A method and device for evaluating robustness of a complex network

Abstract

The application discloses a complex network robustness evaluation method and device. For a given target network G, after an attack sequence Seq and an attack success rate P are obtained, the robustness of the target network can be quickly calculated, and the technical problems that the prior art cannot effectively measure the robustness of the network, and the prior method has large calculation overhead and is very time-consuming in calculating a large-scale complex network are solved.

Description

Technical Field

[0001] This application relates to the field of network reliability research technology, and in particular to a method and apparatus for evaluating the robustness of complex networks. Background Technology

[0002] Complex networks are ubiquitous in our lives and closely related to our daily routines, such as the internet, social networks, communication networks, and power grids. The robustness of complex networks, as an important indicator of network reliability, has always been a hot topic in network science research.

[0003] Robustness of complex networks refers to the network's ability to maintain its functionality even after some of its components (nodes or edges) fail due to faults or malicious attacks. Assessing the robustness of complex networks has two main implications. First, networks that are beneficial to us can cause severe losses if they collapse due to the failure of some of their components. For example, the 2003 blackout in the US and Canada affected approximately 50 million residents and resulted in economic losses of about $30 billion. Assessing the robustness of such networks helps us understand their weaknesses and guides us in improving their robustness. Second, robustness analysis of harmful networks, such as terrorist communication networks, helps us develop effective network dismantling strategies to destroy them. Therefore, assessing the robustness of complex networks is of paramount importance.

[0004] Existing robustness assessment methods for complex networks typically employ attack simulation, which involves attacking (removing) network nodes sequentially in a certain order and recording the changes in network connectivity after each attack.

[0005] Existing technologies typically assume that each node will be destroyed after an attack, without considering the success rate of the attack. However, in real-world applications, attacks on nodes are not always successful. For example, in military communication networks, even if an enemy launches an attack, it may not be able to destroy the target. Therefore, considering the attack success rate, existing technologies cannot effectively measure the robustness of a network. Furthermore, existing methods are computationally expensive, and calculating large-scale, complex networks is extremely time-consuming. Summary of the Invention

[0006] This application provides a method and apparatus for evaluating the robustness of complex networks, which solves the technical problems that existing technologies cannot effectively measure the robustness of networks, and that existing methods have large computational overhead and are very time-consuming to compute large-scale complex networks.

[0007] In view of this, the first aspect of this application provides a method for evaluating the robustness of complex networks, the method comprising:

[0008] S1. Obtain initial data of the target network G, wherein the initial data includes the number of nodes N in the target network G, and the attack sequence Seq = (v1, v2, ..., v N and attack success rate

[0009] S2. Let i = 0, sum = 0, and draw N-dimensional random numbers R = (r1, r2, ..., r N ), where 0≤r i ≤1, i=1,2,...,N;

[0010] S3. Determine the state of the attack sequence based on the relationship between the random number and the corresponding attack success rate.

[0011] S4. Calculate the value of ANC. Where σ(G) represents the initial size of the maximum connected component (GCC) of the target network G, σ(G\V k ) represents the attack set V sequentially from the target network G. k After the nodes in the network, the size of the remaining GCC in the network, When k=0, it represents the initial situation where no node is under attack;

[0012] S5. Update sum based on the value of ANC, sum += ANC(Seq,S);

[0013] S6. Calculate the robustness of the target network G: Robustness = sum.

[0014] Optionally, the initial data of the target network G may also include the number of samplings K.

[0015] Optionally, step S5 further includes: returning to step S4 until i is greater than the number of samplings K.

[0016] Optionally, step S6 specifically involves calculating the robustness of the target network G.

[0017] Optionally, step S3 specifically includes:

[0018] according to Determine the state of the attack sequence

[0019] A second aspect of this application provides a robustness evaluation apparatus for complex networks, the apparatus comprising:

[0020] The acquisition unit is used to acquire initial data of the target network G, wherein the initial data includes the number of nodes N in the target network G, and the attack sequence Seq = (v1, v2, ..., vN and attack success rate

[0021] Extraction unit, used to set i = 0, sum = 0, and extract N-dimensional random numbers R = (r1, r2, ..., r N ), where 0≤r i ≤1, i=1,2,...,N;

[0022] The processing unit is configured to determine the state of the attack sequence based on the relationship between the random number and the corresponding attack success rate.

