062] The embodiments of the present invention have the following technical effects: by combining physical network layer attacks with logical network layer performance suppression, and by precisely analyzing the characteristics of the target's physical network layer, a high-efficiency attack is implemented, which in turn triggers a cascading effect at the logical network layer, weakening its functionality. This ensures the operability of the targeted attack and enables accurate quantitative assessment of the attack's effectiveness, facilitating the optimization of network attack techniques. This solves the problem of the difficulty of effectively attacking the logical network layer at the abstract logical level through physical attacks, and also addresses the problem of attacks that cause losses at the logical network layer but fail to effectively cause loss of control of the corresponding physical network layer.

[0063] Furthermore, for each attack of the target attack mode, calculating the maximum connected slice ratio of the logical network layer after the corresponding attack includes:

[0064] For each attack of the target attack mode, selecting a subnetwork with the largest number of nodes from the multiple subnetworks composed of the remaining logical layer nodes in the logical network layer after the attack as the largest connected slice after the attack;

[0065] According to formula (1), the maximum connected slice ratio after the attack is calculated:

[0066]

[0067] Where M is the maximum connected slice ratio of the logical network layer after the attack; N'All is the number of logical layer nodes in the largest connected slice of the logical network layer after the attack; N is the total number of logical layer nodes in the logical network layer before the attack.

[0068] In some embodiments, after a network is attacked, the remaining nodes may form several fragmented subnetworks. Nodes within a subnetwork can reach each other via connecting edges, but no connecting edges exist between two subnetworks. The subnetwork with the largest number of nodes is called the "maximum connected slice." After a network is damaged, the size of its maximum connected slice will also change accordingly, reflecting, to a certain extent, changes in the network's internal structure. The larger M is, the more robust the network. After a logical network layer is damaged, the original logical network layer may consist of multiple subnetworks, with the subnetwork with the largest number of nodes being the most effective in completing the original logical network layer's functions after damage. The larger the maximum connected slice after the attack, the more robust the logical network layer is and the less effective the attack. Calculating the maximum connected slice ratio can be used to evaluate the effectiveness of the attack.

[0069] The embodiments of the present invention have the following technical effects: by determining the maximum connected slice ratio of the logical network layer, the robustness of the multi-layer network can be quantified, and the attack effect can also be quantified from the reverse side.

[0070] Furthermore, calculating the damage degree index of the multi-layer network corresponding to the target attack mode according to the maximum connected slice ratio corresponding to all attacks of the target attack mode includes:

[0071] The vulnerability index of the multi-layer network corresponding to the target attack method is calculated according to formula (2):

[0072]

[0073] Where F(j) represents the vulnerability index of the multi-layer network after the j-th attack mode is attacked n times; i = 1, 2...n represents the number of attacks under each attack mode; M j (i) represents the maximum connected slice ratio of the logical network layer during the i-th attack of the j-th attack method; (1-M j (i)) represents the collapse degree of the multi-layer network during the i-th attack of the j-th attack method;

[0074] The calculated vulnerability index of the multi-layer network corresponding to the attack mode is used as the damage degree index of the multi-layer network corresponding to the attack mode.

[0075] In some embodiments, the edges of the multi-layer network can be weightless or weighted, and the weight of the edge is not considered when calculating the vulnerability index. For the multi-layer network, the attack efficiency of the logical network layer is used to represent the final attack effect measure. The attack efficiency function of each attack method (attack strategy) is as shown in formula (2). According to formula (2), the vulnerability index of the multi-layer network under the jth attack method can be obtained; the smaller F(j), the worse the effect of this attack method on the multi-layer network. When there are multiple target attack methods, the vulnerability index of the multi-layer network corresponding to each target attack method can be calculated separately according to the embodiment of the present invention. When evaluating the anti-attack performance of multiple multi-layer networks under one or more target attack methods, the vulnerability index of the multiple multi-layer networks under one or more target attack methods is determined based on the embodiment of the present invention as the corresponding damage degree index. By comparing the damage degree index corresponding to each multi-layer network, the optimal multi-layer network among the multiple multi-layer networks can be selected. When selecting the most effective attack method from multiple target attack methods, according to an embodiment of the present invention, the damage degree index corresponding to each target attack method can be determined, and the damage degree indexes corresponding to the multiple target attack methods can be compared to determine the most effective attack method for the multi-layer network. Specifically, the method includes: using the target attack method with the largest vulnerability index of the multi-layer network among the multiple target attack methods as the most effective attack method for the multi-layer network.

