Method for testing robustness of edge attack to network matching based on network topology evolution

Abstract

The invention provides a method for testing robustness of edge attack to network matching based on network topology evolution. The method comprises the steps of constructing a network, constructing a matching energy distribution function, determining a matching energy matrix, setting an attack strategy and constructing an evaluation index. Network structure parameters are introduced, and a continuous evolution model of network matching energy distribution from topological heterogeneity to random features is constructed. The network topology structure feature differentiation measurement is realized, and the evaluation index is set, so that the quantitative evaluation of the network matching robustness under different network topology features is realized, and the influence of the network structure difference on the network matching robustness is explored. The method provides reference for resource scarce network design strategy matching and systematic crash prevention.

Description

Technical Field

[0001] The present invention relates to network security and network decision-making technology, and in particular to a technology for detecting network matching robustness based on edge attacks. Background Art

[0002] Compared with traditional connectivity research, matching robustness extends the perspective to the dynamic equilibrium mechanism of network micro-interactions, focusing on the sustainability of global optimal allocation under resource constraints. Its core lies in exploring the dynamic impact of disturbances on the system's energy landscape. Network matching robustness is crucial to ensuring the integrity of network functions, especially in scenarios such as logistics scheduling and power transmission. For example, in shipping networks, due to local geopolitical conflicts, the closure of routes leads to the interruption of optimal paths, forcing the logistics system to rely on suboptimal paths, resulting in a surge in transportation costs; similarly, in the Internet, accidental fiber optic disconnection causes a decrease in communication efficiency. The matching instability phenomenon caused by such edge failures reveals the limitations of traditional connectivity indicators in functional integrity assessment. Even if the network remains connected, the increase in energy consumption caused by suboptimal matching may still cause systemic risks.

[0003] Edges represent connections between nodes in a network. These connections can reflect communication links, resource allocation paths, dependencies, and more. Edge attacks involve disrupting, interfering with, or manipulating the availability, reliability, or transmission capacity of edges, thereby impairing network functionality. After performing an edge attack on a network, obtaining the post-attack network's system performance can be used to assess and test network matching robustness, which is crucial for designing resilient resource allocation networks.

[0004] Existing network robustness testing primarily focuses on changes in the connectivity of network structures against attacks. Drawing on percolation theory from physics to quantify robustness, the integrity of structural matching is assessed by monitoring the dynamic decay of the size of large connected components as the proportion of node removals increases. Existing network robustness testing is primarily based on simple graph networks, with the core objective being to assess the ability to maintain global connectivity in the face of node or edge failures. The topological characteristics of such networks are characterized by node homogeneity and the likelihood of full connectivity. Therefore, key metrics for testing network robustness include the maximum connected subgraph ratio, which measures structural integrity; the network diameter, which reflects information transmission efficiency; and the clustering coefficient, which characterizes local compactness.

[0005] Network matching robustness testing focuses on bipartite networks, and its core goal is to evaluate the ability of a network to maintain an optimal match when faced with attacks. The topological characteristics of bipartite networks are such that nodes are divided into two categories and only allow connections between different types of nodes, which makes it impossible to directly evaluate their core functions using traditional connectivity metrics. For example, in a bipartite network, there are two types of nodes, category A and category B. When a node i belonging to category A, as an individual, selects a node to connect to, that is, when selecting potential matching objects, it can only choose from category B, that is, taking the nodes in category B as candidates for individual i.

[0006] In network matching robustness testing, using random networks and scale-free networks as comparison models has become a classic research paradigm. In scale-free networks... Although these two network types have the same number of nodes and edges, there are essential differences in their topological structure characteristics: the connections between nodes in a random network are completely randomly generated, and the degree of a random network usually follows a Poisson distribution, with most nodes having similar degrees and lacking hub nodes, and the network structure is uniform; in a scale-free network, a small number of hub nodes connect a large number of edges, most nodes have low degrees, and the node degrees follow a power-law distribution. When designing a network, by strictly controlling the network scale variables, it is possible to effectively separate the influence mechanism of network structure characteristics on robustness, providing important insights for understanding the vulnerability of complex networks. However, the limitations of the above methods are mainly reflected in two aspects: firstly, this binary comparison framework ignores the fact that real-world networks often have mixed characteristics of both randomness and scale-free properties; secondly, the fixed network structure parameters in the experimental design are difficult to reflect the characteristics of the dynamic evolution of real networks. These limitations make it impossible to effectively detect the network matching robustness of more complex network models. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to propose a detection scheme that measures the impact of network structure differences on network matching robustness by introducing continuously adjustable structure parameters to generate edge attacks based on the continuous evolution of network topology.

