A multi-layer network attack resistance evaluation method

Abstract

The embodiment of the application provides a multi-layer network attack resistance evaluation method, comprising the following steps: repeatedly attacking a physical network layer of a multi-layer network by using a target attack mode; the multi-layer network comprises the physical network layer and a logical network layer; for each attack of the target attack mode, calculating a maximum connected piece ratio of the logical 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 piece ratios corresponding to all attacks of the target attack mode.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of network attacks, and in particular to a multi-layer network attack resistance evaluation method. BACKGROUND

[0002] Traditional coupling network damage methods have the same attack ability on nodes of each network layer. In modern warfare, communication networks are crucial. Since the information flow between nodes with different communication relationships is non-physical, there is no physical measurement index for communication relationship nodes, so the communication network can be considered as a logical network at an abstract level and is difficult to be directly damaged. The node damage research on single-layer complex networks has been very mature and in-depth, for example, using machine learning to predict node betweenness, as a measure of node bridging ability, and using machine learning to damage network nodes, which greatly improves the network collapse efficiency.

[0003] In the process of implementing the present application, the applicant found that there are at least the following problems in the prior art:

[0004] The traditional network security evaluation method does not consider the influence of physical network layer damage on the communication nodes of the abstract logical network layer, and the influence of the damaged logical network layer nodes on the physical network layer in turn, thereby leading to incomplete and inaccurate network security evaluation. SUMMARY

[0005] The embodiments of the present application provide a multi-layer network attack resistance evaluation method to solve the problem that the traditional network security evaluation method does not consider the influence of physical network layer damage on the communication nodes of the abstract logical network layer, and the influence of the damaged logical network layer nodes on the physical network layer in turn, thereby leading to incomplete and inaccurate network security evaluation.

[0006] To achieve the above purpose, on the one hand, the embodiments of the present application provide a multi-layer network attack resistance evaluation method, comprising:

[0007] adopting a target attack method to repeatedly attack the physical network layer of the multi-layer network multiple times; the multi-layer network comprises a physical network layer and a logical network layer;

[0008] for each attack of the target attack method, calculating the maximum connected component ratio of the logical network layer after the corresponding attack;

[0009] calculating a damage degree index of the multi-layer network corresponding to the target attack method according to the maximum connected component ratios corresponding to all attacks of the target attack method;

[0010] wherein, the maximum connected component ratio is used to represent the robustness of the logical network layer; and the damage degree index is used to evaluate the attack resistance of the multi-layer network under the target attack method.

[0011] Further, the multiple repeated attacks on the physical network layer of the multi-layer network in the target attack mode include:

[0012] According to the target attack mode, the physical layer nodes of the physical network layer are attacked, the attacked physical layer nodes are deleted, and the direct edges corresponding to the attacked physical layer nodes are deleted.

[0013] According to the type of the deleted attacked physical layer nodes, the logical layer nodes in the logical network layer are deleted.

[0014] Further, for each attack in the target attack mode, the maximum connected component ratio of the logical network layer after the attack is calculated, including:

[0015] For each attack in the target attack mode, the subnetwork with the most nodes is selected from the multiple subnetworks composed of the remaining logical layer nodes in the attacked logical network layer as the maximum connected component after the attack.

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

[0017]

[0018] Wherein, M is the maximum connected component ratio of the attacked logical network layer; N' All is the number of logical layer nodes in the maximum connected component of the attacked logical network layer; N is the total number of logical layer nodes in the logical network layer before the attack.

[0019] Further, the damage degree index of the multi-layer network corresponding to the target attack mode is calculated according to the maximum connected component ratios corresponding to all attacks in the target attack mode, including:

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

[0021]

[0022] Wherein, F(j) represents the vulnerability index of the multi-layer network corresponding to n attacks in the jth target attack mode; i = 1, 2...n represents the number of attacks under each target attack mode; M j (i) represents the maximum connected component ratio of the logical network layer when the ith attack in the jth target attack mode; (1-M j (i)) represents the collapse degree of the multi-layer network when the ith attack in the jth target attack mode.

[0023] The calculated vulnerability index of the multilayer network corresponding to the target attack mode is taken as the damage degree index of the multilayer network corresponding to the target attack mode.

[0024] Further, the deleting the logical layer node in the logical network layer according to the type of the deleted attacked physical layer node comprises:

[0025] In the case where the type of the deleted attacked physical layer node is a critical node, after the attacked physical layer node and all direct edges of the attacked physical layer node are deleted from the physical network layer, 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 are simultaneously deleted.

[0026] The critical node represents that the corresponding physical layer node has a direct connection with the logical layer node in the logical network layer.

[0027] Further, the deleting the logical layer node in the logical network layer according to the type of the deleted attacked physical layer node comprises:

[0028] In the case where the type of the deleted attacked physical layer node is a transition node, a pair of physical layer nodes in the physical network layer which are no longer interconnected due to the deletion of the attacked physical layer node and the corresponding direct edge are identified, and the direct edge between the corresponding logical layer nodes in the logical network layer of the identified pair of physical layer nodes is deleted.