[0076] Furthermore, deleting the logical layer nodes in the logical network layer according to the type of the attacked physical layer nodes to be deleted includes:

[0077] In the case where the type of the attacked physical layer node to be deleted is a key node, after deleting the attacked physical layer node and all direct edges of the attacked physical layer node from the physical network layer, simultaneously delete the logical layer node in the logical network layer corresponding to the attacked physical layer node and all direct edges of the logical layer node;

[0078] The key node indicates that the corresponding physical layer node is directly connected to the logical layer node in the logical network layer.

[0079] In some embodiments, the physical layer node as a key node provides physical resource support for the logical layer node of the corresponding logical network layer. Figure 3As shown in the figure, solid points represent physical layer nodes, and hollow points represent logical layer nodes. The physical layer node pointed by the "attack" arrow has a corresponding logical layer node, which is a critical node. When the physical layer node pointed by the "attack" arrow is destroyed and deleted by the attack, the corresponding logical layer node is also deleted. Accordingly, the direct edge originally connected to the physical layer node pointed by the "attack" arrow is also deleted, as are the direct edges directly connected to the corresponding logical layer node. Deleting a critical node in the physical network layer also causes the deletion of the corresponding logical layer node and corresponding edges in the logical network layer. This is because when a critical node in the physical network layer expires, it directly causes communication failure with the corresponding logical layer node (or the logical layer node that it physically supports) in the logical network layer. If an attack accurately targets a critical node, it will damage both the physical layer node and the logical layer node, resulting in incomplete logical network layer communication, abnormal logical network layer communication, and incomplete monitoring of the physical network layer by the logical network layer. Consequently, the physical attack on the physical network layer causes a bidirectional interaction between the physical and logical network layers.

[0080] Furthermore, deleting the logical layer nodes in the logical network layer according to the type of the attacked physical layer nodes to be deleted includes:

[0081] In a case where the type of the deleted attacked physical layer node is a transition node, identifying physical layer node pairs that are no longer interoperable in the physical network layer due to the deletion of the attacked physical layer node and the corresponding direct connection edge, and deleting the direct connection edge between the corresponding logical layer nodes of the identified physical layer node pairs in the logical network layer;

[0082] The transition node indicates that the corresponding physical layer node does not directly provide physical support for the logical network layer.

[0083] In some embodiments, as Figure 4 As shown, solid points are physical layer nodes, and hollow points are logical layer nodes. Physical layer node 41, pointed to by the "attack" arrow, has no corresponding logical layer node and is a transition node. Physical node 42 corresponds to logical layer node 44, and physical node 43 corresponds to logical layer node 45. Physical layer node 41 connects physical layer nodes 42 and 43 via a direct edge. When physical layer node 41 is deleted, the direct edge between physical layer node 41 and physical layer node 42, as well as the direct edge between physical layer node 41 and physical layer node 43, are also deleted. At the same time, since physical layer nodes 42 and 43 no longer communicate with each other after deleting physical node 41, the edge between logical layer nodes 44 and 45 in the logical network layer needs to be deleted accordingly.

[0084] Furthermore, the edges of the multi-layer network have weights; and the damage degree index of the multi-layer network corresponding to the target attack method is calculated based on the maximum connected piece ratio corresponding to all attacks of the target attack method, including:

[0085] The robustness index of the multi-layer network corresponding to the target attack method is calculated according to formula (3) and formula (4):

[0086] Rank=F(j)-richness(j) (3)

[0087]

[0088] Wherein, Rank represents the robustness index of the multi-layer network corresponding to the target attack mode; F(j) represents the vulnerability index of the multi-layer network corresponding to n attacks with the j-th target attack mode; NP is the number of paths initially existing in the physical network layer; MP is the total path capacity obtained by summing the weights corresponding to NP paths; NP1 is the number of paths existing in the physical network layer after the attack of the multi-layer network corresponding to the j-th target attack mode ends; MP1 is the total remaining path capacity obtained by summing the weights corresponding to NP1 paths existing in the physical network layer after the attack of the multi-layer network corresponding to the j-th target attack mode ends; richness is the richness; α and β are weight parameters greater than 0, α+β=1;

[0089] The calculated robustness index of the multi-layer network corresponding to the target attack mode is used as the damage degree index of the multi-layer network corresponding to the target attack mode.