[0008] The technical solution adopted by the present invention to solve the above technical problem is a method for testing network matching robustness based on edge attacks of network topology evolution, including the steps:

[0009] Step S1. Determine the total number of nodes in the bipartite network in the network. The total number of nodes in the first category is m, and the total number of nodes in the second category is n; the nodes in the first category are individuals, and the nodes in the second category are candidates; set the current structure parameter u, where 0 < u ≤ 1; when u is closer to 0, the bipartite network shows more scale-free network characteristics, and when u is closer to 1, the bipartite network shows more random network characteristics. By adjusting the value of u between 0 and 1, the bipartite network shows mixed characteristics of both random and scale-free networks.

[0010] Step S2. Initialize the initial matching energy ∈′ of the jth node in the individual matching energy distribution function j =j / n, j∈{1,2,…,n}; the initial matching probability of the i-th individual (i∈{1,2,…,m}) is:

[0011]

[0012] in, Represents the initial matching probability between individual i and candidate j under the current structural parameter u, ∈′ j Represents the initial matching energy value of candidate j, ∈′ k is the initial matching energy value of each candidate item k in the candidate item set, k = 1, 2, …, n, ln is the logarithmic function with the natural constant e as the base, exp is the exponential function with the natural constant e as the base, and λ is the parameter that controls the exponential decay rate;

[0013] Step S3. For each individual i, extract candidate items without replacement according to the individual matching probability updated in the previous extraction, and record the matching energy value between individual i and the candidate item. This matching energy value is negatively correlated with the extraction order, and finally obtain a preference sequence consisting of the matching energy values of n candidate items;

[0014] The way to update the individual matching probability is:

[0015]

[0016] in, is the matching probability between individual i and the candidate item at the tth extraction, s is the current extraction sequence number, s = 1, 2, ..., t;

[0017] Step S4. Execute step S3 on m individuals to obtain the group preference matrix E;

[0018] Step S5. Solve the matrix E using the existing minimum cost maximum flow algorithm to obtain the optimal matching solution set M, which contains all matching pairs in the network that have edges with the candidate items;

[0019] Step S6. Set the edge attack strategy and attack ratio f, 0≤f<1;

[0020] Step S7. Complete the edge attack according to the set attack strategy and attack ratio f. For each individual i, delete f*n edges under a specific attack type, and set the elements corresponding to the edges to be deleted in the group preference matrix E to 0 or empty to obtain the group preference matrix E after the attack. a ;

[0021] Step S8. After completing a round of edge attack, use the existing minimum cost maximum flow algorithm toa Solve to update the optimal matching solution set M;

[0022] Step S9. Calculating a detection index of matching robustness based on the optimal matching solution set M obtained in step S8;

[0023] Step S10: When the next round of edge attack matching robustness detection is required, return to steps S6-S9; when the network topology needs to be adjusted, return to step S1.

[0024] Furthermore, the attack strategy includes the selection of three attack types, which are minimum energy attack, random energy attack, and maximum energy attack;

[0025] The minimum energy attack refers to preferentially deleting the edges with the smallest matching energy in the group preference matrix; the random energy attack refers to randomly deleting the matching edges in the group preference matrix; and the max-E attack refers to preferentially deleting the edges with the largest matching energy in the group preference matrix.

[0026] The beneficial effect of the present invention is that by defining a continuously adjustable structural parameter u in a bipartite network composed of two groups, the group where the individual belongs and the group where the candidate belongs, the concept of energy in physics is introduced, the differentiated measurement of network topological structure characteristics is realized, and the evaluation index is set to achieve quantitative evaluation of the network matching robustness under different network topological characteristics, thereby detecting the impact of network structure differences on network matching robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0028] Figure 1 This is a network diagram based on network topology evolution in an embodiment.

[0029] Figure 2 It is a schematic diagram of the attack strategy provided by an embodiment of the present invention.