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

[0030] Further, the edges of the multilayer network have weights; and the damage degree index of the multilayer network corresponding to the target attack mode is calculated according to the maximum connected piece ratio of all attacks corresponding to the target attack mode, comprising:

[0031] The robustness index of the multilayer network corresponding to the target attack mode 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 the target attack mode after n times of attacks; NP is the initial number of paths in the physical network layer; MP is the total capacity of paths obtained by summing the weights of the NP paths; NP1 is the number of paths in the physical network layer after the attack of the multi-layer network corresponding to the jth target attack mode; MP1 is the residual total capacity of the NP1 paths in the physical network layer after the attack of the multi-layer network corresponding to the jth target attack mode; richness is the richness; and a and β are weight parameters greater than 0, and a+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: by repeatedly attacking the physical network of the multi-layer network under the target attack mode, the maximum connected component 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 component ratios after all attacks, the maximum connected component ratio measures the integrity degree of the logical network layer after each attack of the physical network layer, reflects the robustness of the logical network layer, and also reflects the damage degree of the logical network from the opposite direction, and the damage degree index of the multi-layer network reflects the attack resistance of the multi-layer network under the target attack, thereby providing an evaluation method for the damage degree of the multi-layer network under the target attack based on the damage degree of the logical network layer caused by the attack on the physical network, so as to more reasonably determine the network architecture of the multi-layer network in the real scene, and more accurately and effectively determine an efficient attack mode for the existing multi-layer network. BRIEF DESCRIPTION OF DRAWINGS

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments or the prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0038] Figure 1 is a flowchart of a multi-layer network attack resistance evaluation method according to an embodiment of the present application;

[0039] Figure 2 is a physical-logical interdependent network schematic diagram;

[0040] Figure 3is a variation diagram of a physical layer node after being attacked, which is one of the embodiments of the present application;

[0041] Figure 4 is a variation diagram of a logical layer node after being attacked, which is one of the embodiments of the present application;

[0042] Figure 5 is a comparison curve diagram of vulnerability indexes of ER random network, BA scale-free network and Power-Law scale-free network after a double-layer network with 20 nodes in a logical network layer is attacked, which is one of the embodiments of the present application;

[0043] Figure 6 is a comparison curve diagram of vulnerability indexes of ER random network, BA scale-free network and Power-Law scale-free network after a double-layer network with 30 nodes in a logical network layer is attacked, which is one of the embodiments of the present application;

[0044] Figure 7 is a comparison curve diagram of vulnerability indexes of ER random network, BA scale-free network and Power-Law scale-free network after a double-layer network with 40 nodes in a logical network layer is attacked, which is one of the embodiments of the present application;

[0045] Figure 8 is a comparison curve diagram of vulnerability indexes of ER random network, BA scale-free network and Power-Law scale-free network after a double-layer network with 50 nodes in a logical network layer is attacked, which is one of the embodiments of the present application;

[0046] Figure 9 is a comparison curve diagram of vulnerability indexes of ER random network, BA scale-free network and Power-Law scale-free network after a double-layer network with 60 nodes in a logical network layer is attacked, which is one of the embodiments of the present application. DETAILED DESCRIPTION

[0047] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0048] The inventors find that in a physical power station-command relationship network, the command relationship node is an abstract logical definition and cannot be directly solved by physical damage methods. However, damage and communication network are interdependent. Once the entity node in the physical infrastructure network layer is destroyed, it will directly affect the communication effect. Taking the power-communication coupled network structure as an example, the interdependence between the power system and the communication network, the interruption of the power grid can have a serious negative impact on the communication network, and vice versa. The failure of the information infrastructure is a key factor leading to the collapse of the power system. Some networks have multiple interconnected links for each node, and the number of interconnections for each node remains consistent. Some networks have nodes with different numbers of interconnections, and the internal link distribution follows the Poisson distribution. Some networks are based on the "regular allocation" method of internal links to show their improvement in robustness compared to random allocation techniques. Traditional researches explore these network models by simulating cascading failures in smart grids. The damage effect of communication nodes and power nodes after failure on heterogeneous layer nodes is considered to be achieved by physical methods. The current widely used multi-layer network attack resistance evaluation method has obvious shortcomings in practical application although it has a certain systematicness and comprehensiveness in the theoretical level: they often focus on the analysis of network architecture, ignoring the realistic characteristics of the target object, especially the depth consideration of its attackability. This limitation makes it difficult to accurately estimate the attack effect. The inventors find that the loss of communication network nodes may not directly lead to the loss of control of the corresponding power grid components, and the communication nodes at the abstract logical level are difficult to be physically damaged in the real level. The traditional technology lacks consideration of these problems, making it difficult to effectively evaluate the damage degree of interdependent multi-layer networks such as power-communication network when receiving attacks.

[0049] In one aspect, as Figure 1 shown, the embodiment of the present application provides a multi-layer network attack resistance evaluation method, comprising:

[0050] Step S10, repeatedly attack the physical network layer of the multi-layer network by using a target attack method; the multi-layer network comprises a physical network layer and a logical network layer;

[0051] Step S11, for each attack of the target attack method, calculate the maximum connected piece ratio of the logical network layer after the corresponding attack;

[0052] Step S12, calculate the damage degree index of the multi-layer network corresponding to the target attack method according to the maximum connected piece ratio corresponding to all attacks of the target attack method;

[0053] The maximum connected piece ratio is used to represent the robustness of the logical network layer; the damage degree index is used to evaluate the attack resistance of the multi-layer network under the target attack method.

[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 can be interdependent, the power network supplies power for the devices of the communication network, and the communication network is 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 the physical layer node in the physical network layer can not have a corresponding logical layer node in the logical network layer.

[0055] The target attack method (attack strategy) includes but is not limited to hub node attack, high betweenness node attack, closeness centrality attack, and random attack. The method of hub node attack (High-Degree Targeting) is specifically: preferentially attacking the node with the highest degree (number of connections) (such as opinion leaders in social networks, substations in power networks, etc.), and the principle is that the hub node undertakes the core connection function in the network, and the destruction may cause network splitting or performance drop. The method of high betweenness node attack (Betweenness Centrality Targeting) is specifically: attacking the node that acts as a "bridge" in the network (i.e. the node with high betweenness centrality), and the principle is that such node controls a large number of paths, and removal will significantly increase the average path length of the network and reduce connectivity. The method of closeness centrality attack (Closeness Centrality Targeting) is specifically: attacking the node with the shortest average distance to other nodes (the node with high closeness centrality), and the principle is that these nodes are efficient intermediaries for information dissemination, and the destruction may cause information transmission delay or interruption. The method of random attack (Random Attack) is specifically: randomly selecting nodes for destruction, and the principle is that the cost is low but the efficiency is not high, and it is suitable for scale-free networks (Scale-Free Networks) when a large number of nodes need to be destroyed to significantly affect the network.