[0090] In some embodiments, for a weighted multi-layer network model, the edge weight of the physical network layer represents the information capacity on the line. Therefore, the richness can also be added to the attack measurement standard for measurement. Assume that the number of paths initially existing in the physical network layer is NP, and the total capacity of the paths is MP, where the value of MP is obtained by summing the weights corresponding to the NP paths. After the overall attack on the two-layer network is completed, the number of paths existing in the physical network is NP1, and the total capacity of the paths is MP1. The value of MP1 is obtained by summing the weights corresponding to the NP1 paths that still exist after the overall attack is completed. Its richness is defined as formula (4); where α+β=1, both greater than 0, α and β are weight parameters,

[0091] By adjusting the parameters, different potential optimal networks can be constructed. For networks with capacity, the attack efficiency and abundance can be considered together. When subjected to the jth attack strategy, the damage measurement standard of the network considering the edge capacity can be defined as formula (3); for the network structure, the smaller the attack efficiency and the greater the abundance, the stronger the robustness of the network structure. Therefore, for the rank value, the smaller the rank value, the more robust the two-layer network structure. When evaluating the anti-attack capabilities of multiple multi-layer networks under one or more target attack methods, based on the embodiment of the present invention, the corresponding damage degree index of the multiple multi-layer networks under one or more target attack methods is determined. By comparing the corresponding damage degree index of each multi-layer network, the optimal multi-layer network among the multiple multi-layer networks can be selected. When selecting the most effective attack method from multiple target attack methods, the corresponding damage degree index of each target attack method can be determined according to the embodiment of the present invention. The corresponding damage degree index of each target attack method can be compared to determine the most effective attack method for the multi-layer network. Specifically, the attack method with the smallest robustness index of the corresponding multi-layer network among the multiple attack methods is used as the most effective attack method for the multi-layer network.

[0092] The above technical solutions of the embodiments of the present invention are described in detail below with reference to specific application examples. For technical details not introduced during the implementation process, please refer to the relevant description above.

[0093] To address the shortcomings of traditional technologies, the present invention proposes a novel method for damaging interdependent physical-logical networks. Preferably, the multi-layer network is a two-layer network. By constructing a two-layer network structure connecting an abstract logical communication network layer and a concrete physical facility network layer, and defining damage methods and damage effect measurement indicators for this network, the potential for realistic damage to both enemy and friendly communication networks is effectively increased, providing a reference value for the future expansion and planning of this two-layer network. The present invention explores the damage methods and impacts of physical-logical coupled networks in modern warfare and proposes a new damage strategy. Using the logical communication layer as the evaluation indicator layer and the physical communication layer as the actual attack layer, corresponding damage methods and damage effect measurement indicators are defined. Experiments are conducted to preliminarily explore the robustness comparison of two-layer network structures composed of different types of logical networks after damage, and the robustness of two-layer network structures composed of the same type of logical networks is tested under different parameters.

[0094] 1. Physical-logical network structure modeling

[0095] Taking the Power-Communication Coupled Network (PCCN) as an example, its properties can be divided into two general layers: the physical layer (physical network layer) and the network layer (logical network layer). The physical layer is the actual wiring and connection layout (physical signal transmission medium). It is the network composed of various physical connections that support network information transmission services, such as the network constructed by transmission equipment such as optical cables. The logical layer is represented by the communication network. It is the virtual layout of network equipment. The method of data transmission between devices through the network is independent of the physical connections of the devices.

[0096] The embodiment of the present invention adopts a "one-to-many" coupling network, such as Figure 2 As shown, in this two-layer mode, the higher-level logical network divides its corresponding lower-level physical network into several sub-networks.