[0030] Figure 3 It is a schematic diagram of the average matching energy change trend provided by an embodiment of the present invention.

[0031] Figure 4 4 is a schematic diagram of the result of the average matching retention rate change trend provided by an embodiment of the present invention.

[0032] Figure 5 This is a schematic diagram of the result of the average matching energy change trend heat map provided by an embodiment of the present invention.

[0033] Figure 6 It is a schematic diagram of the result of the heat map of the change trend of the average matching retention rate provided by the embodiment of the present invention. Detailed implementation manners

[0034] Define the matching energy to represent the importance of the edge between two nodes. The lower the matching energy, the higher the importance of the edge.

[0035] The individual matching energy is the importance of the edge between each node in the network and its candidate nodes.

[0036] The individual preference is the ranking of the connection requirements of each node in the network for candidate nodes, which comprehensively considers the priority, status, resource requirements, and ability level. The group preference is the ranking of the connection requirements of a class of nodes in the network for candidate nodes.

[0037] The structural parameter u introduced in the present invention is used to make the network topology structure characteristics continuously adjustable, where 0 < u ≤ 1. As Figure 1 shown, after setting the initial group preference, when the parameter u → 0, the network shows completely homogeneous characteristics, and the individual preference tends to be consistent with the initial preference, that is, the group preference shows a high degree of similarity. At this time, the edges with the minimum matching energy are completely concentrated in a few candidates, corresponding to the characteristics of the scale-free network. As u increases, the distribution of the minimum matching energy gradually transitions from homogeneity to randomness, that is, the energy distribution shows a mixed characteristic; when u → 1, the network shows typical random characteristics, at which time the group preference shows complete randomness, and the edges with the minimum matching energy are evenly distributed, corresponding to the characteristics of the random network.

[0038] Based on the above continuous regulation mechanism, the present invention establishes a probability function to describe the individual preference distribution, and then constructs a preference matrix reflecting the group selection behavior. And on this basis, three types of attack strategies and two types of evaluation indexes are set. The application of the edge attack on the network matching robustness test based on the continuous evolution of the network topology in network design includes the following steps:

[0039] Step S1. Determine the total number of nodes in the bipartite network including type A and type B nodes in the network. The total number of type A nodes is m, and the total number of type B nodes is n. In the embodiment, each node in type B is connected to each node in type A as a candidate. The nodes in type A are called individuals, and the nodes in type B are called candidates. Determine the current structural parameter u.

[0040] Step S2. Initialize the individual matching energy distribution function. Given the initial matching energy ∈′ of the j-th node in the candidate set j = j / n, j ∈ {1, 2,..., n}. The matching energy distribution function is composed of the matching probabilities of each individual with other nodes in the network. For the i-th individual (i ∈ {1, 2,..., m}), the matching probability expression is as follows:

[0041]

[0042] in, Represents the initial matching probability between individual i and candidate j under parameter u, ∈′ j Represents the initial matching energy value of candidate j, ∈′ k is the initial matching energy value for each candidate k in the candidate set, where k = 1, 2, …, n, ln is the logarithmic function with the natural constant e as the base, exp is the exponential function with the natural constant e as the base, and λ is the parameter that controls the exponential decay rate. As u → 0, ln(u) → ∞, the steeper the exponential decay, the greater the variance in the probability distribution, corresponding to a power-law distribution. As u → 1, ln(u) → 0, the slower the exponential decay, the more uniform the probability distribution, corresponding to a random distribution.

[0043] Step S3: Generate individual preference sequences. To balance deterministic preferences and randomness, the probability weights of preference distributions are converted into preference rankings through step-by-step sampling without replacement using the Plackett-Luce ranking selection model.

[0044] The specific process is as follows:

[0045] (1) Initialization: For each individual i, initialize its preference sequence E i Empty, initialize the sorting sequence number t=1;

[0046] (2) Sampling at step t: At step t, the individual matching probability in the current probability distribution is Extract the tth preference candidate j without replacement t ;

[0047] (3) Record matching energy: record the matching energy between individual i and candidate j t Matching energy value

[0048]

[0049] Where t represents individual i’s response to candidate j t The preference ranking value, n represents the number of all candidate items. The matching energy value corresponds to the ranking in the preference list. The higher the ranking, the smaller the matching energy value, which means the matching is more stable.