[0023] The first calculation unit is used to calculate the value of ANC. Where σ(G) represents the initial size of the maximum connected component (GCC) of the target network G, σ(G\V k ) represents the attack set V sequentially from the target network G. k After the nodes in the network, the size of the remaining GCC in the network, When k=0, it represents the initial situation where no node is under attack;

[0024] The update unit is used to update sum based on the value of ANC, sum += ANC(Seq,S);

[0025] The second computing unit is used to calculate the robustness = sum of the target network G.

[0026] Optionally, the initial data of the target network G may also include the number of samplings K.

[0027] Optionally, the update unit is further configured to: jump to the first calculation unit until i is greater than the number of samplings K.

[0028] Optionally, the second computing unit is specifically used to calculate the robustness of the target network G.

[0029]

[0030] Optionally, the processing unit is specifically used for:

[0031] according to Determine the state of the attack sequence

[0032] As can be seen from the above technical solutions, the embodiments of this application have the following advantages:

[0033] This application provides a method and apparatus for evaluating the robustness of complex networks. For a given target network G, after obtaining the attack sequence Seq and the attack success rate P, the user can quickly calculate the robustness of the target network. This solves the technical problems that existing technologies cannot effectively measure the robustness of networks, and that existing methods have large computational overhead and are very time-consuming to calculate large-scale complex networks. Attached Figure Description

[0034] Figure 1 This is a flowchart of the robustness evaluation method for complex networks in the embodiments of this application;

[0035] Figure 2 This is a schematic diagram of the structure of the robustness evaluation device for complex networks in the embodiments of this application. Detailed Implementation

[0036] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0037] This application designs a method and apparatus for evaluating the robustness of complex networks, which solves the technical problems that existing technologies cannot effectively measure the robustness of networks, and that existing methods have large computational overhead and are very time-consuming to compute large-scale complex networks.

[0038] For easier understanding, please refer to Figure 1 , Figure 1 This is a flowchart of the robustness evaluation method for complex networks in the embodiments of this application, such as... Figure 1 As shown, specifically:

[0039] S1. Obtain the initial data of the target network G. The initial data includes the number of nodes N in the target network G, and the attack sequence Seq = (v1, v2, ..., v...). N and attack success rate

[0040] S2. Let i = 0, sum = 0, and draw N-dimensional random numbers R = (r1, r2, ..., r N ), where 0≤r i ≤1, i=1,2,…,N;

[0041] S3. Determine the state of the attack sequence based on the relationship between the random number and the corresponding attack success rate.

[0042]

[0043] S4. Calculate the value of ANC. Where σ(G) represents the initial size of the maximum connected component (GCC) of the target network G, σ(G\V k ) represents attacking set V sequentially from the target network G. k After the nodes in the network, the size of the remaining GCC in the network, When k=0, it represents the initial situation where no node is under attack;

[0044] S5. Update sum based on the value of ANC, sum += ANC(Seq,S);

[0045] S6. Calculate the robustness of the target network G: Robustness = sum.

[0046] Furthermore, the initial data for the target network G also includes the number of samples K.

[0047] Furthermore, step S5 also includes: returning to step S4 until i is greater than the number of samples K.

[0048] Furthermore, step S6 specifically involves calculating the robustness of the target network G.

[0049] Furthermore, step S3 specifically includes:

[0050] according to Determine the state of the attack sequence

[0051] Please see Figure 2 , Figure 2 This is a schematic diagram of the structure of the robustness evaluation device for complex networks in the embodiments of this application, as shown below. Figure 2 As shown, specifically:

[0052] Acquisition unit 201 is used to acquire initial data of the target network G. The initial data includes the number of nodes N in the target network G and the attack sequence Seq = (v1, v2, ..., v N and attack success rate

[0053] Extraction unit 202 is used to set i = 0, sum = 0, and extract N-dimensional random numbers R = (r1, r2, ..., r N ), where 0≤r i ≤1, i=1,2,…,N;

[0054] Processing unit 203 is used to determine the state of the attack sequence based on the relationship between the random number and the corresponding attack success rate.