[0097] (1) Physical power network modeling

[0098] Take the power network as an example. There are many more power stations than abstract layer nodes, which are mainly responsible for physical signal transmission. The high-voltage transmission lines between power stations are equivalent to edges. The power network can be represented as G p =(V p ,E p ), where V p ={v p1 ,v p2 …v pn} is the set of power nodes, and n is the number of power nodes. p is the set of edges in the network. The embodiment of the present invention adds a distinguishing attribute to each power node, namely v pn =(x pn ,y pn ,z pn ), where (x pn ,y pn ) is the two-dimensional coordinate of the node, and

[0099]

[0100] z pn According to the data, power layer nodes are divided into two categories based on their attributes. One category is key nodes that are directly connected to abstract logic layer nodes. In addition to transporting electrical signals, they are also locations for building communication base stations. Their attribute is marked as 1. The other category is transition nodes that have no direct connection with abstract layer nodes and are only responsible for transmitting electrical signals. Their attribute is marked as 0.

[0101] (2) Abstract communication network model

[0102] The communication network layer is abstracted into an undirected unweighted graph, represented as G c =(Vc ,E c ), where V c ={v c1 ,v c2 …v cm} is the set of communication network nodes, and m is the total number of nodes. cm =(x cm ,y cm ), is the two-dimensional coordinate of the node. According to the structural characteristics, each logical communication layer node v cm The coordinates of pn =1, the physical power layer node coordinates are consistent.

[0103] 2. Physical-Logical Network Cascade Damage Methods and Measurement Standards

[0104] After the network structure model is constructed, the network is attacked. Since the nodes and edges of the logical communication network are at an abstract level and difficult to attack physically, when attacking this two-layer network model, only the nodes at the physical layer are manually selected and deleted. The prerequisites for this two-layer network are that all logical nodes can find corresponding physical layer key nodes, and in the initial network, there must be a physical layer reachable path for any logical node pair that is reachable by a path. When a node in the physical layer is damaged, all the inter-layer edges in the physical network layer corresponding to the node are deleted. When considering the impact of deleting a physical node on the logical layer node, it is necessary to consider the z attribute of the physical node, that is, whether it is a key node or a transition node.

[0105] (1) The key nodes are removed

[0106] If you remove the v in =(x in ,y in ,1), is a key node that is directly connected to the logical layer node. After deleting the node and all its edges at the physical layer, the corresponding logical layer node and all its edges are deleted at the same time. Because the failure of the key node at the physical layer will directly lead to the failure of the signal point at the communication layer. Figure 3 shown.

[0107] (2) The node removed is the transition node

[0108] If you remove the v jn =(x jn ,y jn,0), is a transition node that only transmits electrical signals. First, delete this node and all its edges at the physical layer. Then, examine which node pairs, among those that originally had paths at both the logical and physical layers, are no longer interconnected at the physical layer due to the loss of this node. These node pairs will also be blocked from connecting at the logical layer. Blockages are handled as follows:

[0109] Now, the logical node pairs that need to be blocked can be divided into two situations: one is that there is a direct edge between the two nodes; the other is that the two nodes are connected through other nodes. Delete all paths between directly connected node pairs. After this operation, it can be ensured that the paths between node pairs connected through other nodes are also invalid. Figure 4 shown.

[0110] In the final network attack measurement indicator, the embodiment of the present invention considers the communication effect of the entire network. Therefore, the logical network layer is used as the standard to calculate the network integrity of the network layer after the overall attack ends.

[0111] The present invention first introduces the concept of a maximum connected patch: after a network is attacked, the remaining nodes will form several fragmented subnetworks. The subnetwork with the largest number of nodes is called the "maximum connected patch." After the network is damaged by external forces, the size of its maximum connected patch will also change accordingly, which can reflect the changes in the internal structure of the network to a certain extent. It can be expressed as formula (1):

[0112]

[0113] Among them, N' All , N are the number of valid nodes remaining after the network failure and the total number of nodes in the network before the failure. The larger M is, the stronger the robustness of the network is.

[0114] After the ratio is calculated, the attack efficiency of the logical network layer is used to represent the final attack effect measurement. The attack efficiency function of each attack strategy is as shown in formula (2):

[0115]

[0116] Where j represents different attack strategies, i=1, 2...n represents the number of attacks under each strategy, (1-M j (i)) represents the degree of collapse of the multi-layer network when the j-th attack strategy attacks for the i-th time, and F(j) represents the sum of the vulnerability sizes after the j-th attack strategy attacks for n times. The smaller F(j), the worse the effect of this attack strategy on the multi-layer network.