[0050] (4) Update probability distribution: Update the probability distribution of the remaining candidates by normalization, where the matching probability for the i-th individual in step t is for:

[0051]

[0052] Among them, s is the current extraction sequence number, s=1,2,…,t, Represents the cumulative probability of all removed candidates. Normalization is used to ensure that the sum of the probabilities of all selectable candidates is equal to 1 at each sampling;

[0053] (5) Get And determine whether t=n is satisfied. If so, proceed to step (6). Otherwise, update t=t+1 and execute steps (2)-(4).

[0054] (6) Generate preference sequence: record the candidate items extracted n times and their corresponding matching energy, so as to obtain the preference sequence E of individual i i :

[0055] E i =[∈ i1 ∈ i2 …∈ ij …∈ in ]

[0056] Step S4. Construct a group preference matrix. Repeat steps (1)-(6) for m individuals to obtain the group preference matrix E:

[0057]

[0058] The group preference matrix E corresponds to a fully connected bipartite network consisting of m individuals and n candidates.

[0059] Step S5. Solve the matrix E using the existing minimum cost maximum flow algorithm to obtain the optimal matching solution set M. The optimal matching solution set M contains all matching pairs of entities and candidates in the network that have edges. The optimal matching solution set M obtained based on the matrix E is compared with the matrix E after being attacked by edges. a The obtained optimal matching solution set M has the largest number of matching pairs.

[0060] Step S6. Set the attack strategy. In order to systematically detect the matching robustness of the network under adversarial conditions, the embodiment designs three edge-based attack strategies, such as Figure 2 As shown: minimum energy attack min-E, random energy attack ran-E and maximum energy attack max-E. Among them, min-E attack refers to the priority deletion of the edge with the smallest matching energy in the group preference matrix, which aims to evaluate the vulnerability of the network to the targeted deletion of key low-energy edges; ran-E attack refers to the random deletion of matching edges in the group preference matrix, simulating random failures or non-targeted adversarial behavior; max-E attack refers to the priority deletion of the edge with the largest matching energy in the group preference matrix, which aims to evaluate the role of redundant high-energy edges in maintaining network robustness. Among them, the group preference matrix is deleted in the matrix E during the first attack, and then in the latest matrix Ea Delete in.

[0061] The construction uses a fully connected bipartite network as the initial state to establish an idealized limit reference system, eliminating interference caused by initial topological heterogeneity and ensuring that differences in the optimal matching solution set are entirely due to different edge attack strategies. By gradually increasing the attack ratio f from 0, 0≤f<1, the impact of three typical attack strategies on the network's optimal matching energy is quantified.

[0062] Step S7. Complete the edge attack according to the set attack strategy. According to the current attack ratio f and the attack strategy, for each individual i, delete f*n edges under the specific attack type. The operation of deleting edges is as follows: for the edge between the individual i and the candidate j to be deleted, the element corresponding to the edge in the group preference matrix E is set to 0 or empty to obtain the group preference matrix E after the attack. a .

[0063] Step S8. After completing a round of edge attack, use the existing minimum cost maximum flow algorithm to a Solve to update the optimal matching solution set M.

[0064] Step S9. Calculate detection indicators. In order to evaluate the robustness of the network against attacks, two types of evaluation indicators are constructed: average matching energy and average matching retention rate.

[0065] (1) Average matching energy

[0066]

[0067] in, represents the average matching energy of the group, ∈ ij represents the matching energy of the matching pair between individual i and candidate j in the optimal solution set M, and |M| represents the number of matching pairs in the optimal solution set M. The lower it is, the more robust the network is. By quantifying the system energy increment caused by matching conflicts, we can accurately reflect the dynamic impact of attacks on matching quality: when the optimal match is destroyed, the suboptimal match will generate higher system energy. This energy change directly represents the degree of degradation of matching quality. Figure 3 and Figure 5 shown.

[0068] (2) Average matching retention rate

[0069]

[0070] where |M max| is the number of matching pairs in the optimal matching solution set M corresponding to the attack ratio f is zero. The higher the p value, the higher the robustness of the network. The indicator p measures the proportion of matching that remains after the attack from a macro level. Figure 4 and Figure 6 shown.