[0056] The multi-layer network includes a physical network layer and a logical network layer; 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 embodiment of the present application has the following technical effects: the embodiment of the present application repeatedly attacks the multi-layer network for the target attack mode multiple times, evaluates the robustness of the logical network layer after each attack, that is, the maximum connected piece ratio, and then comprehensively obtains the damage degree index of the target attack mode to the multi-layer network based on the maximum connected piece ratio of the logical network layer after all attacks under the target attack mode. Based on the damage degree index, the anti-attack ability of the multi-layer network under the target attack mode can be evaluated. Based on the embodiment of the present application, a plurality of target attack modes are applied to a plurality of candidate multi-layer networks, and the damage degree index corresponding to each multi-layer network under a plurality of target attack modes can be obtained. By comparing the damage degree index corresponding to a plurality of target attack modes between different multi-layer networks, the best multi-layer network with the best robustness under a plurality of target attack modes can be selected from a plurality of multi-layer networks, and the rationality of network structure selection is improved. Based on the embodiment of the present application, the existing multi-layer network can also be attacked by a plurality of different target attack modes, and the damage degree index of the multi-layer network under each attack mode (attack strategy) can be obtained. By comparing the damage degree index corresponding to each target attack mode (attack strategy), the target attack mode (attack strategy) with the best attack effect that can cause the most damage to the attacked multi-layer network can be found from a plurality of target attack modes (attack strategies), so that the attack mode with the strongest attack ability and the most destructive to the logical network layer can be selected when the network attack war is carried out, and the effect of improving the physical damage degree of the logical network layer in the dependent network on the real level is achieved.

[0058] Further, the target attack mode is used to repeatedly attack the physical network layer of the multi-layer network multiple times, including:

[0059] According to the target attack mode, the physical layer nodes of the physical network layer are attacked, the attacked physical layer nodes are deleted, and the direct edges corresponding to the attacked physical layer nodes are deleted.

[0060] According to the type of the deleted attacked physical layer node, the logical layer node in the logical network layer is deleted.

[0061] In some embodiments, the physical network layer is generally an entity network, and is easy to be attacked by an entity attack. The logical layer nodes and edges of the logical network layer are at an abstract level, and are difficult to be effectively attacked and damaged by an entity attack. By attacking the physical network layer, the physical layer nodes are damaged, and the corresponding physical layer nodes are deleted from the network, and the direct edges connected with the deleted physical layer nodes are also deleted, thereby reducing the connection paths in the physical network layer. Since the logical network layer and the physical network layer are dependent, the logical layer nodes in the logical network layer correspond to the physical layer nodes in the physical network layer. When the physical layer nodes in the physical network layer are damaged, if the physical layer nodes correspond to the logical layer nodes, the corresponding logical layer nodes in the logical network layer are also damaged. For the damage of the physical layer nodes without corresponding logical layer nodes, the logical layer nodes are not damaged. By combining the attack on the physical network layer with the robustness (maximum connected component ratio) evaluation of the logical network layer after the attack, the effect of the damage of the logical network layer caused by the attack on the physical network layer by an entity attack can be evaluated, and the damage degree of the entire multi-layer network can be evaluated. When the damage of the physical layer nodes leads to the damage of the logical layer nodes, in turn, the control ability of the damaged logical network layer on the physical network layer is also damaged, thereby causing a deep damage to the multi-layer network.

[0062] The embodiment of the present application has the following technical effects: by combining the attack on the physical network layer with the performance suppression of the logical network layer, the characteristics of the target physical network layer are accurately analyzed, an efficient attack is implemented, and a cascade effect is triggered in the logical network layer to weaken its function, thereby ensuring the operability of the target attack, accurately quantifying the attack effect, and being beneficial to the optimization of network attack technology. The problems of the difficulty in effectively attacking the logical network layer at an abstract logical level by an entity attack and the inability of the damage of the logical network layer to effectively cause the loss of control of the corresponding physical network layer are solved.

[0063] Further, for each attack of the target attack mode, the maximum connected component ratio of the logical network layer after the attack is calculated, comprising:

[0064] For each attack of the target attack mode, the sub-network with the largest number of nodes is selected from the multiple sub-networks composed of the logical layer nodes remaining in the logical network layer after the attack, as the maximum connected component after the attack.

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

[0066]

[0067] Wherein, M is the maximum connected component ratio of the logical network layer after the attack; N'All M is the number of logical layer nodes in the largest connected component 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 an attack on a network, the remaining nodes form several fragmented sub-networks, the nodes in a sub-network can reach each other through connecting edges, and there is no connecting edge between two sub-networks. The sub-network with the largest number of nodes is called the "largest connected component". After the network is damaged by external attacks, the size of the largest connected component will change accordingly, which can reflect the changes in the internal structure of the network to some extent. The larger M is, the stronger the robustness of the network is. After the logical network layer is damaged, the original logical network layer may have multiple sub-networks, and the sub-network with the largest number of nodes becomes the largest sub-network that can complete the function of the original logical network layer after being damaged. The larger the largest connected component after the attack is, the better the robustness of the logical network layer is, and the worse the attack effect is. By calculating the largest connected component ratio, the effect of the corresponding attack can be evaluated.