[0117] Attack strategies (attack methods) include but are not limited to hub node attacks, high-betweenness node attacks, closeness centrality attacks, and random attacks. High-degree targeting prioritizes attacking nodes with the highest degree (number of connections) (e.g., opinion leaders in social networks, substations in power grids, etc.). This is based on the principle that hub nodes serve as core connectivity within a network, and their destruction can lead to network fragmentation or a sharp drop in performance. High-betweenness centrality targeting targets nodes that act as "bridges" in the network (i.e., nodes with high betweenness centrality). This is based on the principle that these nodes control a large number of paths, and their removal significantly increases the average path length of the network, reducing connectivity. Closeness centrality targeting targets nodes with the shortest average distance to other nodes (nodes with high closeness centrality). This is based on the principle that these nodes are efficient intermediaries for information dissemination, and their destruction can cause delays or interruptions in information transmission. The specific method of random attack is to randomly select nodes for destruction. Its principle is low cost but low efficiency. When it is applicable to scale-free networks, a large number of nodes must be destroyed to significantly affect the network.

[0118] Therefore, when calculating the degree of damage to the network, the degree of damage to the entire network can be calculated by calculating the maximum connected slice ratio of the logical network layer, and the entire network can be repeatedly attacked using different attack methods. The optimal attack method can be found by comparing the attack efficiency of the logical network layer.

[0119] For a weighted two-layer network model, the edge weights of the physical network layer represent the information capacity on the line. Therefore, the richness can also be added to the attack measurement standard for measurement. Assume that the number of paths initially existing in the physical network layer is NP, and the total capacity of the paths is MP, where the value of MP is obtained by summing the weights corresponding to the NP paths. After the overall attack on the two-layer network ends, the number of paths existing in the physical network is NP1, and the total path capacity is MP1. The value of MP1 is obtained by summing the weights corresponding to the NP1 paths that still exist after the overall attack ends. Its richness is defined as formula (4):

[0120]

[0121] Where α + β = 1, both are greater than 0. α and β are weight parameters. By adjusting the parameters, different potential optimal networks can be constructed. For networks with capacity, attack efficiency and abundance can be considered together. When subjected to the jth attack strategy, the damage measurement standard of the network considering the edge capacity can be defined as formula (3):

[0122] Rank=F(j)-richness(j) (3)

[0123] Wherein, Rank represents the robustness index of the multi-layer network corresponding to the attack method; F(j) represents the vulnerability index of the multi-layer network corresponding to n attacks with the j-th attack method.

[0124] For the network structure, the lower the attack efficiency and the greater the abundance, the more robust the network structure is. Therefore, for the rank value, the smaller the rank value, the more robust the two-layer network structure is.

[0125] 3. Analysis of Double-Layer Network Damage Examples

[0126] 3.1 Logical Network Type

[0127] Under the condition that the physical network maintains high connectivity, different types of logical communication networks are designed for experimental analysis. Five groups of experiments with different node numbers are designed for three types of logical networks for comparison. The number of nodes in the logical network layer is 20, 30, 40, 50 and 60 respectively, and the number of nodes in the physical layer is twice that of the logical layer. Each group of logical networks with the same number of nodes corresponds to the following network type: ER random network with an average degree distribution of k=4 (Erdos-Reni random network, – Random Network), BA scale-free network with m=2 newly added edges each time (Barabasi-Albert scale-free network, -Albert Scale-Free Network), and the Power-Law scale-free network with power-law distribution exponent gamma=2 and average degree distribution k=4 (a scale-free network based on power-law distribution).

[0128] Power-Law scale-free networks typically connect nodes by simulating a power-law degree distribution. The degree distribution of such networks follows a power-law distribution, meaning a small number of nodes have very high degrees, while the majority have low degrees. This implies the presence of a small number of "supernodes" in the network, which wield enormous influence.

[0129] BA scale-free networks use a "preferential connection" mechanism. The degree distribution of BA scale-free networks is also a power-law distribution, but its distribution shape is more gentle. In comparison, the number of super nodes in BA scale-free networks is less than that in Power-Law distribution networks.