[0055] The first calculation unit 204 is used to calculate the value of ANC. Where σ(G) represents the initial size of the maximum connected component (GCC) of the target network G, σ(G\V k ) represents attacking set V sequentially from the target network G. k After the nodes in the network, the size of the remaining GCC in the network, When k=0, it represents the initial situation where no node is under attack;

[0056] Update unit 205 is used to update sum based on the value of ANC, sum += ANC(Seq,S);

[0057] The second computing unit 206 is used to calculate the robustness of the target network G, which is sum.

[0058] Furthermore, the initial data for the target network G also includes the number of samples K.

[0059] Furthermore, the update unit is also used to: jump to the first calculation unit until i is greater than the number of samples K.

[0060] Furthermore, the second computational unit is specifically used to compute the robustness of the target network G.

[0061]

[0062] Furthermore, the processing unit is specifically used for:

[0063] according to Determine the state of the attack sequence

[0064] This application provides a method and apparatus for evaluating the robustness of complex networks. For a given target network G, after obtaining the attack sequence Seq and the attack success rate P, the user can quickly calculate the robustness of the target network. This solves the technical problems that the existing technology cannot effectively measure the robustness of the network, and that the existing methods have large computational overhead and are very time-consuming to calculate large-scale complex networks.

[0065] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0066] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented, for example, in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0067] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0068] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between apparatuses or units through some interfaces, and may be electrical, mechanical, or other forms.

[0069] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0070] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0071] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes: USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, optical disks, and other media capable of storing program code.

[0072] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for evaluating the robustness of complex networks, characterized in that, include: S1. Obtain initial data of the target network G, wherein the initial data includes the number of nodes N in the target network G, and the attack sequence Seq = (v1, v2, ..., v N and attack success rate S2. Let i = 0, sum = 0, and draw N-dimensional random numbers R = (r1, r2, ..., r N ), where 0≤r i ≤1, i=1,2,...,N; S3. Determine the state of the attack sequence based on the relationship between the random number and the corresponding attack success rate. S4. Calculate the value of ANC. Where σ(G) represents the initial size of the maximum connected component (GCC) of the target network G, σ(G\V k ) represents the attack set V sequentially from the target network G. k After the nodes in the network, the size of the remaining GCC in the network, When k=0, it represents the initial situation where no node is under attack; S5. Update sum based on the value of ANC, sum += ANC(Seq,S); S6. Calculate the robustness of the target network G: Robustness = sum.

2. The robustness evaluation method for complex networks according to claim 1, characterized in that, The initial data for the target network G also includes the number of samples K.

3. The robustness evaluation method for complex networks according to claim 2, characterized in that, Step S5 further includes: returning to step S4 until i is greater than the number of samplings K.

4. The robustness evaluation method for complex networks according to claim 3, characterized in that, Step S6 specifically involves calculating the robustness of the target network G.

5. The robustness evaluation method for complex networks according to claim 1, characterized in that, Step S3 specifically involves: according to Determine the state of the attack sequence 6. A robustness evaluation device for complex networks, characterized in that, include: The acquisition unit is used to acquire initial data of the target network G, wherein the initial data includes the number of nodes N in the target network G, and the attack sequence Seq = (v1, v2, ..., v N and attack success rate Extraction unit, used to set i = 0, sum = 0, and extract N-dimensional random numbers R = (r1, r2, ..., r N ), where 0≤r i ≤1, i=1,2,...,N; The processing unit is configured to determine the state of the attack sequence based on the relationship between the random number and the corresponding attack success rate. The first calculation unit is used to calculate the value of ANC. Where σ(G) represents the initial size of the maximum connected component (GCC) of the target network G, σ(G\V k ) represents the attack set V sequentially from the target network G. k After the nodes in the network, the size of the remaining GCC in the network, When k=0, it represents the initial situation where no node is under attack; The update unit is used to update sum based on the value of ANC, sum += ANC(Seq,S); The second computing unit is used to calculate the robustness = sum of the target network G.

7. The robustness evaluation device for complex networks according to claim 6, characterized in that, The initial data for the target network G also includes the number of samples K.

8. The robustness evaluation device for complex networks according to claim 7, characterized in that, The update unit is also used to: jump to the first calculation unit until i is greater than the number of samplings K.

9. The robustness evaluation device for complex networks according to claim 8, characterized in that, The second computing unit is specifically used to calculate the robustness of the target network G.

10. The robustness evaluation device for complex networks according to claim 6, characterized in that, The processing unit is specifically used for: according to Determine the state of the attack sequence

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