[0069] The embodiments of the present application have the following technical effects: by determining the largest connected component 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 negative side.

[0070] Further, the damage degree index of the multi-layer network corresponding to the target attack mode is calculated according to the largest connected component ratios corresponding to all attacks of the target attack mode, comprising:

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

[0072]

[0073] Wherein, F(j) represents the vulnerability index of the multi-layer network corresponding to n times of attack in the jth attack mode; i=1, 2...n represents the number of attacks in each attack mode; M j (i) represents the largest connected component ratio of the logical network layer in the ith attack in the jth attack mode; (1-M j (i)) represents the collapse degree of the multi-layer network in the ith attack in the jth attack mode.

[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 multilayer network can be weightless or weighted, and the weights of the edges are not considered when calculating the vulnerability index. The attack efficiency of the logical network layer is used to represent the final attack effect measure for the multilayer network. The attack efficiency function of each attack mode (attack strategy) is as formula (2), and the vulnerability index of the multilayer network under the jth attack mode can be obtained according to formula (2); the smaller F(j) is, the worse the attack effect of the multilayer network under this attack mode is. When the target attack mode is multiple, the vulnerability index of the multilayer network corresponding to each target attack mode can be calculated respectively according to the embodiments of the present application. When evaluating the attack resistance of multiple multilayer networks under one or more target attack modes, the vulnerability index of the multiple multilayer networks under one or more target attack modes is determined as the corresponding damage degree index based on the embodiments of the present application, and by comparing the damage degree index corresponding to each multilayer network, the optimal multilayer network in the multiple multilayer networks can be selected. When the most effective attack mode is selected from multiple target attack modes, the damage degree index corresponding to each target attack mode can be determined according to the embodiments of the present application, the damage degree index corresponding to each target attack mode is compared, and the most effective attack mode for the multilayer network is determined, which specifically includes: the target attack mode corresponding to the largest vulnerability index of the multilayer network in the multiple target attack modes is taken as the most effective attack mode for the multilayer network.

[0076] Further, the deleting the logical layer node in the logical network layer according to the type of the deleted attacked physical layer node includes:

[0077] In the case where the type of the deleted attacked physical layer node 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, 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 are also deleted.

[0078] The key node represents that the corresponding physical layer node has a direct connection with 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. For example, Figure 3As shown, the solid points are physical layer nodes, and the hollow points are logical layer nodes. The physical layer nodes pointed by the "attack" arrows have corresponding logical layer nodes, and are key nodes. When the physical layer nodes pointed by the "attack" arrows are attacked and deleted, the corresponding logical layer nodes are also deleted. Correspondingly, the direct edges connecting the physical layer nodes pointed by the "attack" arrows are also deleted, and the direct edges connecting the corresponding logical layer nodes are also deleted. When the key nodes of the physical network layer are deleted, the corresponding logical layer nodes and the corresponding edges in the logical network layer are also deleted, because when the key nodes of the physical network layer are attacked, the communication of the logical layer nodes corresponding to (or physically supported by) the key nodes of the physical network layer will be directly affected. When the attack can accurately target the key nodes, the physical layer nodes will be damaged, and the logical layer nodes will also be damaged, thereby causing the logical network layer to be incomplete, and further causing the communication of the logical network layer to be abnormal, and causing the monitoring of the logical network layer on the physical network layer to be incomplete. Thus, the physical network layer and the logical network layer are bidirectionally affected by the attack on the physical network layer.

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

[0081] In the case where the type of the deleted physical layer nodes attacked is a transition node, the direct edges between the corresponding logical layer nodes in the logical network layer are deleted, which are caused by the deletion of the physical layer nodes attacked and the corresponding direct edges.

[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, the solid points are physical layer nodes, and the hollow points are logical layer nodes. The physical layer node 41 pointed by the "attack" arrow has no corresponding logical layer node, and is a transition node. The physical node 42 corresponds to the logical layer node 44, and the physical node 43 corresponds to the logical layer node 45. The physical layer node 41 is connected to the physical layer node 42 and the physical layer node 43 through direct edges. When the physical layer node 41 is deleted, the direct edges between the physical layer node 41 and the physical layer node 42 and the direct edges between the physical layer node 41 and the physical layer node 43 are also deleted. At the same time, since the physical node 42 and the physical node 43 are no longer in communication after the physical node 41 is deleted, the edges between the logical layer node 44 and the logical layer node 45 in the logical network layer need to be deleted correspondingly.

[0084] Further, edges of the multilayer network have weights; the damage degree index of the multilayer network corresponding to the target attack mode is calculated according to the maximum connected piece ratio corresponding to all attacks of the target attack mode, comprising:

[0085] The robustness index of the multilayer network corresponding to the target attack mode 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 multilayer network corresponding to the target attack mode; F(j) represents the vulnerability index of the multilayer network corresponding to n times of attacks in the jth target attack mode; NP is the initial number of paths in the physical network layer; MP is the total capacity of paths obtained by summing the weights of NP paths; NP1 is the number of paths in the physical network layer after the attack of the multilayer network corresponding to the jth target attack mode; MP1 is the residual total capacity of paths obtained by summing the weights of NP1 paths in the physical network layer after the attack of the multilayer network corresponding to the jth target attack mode; richness is the richness; and α and β are weight parameters greater than 0, and α+β=1;

[0089] The calculated robustness index of the multilayer network corresponding to the target attack mode is taken as the damage degree index of the multilayer network corresponding to the target attack mode.