[0130] Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 and Figure 9 The horizontal axis represents the ratio p of the number of physical layer nodes remaining after each round of attack to the total number of physical layer nodes. Data with p greater than or equal to 0.2 are analyzed. The value range of p is between 0.2 and 1.0. Correspondingly, the ratio of the number of physical layer nodes in each round of random attack to the total number of physical layer nodes is 1-p. The vertical axis represents the attack efficiency function F(j) (i.e., vulnerability index), which is the ratio of the connectivity level of the logical network after it is destroyed to the original connectivity level. Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 and Figure 9 The number of nodes in the logical network layer (logical network nodes) in the corresponding two-layer network is 20, 30, 40, 50 and 60 respectively, and the number of nodes in the physical network layer (physical network nodes) is twice the number of nodes in the corresponding logical network layer. Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 and Figure 9 Each figure compares the attack efficiency function F(j) corresponding to the ER random network with an average degree distribution of k=4, the BA scale-free network with m=2 newly added edges each time, and the Power-Law scale-free network with a power-law distribution exponent gamma=2 and an average degree distribution of k=4.

[0131] After t=6 complete attack processes are performed on each physical network layer, the average value of the 6 times is plotted and calculated. By conducting attack simulation experiments on ER random networks, BA scale-free networks, and Power-Law scale-free networks, the robustness of different types of logical networks under different attack probabilities is observed. Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 and Figure 9As can be seen from the data, the effectiveness of attacks using this damage method is similar between Power-Law and BA scale-free networks under different node numbers and attack probabilities. However, for ER random networks, when the attack probability is between 0.6 and 0.7, the robustness of this type of network changes compared to the other two networks. When p < 0.6, the robustness of the ER random network is generally lower than that of the scale-free networks (Power-Law and BA), while when p > 0.7, the robustness of the ER random network is superior to that of the scale-free networks (Power-Law and BA). The advantage of the ER random network becomes more pronounced as the proportion of attacked nodes increases. Specifically, when the proportion of attacked physical nodes exceeds half, the ER random network structure is selected for communication, resulting in greater resilience at the logical network layer.

[0132] 3.2 Exploration of Degree Distribution and Power Law Index of Logical Networks

[0133] Different network types with 60 nodes were analyzed using different parameter settings. For ER random networks, attacks were performed on ER random networks with average degree distributions of k = 5, 10, 15, 20, and 25. Specifically, random attacks were performed on physical layer networks with twice the number of nodes in the ER random network, and the damage rate was observed. For BA scale-free networks, attacks were performed on BA scale-free networks with single-connection edges of m = 2, 4, 6, 8, and 10. Specifically, random attacks were performed on physical layer networks with twice the number of nodes in the BA scale-free network, and the damage rate was observed. For Power-Law scale-free networks, attacks were performed on Power-Law scale-free networks with power-law degree distributions of gamma = 2, 2.25, 2.5, 2.75, and 3. Specifically, random attacks were performed on physical layer networks with twice the number of nodes in the Power-Law scale-free network, and the damage rate was observed. The logical network damage degree corresponding to the total proportion of damaged physical nodes observed in the above network is in the range of 0.2 to 1.

[0134] Observations of ER random networks show that as the average degree distribution increases, the network's invulnerability first increases and then decreases. When the number of logical network nodes is 60, the average degree distribution is most robust around k = 15. Observations of BA scale-free networks show that increasing the number of single-connection edges causes the network's invulnerability to first decrease and then increase, reaching its peak when m = 6. Analysis of Power-Law scale-free networks also shows that increasing the power-law degree also causes the network's invulnerability to first decrease and then increase. In theory, in real-world scale-free networks, a gamma value of 2 generally results in strong robustness under the attack method used in the test (random attack method).

[0135] It should be understood that the specific order or hierarchy of steps in the disclosed processes is an example of an exemplary method. Based on design preferences, it should be understood that the specific order or hierarchy of steps in the process can be rearranged without departing from the scope of the present disclosure. The accompanying method claims present elements of the various steps in an exemplary order and are not intended to be limited to the specific order or hierarchy described.

[0136] In the foregoing detailed description, various features are grouped together in a single embodiment to simplify the disclosure. This method of disclosure should not be interpreted as reflecting an intention that embodiments of the claimed subject matter require more features than are expressly recited in each claim. On the contrary, as reflected in the appended claims, the invention comprises less than all the features of any individual disclosed embodiment. The appended claims are hereby expressly incorporated into the detailed description, with each claim standing on its own as a separate preferred embodiment of the invention.

[0137] The above description of the disclosed embodiments is intended to enable any person skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments without departing from the spirit and scope of the present disclosure. Therefore, the present disclosure is not limited to the embodiments presented herein but is intended to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0138] The above description includes examples of one or more embodiments. Of course, it is impossible to describe all possible combinations of components or methods for the purpose of describing the above embodiments, but it will be appreciated by those skilled in the art that the various embodiments may be further combined and arranged. Therefore, the embodiments described herein are intended to encompass all such changes, modifications and variations that fall within the scope of protection of the appended claims. In addition, to the extent the term "comprising" is used in the specification or claims, the term is intended to be encompassed in a manner similar to the term "including". In addition, any use of the term "or" in the specification of the claims is intended to mean a "non-exclusive or".

[0139] Those skilled in the art will also appreciate that the various illustrative logical blocks, units, and steps listed in the embodiments of the present invention can be implemented by electronic hardware, computer software, or a combination of the two. To clearly demonstrate the interchangeability of hardware and software, the various illustrative components, units, and steps described above have generally described their functions. Whether such functions are implemented by hardware or software depends on the specific application and the design requirements of the entire system. Those skilled in the art may use various methods to implement the described functions for each specific application, but such implementation should not be understood as exceeding the scope of protection of the embodiments of the present invention.

[0140] The various illustrative logic blocks or units described in the embodiments of the present invention can be implemented or operated by a general-purpose processor, a digital signal processor, an application-specific integrated circuit (ASIC), a field programmable gate array or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof. The general-purpose processor can be a microprocessor, and optionally, the general-purpose processor can also be any conventional processor, controller, microcontroller or state machine. The processor can also be implemented by a combination of computing devices, such as a digital signal processor and a microprocessor, a plurality of microprocessors, one or more microprocessors combined with a digital signal processor core, or any other similar configuration.

[0141] The steps of the methods or algorithms described in the embodiments of the present invention may be directly embedded in hardware, a software module executed by a processor, or a combination of the two. The software module may be stored in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. For example, the storage medium may be connected to the processor so that the processor can read information from the storage medium and write information to the storage medium. Alternatively, the storage medium may also be integrated into the processor. The processor and storage medium may be provided in an ASIC, which may be provided in a user terminal. Alternatively, the processor and storage medium may also be provided in different components in the user terminal.

[0142] In one or more exemplary designs, the above-mentioned functions described in the embodiments of the present invention can be implemented in hardware, software, firmware, or any combination of the three. If implemented in software, these functions can be stored on a computer-readable medium or transmitted in the form of one or more instructions or codes on a computer-readable medium. Computer-readable media include computer storage media and communication media that facilitate the transfer of computer programs from one location to another. Storage media can be any available medium that can be accessed by a general or special computer. For example, such computer-readable media can include but are not limited to RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store program code in the form of instructions or data structures and other forms that can be read by a general or special computer, or a general or special processor. In addition, any connection can be appropriately defined as a computer-readable medium. For example, if the software is transmitted from a website, server or other remote resource via a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless methods such as infrared, wireless, and microwave, it is also included in the definition of computer-readable media. The disks and discs mentioned above include compact disks, laser disks, optical disks, DVDs, floppy disks, and Blu-ray discs. Disks typically reproduce data magnetically, while discs typically reproduce data optically with lasers. Combinations of the above may also be included in computer-readable media.

[0143] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-layer network anti-attack evaluation method, characterized in that: include: Conducting multiple repeated attacks on the physical network layer of a multi-layer network using a targeted attack method; the multi-layer network includes a physical network layer and a logical network layer; For each attack of the target attack mode, calculating the maximum connected slice ratio of the logical network layer after the corresponding attack; Calculating the damage degree index of the multi-layer network corresponding to the target attack mode according to the maximum connected slice ratio corresponding to all attacks of the target attack mode; The maximum connected slice ratio is used to represent the robustness of the logical network layer; and the damage degree index is used to evaluate the anti-attack capability of the multi-layer network under the target attack mode.