[0090] In some embodiments, for the multilayer network model with weights, the edge weight of the physical network layer represents the information capacity on the line, so the attack measure standard can also be measured by adding the richness. Assuming that the initial number of paths in the physical network layer is NP, and the total capacity of the paths is MP, wherein the value of MP is obtained by summing the weights of NP paths, after the overall attack on the double-layer network, the number of paths in the physical network is NP1, and the path capacity sum is MP1, wherein the value of MP1 is obtained by summing the weights of NP1 paths still existing after the overall attack, and the richness is defined as formula (4); wherein α+β=1, both are greater than 0, and α and β are weight parameters,

[0091] By adjusting parameters, different potential optimal networks are constructed. For a network with capacity, the attack efficiency and the richness can be considered jointly. When subjected to the jth attack strategy, the damage measure criterion of the network with edge capacity can be defined as formula (3); for the network structure, the smaller the attack efficiency is, the greater the richness is, and it is proved that the stronger the robustness of the network structure is. Therefore, for the rank value, the smaller the rank value is, the more robust the double-layer network structure is. When evaluating the attack resistance of multiple multi-layer networks under one or more target attack modes, the damage degree indicators of the multiple multi-layer networks corresponding to the one or more target attack modes are determined based on the embodiments of the present application. By comparing the damage degree indicators corresponding to each multi-layer network, the optimal multi-layer network in the multiple multi-layer networks can be selected. When the most effective attack mode is selected from multiple target attack modes, the damage degree indicators corresponding to each target attack mode can be determined according to the embodiments of the present application. The damage degree indicators corresponding to the multiple target attack modes are compared to determine the most effective attack mode for the multi-layer network, specifically including: taking the attack mode corresponding to the smallest robustness indicator of the multi-layer network in the multiple attack modes as the most effective attack mode for the multi-layer network.

[0092] The above technical solutions of the embodiments of the present application will be described in detail below in combination with specific application examples. Technical details not introduced in the implementation process can be referred to the related description in the foregoing.

[0093] Based on the deficiencies of the traditional technology, the embodiments of the present application propose a new physical-logical interdependent network damage mode. Preferably, the multi-layer network is a double-layer network; by constructing a double-layer network structure that connects the abstract logical communication network layer and the concrete physical facility network layer, and defining the damage mode and damage effect degree measurement indicators of the network, the possibility of real damage to the communication network of the enemy and ourselves in the real situation is effectively improved, which has a certain reference value for the expansion and planning of the future double-layer network. The embodiments of the present application explore the damage mode and its influence of the physical-logical coupled network in modern warfare, and propose a new damage strategy. The logical communication layer is taken as the evaluation index layer, and the physical communication layer is taken as the actual attack layer. The corresponding damage mode and damage effect degree measurement indicators are defined, and related experiments are carried out. The robustness of the double-layer network structure of different types of logical networks after damage is preliminarily explored, and the robustness of the double-layer network structure composed of the same type of logical network is tested under different parameters.

[0094] 1. Physical-logical network structure modeling

[0095] Take the power-communication coupled network (PCCN) as an example, which can be divided into two general layers in attribute: 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), which is a network composed of various physical connections supporting network information transmission services, such as a network constructed by transmission equipment such as optical cables; the logical layer is represented by a communication network, which is a virtual layout of network equipment, and data is transmitted between devices through the network, regardless of the physical connection of the device.

[0096] Embodiments of the present application adopt a "one-to-many" coupled network, as shown in the figure, in this two-layer mode, the higher-level logical network divides its corresponding lower-level physical network into several sub-networks. Figure 2

[0097] (1) Physical power network modeling

[0098] Take the power network as an example, in which the power station is much more than the abstract layer node, mainly undertakes the signal transmission of the entity. The high-voltage transmission line between each power station is equivalent to an edge. Then the power network can be represented as G p =(V p ,E p ), wherein V p ={v p1 ,v p2 …v pn} is a set of power nodes, and n is the number of power nodes. E p is a set of edges in the network. Embodiments of the present application add a distinguishing attribute to each power node, i.e. v pn =(x pn ,y pn ,z pn ), wherein (x pn ,y pn ) is the two-dimensional coordinate of the node, and

[0099]

[0100] z pn indicates that the power layer node is divided into two categories according to the attribute, one is the key node directly connected with the abstract logical layer node, which undertakes the transportation of electrical signals and is also the location of building a communication base station, and the attribute is marked as 1. The other is a transition node that does not have direct contact with the abstract layer node and only undertakes the transmission of electrical signals, and the attribute is marked as 0.

[0101] (2) Abstract communication network model

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

[0103] 2. Physical-logical network cascade damage mode and measurement standard

[0104] After the network structure model is constructed, the network is attacked. Since the nodes and edges of the logical communication network are at the abstract level, it is difficult to attack the entity, so when attacking the double-layer network model, only the nodes at the physical level are artificially selected and deleted. The prerequisite for this double-layer network to meet is that all logical nodes can find corresponding physical layer key nodes, and there is a physical layer reachable path for the pair of logical nodes with reachable paths in the initial network. When a node in the physical layer is damaged, all the interlayer edges of the physical network layer corresponding to the node are deleted. When considering the impact of deleting a physical node on the logical layer node, the z attribute of the physical node needs to be considered, i.e., whether it is a key node or a transition node.

[0105] (1) The key node is removed

[0106] If the removed v in = (x in , y in , 1) is a key node directly connected to the logical layer node, then after deleting the node and all its edges in the physical layer, the corresponding logical layer node and all its edges are also deleted. Because the failure of the key node in the physical layer will directly lead to the failure of the signal point at the communication level. As shown in Figure 3 .