2. The multi-layer network anti-attack evaluation method according to claim 1, characterized in that: The targeted attack method is used to repeatedly attack the physical network layer of the multi-layer network, including: Attacking a physical layer node of a physical network layer according to the target attack mode, deleting the attacked physical layer node, and deleting the direct edge corresponding to the attacked physical layer node; Delete the logical layer nodes in the logical network layer according to the type of the deleted attacked physical layer nodes.

3. The multi-layer network anti-attack evaluation method according to claim 1, wherein: For each attack of the target attack mode, calculating the maximum connected slice ratio of the logical network layer after the corresponding attack includes: For each attack of the target attack mode, selecting a subnetwork with the largest number of nodes from the multiple subnetworks composed of the remaining logical layer nodes in the logical network layer after the attack as the largest connected slice after the attack; The maximum connected slice ratio after the attack is calculated according to the following formula: Where M is the maximum connected slice ratio of the logical network layer after the attack; N' All is the number of logical layer nodes in the largest connected slice of the logical network layer after the attack; N is the total number of logical layer nodes in the logical network layer before the attack.

4. The multi-layer network anti-attack evaluation method according to claim 1, wherein: Calculating a damage degree index of a multi-layer network corresponding to the target attack mode according to the maximum connected slice ratio corresponding to all attacks of the target attack mode, including: The vulnerability index of the multi-layer network corresponding to the target attack method is calculated according to the following formula: Where F(j) represents the vulnerability index of the multi-layer network after n attacks with the jth target attack method; i = 1, 2...n represents the number of attacks under each target attack method; M j (i) represents the maximum connected slice ratio of the logical network layer during the i-th attack of the j-th target attack method; (1-M j (i)) represents the collapse degree of the multi-layer network during the i-th attack of the j-th target attack method; The calculated vulnerability index of the multi-layer network corresponding to the target attack mode is used as the damage degree index of the multi-layer network corresponding to the target attack mode.

5. The multi-layer network anti-attack evaluation method according to claim 2, characterized in that: The deleting the logical layer node in the logical network layer according to the type of the attacked physical layer node to be deleted includes: In the case where the type of the attacked physical layer node to be deleted is a key node, after deleting the attacked physical layer node and all direct edges of the attacked physical layer node from the physical network layer, simultaneously delete the logical layer node in the logical network layer corresponding to the attacked physical layer node and all direct edges of the logical layer node; The key node indicates that the corresponding physical layer node is directly connected to the logical layer node in the logical network layer.

6. The multi-layer network anti-attack evaluation method according to claim 2, characterized in that: The deleting the logical layer node in the logical network layer according to the type of the attacked physical layer node to be deleted includes: In a case where the type of the deleted attacked physical layer node is a transition node, identifying physical layer node pairs that are no longer interoperable in the physical network layer due to the deletion of the attacked physical layer node and the corresponding direct connection edge, and deleting the direct connection edge between the corresponding logical layer nodes of the identified physical layer node pairs in the logical network layer; The transition node indicates that the corresponding physical layer node does not directly provide physical support for the logical network layer.

7. The multi-layer network anti-attack evaluation method according to claim 4, characterized in that: The edges of the multi-layer network have weights; and the damage degree index of the multi-layer network corresponding to the target attack method is calculated based on the maximum connected piece ratio corresponding to all attacks of the target attack method, including: The robustness index of the multi-layer network corresponding to the target attack method is calculated according to the following formula: Rank = F(j) - richness(j) Wherein, Rank represents the robustness index of the multi-layer network corresponding to the target attack mode; F(j) represents the vulnerability index of the multi-layer network corresponding to n attacks with the j-th target attack mode; NP is the number of paths initially existing in the physical network layer; MP is the total path capacity obtained by summing the weights corresponding to NP paths; NP1 is the number of paths existing in the physical network layer after the attack of the multi-layer network corresponding to the j-th target attack mode ends; MP1 is the total remaining path capacity obtained by summing the weights corresponding to NP1 paths existing in the physical network layer after the attack of the multi-layer network corresponding to the j-th target attack mode ends; richness is the richness; α and β are weight parameters greater than 0, α+β=1; The calculated robustness index of the multi-layer network corresponding to the target attack mode is used as the damage degree index of the multi-layer network corresponding to the target attack mode.

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