[0107] (2) The transition node is removed

[0108] If the removed v jn = (x jn , y jn,0), is a transition node only responsible for the transmission of electrical signals, the node and all its edges are first deleted at the physical layer. Then examine the node pairs that originally exist in the logical layer and the physical layer, due to the absence of the node, which node pairs no longer intercommunicate on the physical layer. The connectivity of these node pairs at the logical level will also be blocked. The blocking processing method is as follows:

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

[0110] In the final network attack measure index, the embodiment of the application considers the communication effect of the whole network. Therefore, the network integrity after the whole attack is calculated based on the logical network layer.

[0111] The embodiment of the application first introduces the concept of the maximum connected piece: several broken sub-networks formed by the remaining nodes after the network is attacked, and the sub-network with the largest number of nodes is called the "maximum connected piece". After the network is damaged by the outside world, the size of the maximum connected piece will also change accordingly, which can reflect the change of the internal structure of the network to a certain extent. It is expressed as formula (1):

[0112]

[0113] Wherein, N' All , N are the number of effective nodes remaining after the network fails and the total number of nodes in the network before the failure respectively. 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 measure. The attack efficiency function of each attack strategy is as formula (2):

[0115]

[0116] Wherein j represents different attack strategies, i = 1, 2...n represents the number of attacks under each strategy, (1-M j (i)) represents the collapse degree of the multi-layer network when the jth attack strategy attacks the ith time, F(j) represents the total vulnerability of the jth attack strategy after n times of attack, the smaller F(j) is, the worse the effect of the attack strategy on the multi-layer network is.

[0117] Among them, the attack strategy (attack mode) includes but is not limited to hub node attack, high betweenness node attack, closeness centrality attack, random attack; The method of hub node attack (High-Degree Targeting) is specifically: preferentially attack the node with the highest degree (connection number) (such as opinion leaders in social networks, substations in power networks, etc.), the principle is that the hub node undertakes the core connection function in the network, which may cause network splitting or performance drop after being destroyed. The method of high betweenness node attack (Betweenness Centrality Targeting) is specifically: attack the node that acts as a "bridge" in the network (i.e. the node with high betweenness centrality), the principle is that such nodes control a large number of paths, and removing them will significantly increase the average path length of the network and reduce connectivity. The method of closeness centrality attack (Closeness Centrality Targeting) is specifically: attack the node with the shortest average distance to other nodes (the node with high closeness centrality), the principle is that these nodes are efficient intermediaries for information dissemination, and destruction may cause information transmission delay or interruption. The method of random attack (Random Attack) is specifically: randomly select nodes for destruction, the principle is that the cost is low but the efficiency is not high, which is suitable for scale-free networks (Scale-Free Networks) when a large number of nodes need to be destroyed to significantly affect the network.

[0118] Therefore, when calculating the damage degree of the network, the damage degree of the overall network can be calculated by calculating the maximum connected piece ratio of the logical network layer, and different attack modes are used to repeatedly attack the overall network, and the best attack mode is found by comparing the attack efficiency of the logical network layer.

[0119] For the weighted double-layer network model, the edge weight of the physical network layer represents the information capacity on the line, so the richness can also be added to measure the attack measure standard. Assuming that in the physical network layer, the initial number of paths is NP, and the total capacity of the path is MP, wherein the value of MP is obtained by summing the weights corresponding to the NP paths, after the overall attack on the double-layer network is completed, the number of paths existing in the physical network is NP1, and the path capacity sum is MP1, wherein the value of MP1 is obtained by summing the weights corresponding to the NP1 paths still existing after the overall attack is completed, and the richness is defined as formula (4):

[0120]

[0121] where a+β=1, both greater than 0, a and β are weight parameters, by adjusting the parameters, different potential optimal networks are constructed. For networks with capacity, the attack efficiency and richness can be considered jointly, when subjected to the jth attack strategy, the damage measure standard of the network considering the link 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 mode; F(j) represents the vulnerability index of the multi-layer network after n times of attack in the jth attack mode.

[0124] For network structure, the smaller the attack efficiency, the greater the richness, and the stronger the robustness of the network structure. Therefore, for the rank value, the smaller the rank value, the more robust the double-layer network structure.

[0125] 3. Double-layer network damage instance analysis

[0126] 3.1 Logical network type

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

[0128] The connection mode of the nodes of the Power-Law scale-free network is usually to generate the network by simulating the degree sequence of the power-law distribution. The degree distribution of such a network conforms to the power-law distribution, that is, there are a few nodes with very high degrees, and most nodes have low degrees. This means that there are a few "super nodes" in the network, which have great influence.

[0129] The BA scale-free network adopts a "preferential connection" mechanism. The degree distribution of the BA scale-free network is also a power-law distribution, but the distribution is more flat, and the number of super nodes in the BA scale-free network is less than that in the Power-Law distribution network.

[0130] Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 and Figure 9 The horizontal axis in FIGS. 1 to 8 represents the proportion p of the number of physical layer nodes remaining after each round of attack to the total number of physical layer nodes. The data with p greater than or equal to 0.2 is analyzed, and the value of p ranges from 0.2 to 1.0. Correspondingly, the proportion of the number of physical layer nodes subjected to random attack in each round to the total number of physical layer nodes is 1-p. The vertical axis represents the attack efficiency function F(j) (i.e., the vulnerability index), which is the ratio of the connectivity degree of the logical network after damage to the original connectivity degree. 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 double-layer network in FIGS. 1 to 8 is 20, 30, 40, 50, and 60, respectively. 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 In each of FIGS. 1 to 8, the values of the attack efficiency function F(j) corresponding to the ER random network with an average degree distribution k = 4, the BA scale-free network with m = 2 new edges added each time, and the Power-Law scale-free network with a power-law distribution and an index gamma = 2 and an average degree distribution k = 4 are compared.

[0131] After t = 6 complete attack processes on each physical network layer, the average value of the 6 times is plotted and calculated. Through attack simulation experiments on the ER random network, the BA scale-free network, and the Power-Law scale-free network, the robustness of different types of logical networks under different attack probabilities is observed. From the broken line Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 and Figure 9It can be seen that the attack effect of the damage mode through the Power-Law scale-free network and the BA scale-free network is not much different under different node numbers and attack probabilities, and for the ER random network, when the attack probability is 0.6-0.7, the robustness of the network compared to the other two networks will change, when p<0.6, the robustness of the ER random network is generally less than that of the scale-free network (Power-Law scale-free network and BA scale-free network), and when p>0.7, the robustness of the ER random network is better than that of the scale-free network (Power-Law scale-free network and BA scale-free network). With the increase of the proportion of attacked nodes, the advantage of the ER random network becomes more and more obvious. That is, when the proportion of attacked physical nodes exceeds half, the logical network layer has stronger anti-destroying ability when the communication connection is arranged in the ER random network structure.

[0132] 3.2 Exploration of logical network degree distribution and power-law index

[0133] For different types of networks with 60 nodes, different parameters are set for analysis. For the ER random network, the average degree distribution is k=5, 10, 15, 20 and 25, and the attack analysis is carried out, specifically, after random attack on the physical layer network which is twice the number of nodes of the ER random network, the damage rate is observed; for the BA scale-free network, the number of single connection edges is m=2, 4, 6, 8 and 10, and the attack analysis is carried out, specifically, after random attack on the physical layer network which is twice the number of nodes of the BA scale-free network, the damage rate is observed; for the Power-Law scale-free network, the power-law degree distribution is gamma=2, 2.25, 2.5, 2.75 and 3, and the attack analysis is carried out, specifically, after random attack on the physical layer network which is twice the number of nodes of the Power-Law scale-free network, the damage rate is observed. For the above networks, the total proportion of destroyed physical nodes in the range of 0.2 to 1 is observed to obtain the corresponding logical network damage degree.

[0134] For the ER random network, with the increase of the average degree distribution, the network's anti-destroying ability presents a trend of first increasing and then weakening, when the number of logical network nodes is 60, the average degree distribution is k=15, and the network has the most robustness. For the BA scale-free network, the increase of the number of single connection edges makes the network's anti-destroying ability first weaken and then strengthen, and when m=6, the network is most vulnerable. For the Power-Law scale-free network, the increase of the power-law degree also makes the network's anti-destroying ability first weaken and then strengthen, and in theory, the value of gamma of the scale-free network in real life is generally 2, and in the test using the attack mode (random attack mode), the network has strong robustness.

[0135] It should be understood that the particular order in which the steps of processes presented in the disclosure have been presented can be rearranged. Furthermore, various aspects of the disclosure can be used alone or in combination with one another. It is therefore intended that this disclosure not be limited to the particular disclosure immediately described above, but include all such modifications, permutations and combinations as fall within the scope of the appended claims. Methods recited herein need not be performed in the order recited.

[0136] In the foregoing detailed description, various features are grouped together in single embodiments for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the embodiments of the claimed subject matter require more features than are expressly recited in each claim. Rather, as the claims below reflect, inventive subject matter lies in less than all features of a single disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate preferred embodiment.

[0137] The disclosed embodiments have been described above. Those skilled in the art will readily devi se variations from the embodiments discussed without departing from the essential characteristics of the disclosure. The scope of the application is therefore intended to be only as is set forth in the following claims. In the claims, means-plus-function clauses are used where it would be clear that such clauses are intended to cover both implementation- specific and abstract-expressive units.

[0138] The foregoing description includes example of one or more embodiments. Of course, not all possible combinations of components or methods described above will be described as embodiments. However, one of ordinary skill in the art will recognize that further combinations and permutations of the embodiments described herein are possible. Accordingly, the disclosure is intended to embrace all such alterations, modifications and variations which fall within the scope of the appended claims. Furthermore, to the extent permitted, the disclosure includes all such modifications and variations as fall within the scope of the appended claims. Additionally, the term "comprising" as used in the specification and in the following claims is to be construed as meaning "including, but not limited to." Furthermore, any term "or" as used in the specification and in the following claims is to be construed as "non-exclusive or." Thus, the scope of the present disclosure should be determined by the appropriate scope of the appended claims and their equivalents, rather than by the description of the embodiments above.

[0139] Those of skill would further appreciate that the various illustrative logical blocks, modules, circuits, and steps described in connection with the embodiments disclosed herein can be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans can implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present embodiments.

[0140] The various illustrative logical blocks, modules, and circuits described in connection with the embodiments disclosed herein can be implemented or performed with 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 designed to perform the functions described herein. A general purpose processor can be a microprocessor, but in the alternative, the general purpose processor can be any conventional processor, controller, microcontroller, or state machine. A processor can also be implemented as a combination of computing devices, e.g., a combination of a digital signal processor and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a digital signal processor core, or any other such configuration.

[0141] The steps of a method or algorithm described in connection with the embodiments disclosed herein can be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module can reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is tangible. A storage medium can be coupled to the processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium can be integral to the processor. The processor and the storage medium can reside in an ASIC. The ASIC can reside in a user terminal. In the alternative, the processor and the storage medium can reside as discrete components in a user terminal. The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present embodiments. The various methods described herein can be implemented on a computer readable medium to provide a computer program product. The various methods described herein can be implemented as a routine embedded in a computer program product. The computer readable medium can include a computer readable storage medium to store or transfer the computer program product and a computer readable communication medium to transfer the computer program product. The computer storage medium can include volatile and non-volatile, removable and non-removable media implemented in a method or technology for storage and / or transfer of information such as computer readable instructions, data structures, program modules or other data. The computer storage medium can include, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tapes, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store or transfer the computer program product and which can be read by a computer. Also, any connection is properly termed a computer readable medium. For example, if the computer readable medium is a modular, portable memory

[0142] In one or more exemplary designs, the functions described can be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions can be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. Storage media can be any available media that can be accessed by a computer. By way of example, such computer-readable media can comprise 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 desired program code in the form of instructions or data structures and that can be accessed by a general-purpose or special-purpose computer, or a general-purpose or special-purpose processor. Also, any connection is properly termed a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or other wire-based, fiber- optic based, or wireless based communications, then the coaxial cable, fiber optic cable, twisted pair, DSL, or other wire-based, fiber-optic based, or wireless based communications are included in the definition of medium. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, DVD, floppy disk, and Blu-ray® disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media.

[0143] The above description is provided as an example only and is not intended to limit the scope of the present application.

Claims

1. A method for evaluating attack resistance of a multi-layer network, characterized by, The method comprises the following steps: adopting a target attack mode to repeatedly attack a physical network layer of a multi-layer network; the multi-layer network comprises a physical network layer and a logical network layer; for each attack of the target attack mode, calculating a maximum connected component ratio of the logical network layer after the attack; calculating a damage degree index of the multi-layer network corresponding to the target attack mode according to the maximum connected component ratios corresponding to all attacks of the target attack mode; wherein the maximum connected component ratio is used to represent the robustness of the logical network layer; and the damage degree index is used to evaluate the attack resistance of the multi-layer network under the target attack mode; the step of adopting a target attack mode to repeatedly attack a physical network layer of a multi-layer network comprises the following steps: attacking a physical layer node of the physical network layer according to the target attack mode, deleting the attacked physical layer node, and deleting direct edges corresponding to the attacked physical layer node; according to the type of the deleted attacked physical layer node, deleting a logical layer node in the logical network layer; the step of according to the type of the deleted attacked physical layer node, deleting a logical layer node in the logical network layer comprises the following steps: in the case that the type of the deleted attacked physical layer node 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 deleting a 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 represents that the corresponding physical layer node has direct connection with a logical layer node in the logical network layer; the step of according to the type of the deleted attacked physical layer node, deleting a logical layer node in the logical network layer comprises the following steps: in the case that the type of the deleted attacked physical layer node is a transition node, deleting direct edges between corresponding logical layer nodes in the logical network layer for a pair of physical layer nodes which are no longer interconnected in the physical network layer due to the deletion of the attacked physical layer node and corresponding direct edges; the transition node represents that the corresponding physical layer node does not directly provide physical support for the logical network layer.

2. The multi-layer network anti-attack evaluation method as described in claim 1, characterized in that, the step of for each attack of the target attack mode, calculating a maximum connected component ratio of the logical network layer after the attack comprises the following steps: for each attack of the target attack mode, selecting a sub-network with the largest number of nodes from a plurality of sub-networks composed of logical layer nodes remaining in the logical network layer after the attack, as the maximum connected component after the attack; calculating the maximum connected component ratio of the logical network layer after the attack according to the following formula: M= wherein M is the maximum connected component ratio of the logical network layer after the attack; is the number of logical layer nodes in the maximum connected component of the logical network layer after the attack; is the total number of logical layer nodes in the logical network layer before the attack.

3. The multi-layer network anti-attack evaluation method as described in claim 1, characterized in that, the step of calculating a damage degree index of the multi-layer network corresponding to the target attack mode according to the maximum connected component ratios corresponding to all attacks of the target attack mode comprises the following steps: calculating a vulnerability index of the multi-layer network corresponding to the target attack mode according to the following formula: ) wherein, represents the vulnerability index of the multi-layer network after n attacks with the jth target attack mode; i = 1, 2...n represents the number of attacks under each target attack mode; represents the maximum connected piece ratio of the logical network layer when the ith attack of the jth target attack mode; represents the collapse degree of the multi-layer network when the ith attack of the jth target attack mode; taking the calculated vulnerability index of the multi-layer network corresponding to the target attack mode as the damage degree index of the multi-layer network corresponding to the target attack mode.

4. The method of claim 3, wherein the attack resistance of the multi-layer network is evaluated by: ###0002### where N is the number of nodes in the multi-layer network, and N is the number of nodes in the single-layer network. The edges of the multilayer network have weights; and the damage degree index of the multilayer network corresponding to the target attack mode is calculated according to the maximum connected piece ratio corresponding to all attacks of the target attack mode, comprising: The robustness index of the multilayer network corresponding to the target attack mode is calculated according to the following formula: Rank + wherein Rank represents a robustness index of the multi-layer network corresponding to the target attack mode; represents a vulnerability index of the multi-layer network corresponding to n times of attacks by the jth target attack mode; NP is the number of paths initially existing in the physical network layer; MP is the total capacity of paths obtained by summing the weights of the NP paths; is the number of paths existing in the physical network layer after the attack of the multi-layer network corresponding to the jth target attack mode; is the number of paths existing in the physical network layer after the attack of the multi-layer network corresponding to the jth target attack mode is the total capacity of remaining paths obtained by summing the weights of the NP paths existing in the physical network layer after the attack of the multi-layer network corresponding to the jth target attack mode; is the richness; and is a weight parameter greater than 0, + = 1. The calculated robustness index of the multilayer network corresponding to the target attack mode is taken as the damage degree index of the multilayer network corresponding to the target attack mode. The robustness index of the multilayer network corresponding to the target attack mode is calculated according to the following formula: The calculated robustness index of the multilayer network corresponding to the target attack mode is taken as the damage degree index of the multilayer network corresponding to the target attack mode.

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