[0071] index The combination of the two and the index p can comprehensively evaluate the matching robustness of the bipartite network after this round of edge attack.

[0072] Step S10: If the next round of edge attack matching robustness test is required, the existing attack ratio f is increased and updated, and the process returns to steps S6-S9. If the network topology needs to be adjusted, the process returns to step S1.

[0073] Through the above steps, the network topology with the best robustness can be determined, providing support for network topology design and prevention of systemic collapse.

Claims

1. A network matching robustness test method based on edge attack of network topology evolution, characterized by: Including steps: Step S1. Determine the total number of nodes in the bipartite network. The total number of nodes in the first category is m, and the total number of nodes in the second category is n. The nodes in the first category are individuals, and the nodes in the second category are candidates. Set the current structural parameters u, 0 <u≤1; When u is closer to 0, the bipartite network shows more scale-free network characteristics. When u is closer to 1, the bipartite network shows more random network characteristics. By adjusting the size of u between 0 and 1, the bipartite network shows mixed characteristics of both random networks and scale-free networks. Step S2. Initialize the initial matching energy ∈′ of the jth node in the individual matching energy distribution function j =j / n, j∈{1,2,…,n}; the initial matching probability of the i-th individual is: in, Represents the initial matching probability between individual i and candidate j under the current structural parameter u, i∈{1,2,…,m},∈′ j Represents the initial matching energy value of candidate j, ∈′ k is the initial matching energy value of each candidate item k in the candidate item set, k = 1, 2, …, n, ln is the logarithmic function with the natural constant e as the base, exp is the exponential function with the natural constant e as the base, and λ is the parameter that controls the exponential decay rate; Step S3. For each individual i, extract candidate items without replacement according to the individual matching probability updated in the previous extraction, and record the matching energy value between individual i and the candidate item. This matching energy value is negatively correlated with the extraction order, and finally obtain a preference sequence consisting of the matching energy values of n candidate items; The way to update the individual matching probability is: in, is the matching probability between individual i and the candidate item at the tth extraction, s is the current extraction sequence number, s = 1, 2, ..., t; Step S4. Execute step S3 on m individuals to obtain the group preference matrix E; Step S5. Solve the matrix E using the existing minimum cost maximum flow algorithm to obtain the optimal matching solution set M, which contains all matching pairs in the network that have edges with the candidate items; Step S6. Set the edge attack strategy and attack ratio f, 0≤f<1; Step S7. Complete the edge attack according to the set attack strategy and attack ratio f. For each individual i, delete f*n edges under a specific attack type, and set the elements corresponding to the edges to be deleted in the group preference matrix E to 0 or empty to obtain the group preference matrix E after the attack. a ; Step S8. After completing a round of edge attack, use the existing minimum cost maximum flow algorithm to a Solve to update the optimal matching solution set M; Step S9. Calculating a detection index of matching robustness based on the optimal matching solution set M obtained in step S8; Step S10: When the next round of edge attack matching robustness detection is required, return to steps S6-S9.

2. The method according to claim 1, wherein The specific process of step S3 is as follows: (1) For each individual i, initialize its preference sequence E i Empty, initialize the sorting sequence number t=1; (2) At step t, according to the individual matching probability in the current probability distribution Extract the tth candidate j without replacement t ; (3) Record individual i and candidate j t Matching energy value Where t represents individual i’s response to candidate j t The preference ranking value of (4) Update the probability distribution of the remaining candidates by normalization, where in step t, for individual i and candidate j, t Matching probability for: Where s is the current extraction sequence number, s = 1, 2, ..., t; (5) Get And determine whether t=n is satisfied. If so, proceed to step (6). Otherwise, update t=t+1 and execute steps (2)-(4). (6) Record the candidate items extracted n times and their corresponding matching energies, thereby obtaining the preference sequence E of individual i i =[∈ i1 ∈ i2 …∈ ij …∈ in ].

3. The method according to claim 1, wherein: The attack strategy includes the choice of three attack types: minimum energy attack, random energy attack, and maximum energy attack; The minimum energy attack refers to preferentially deleting the edges with the smallest matching energy in the group preference matrix; the random energy attack refers to randomly deleting the matching edges in the group preference matrix; and the max-E attack refers to preferentially deleting the edges with the largest matching energy in the group preference matrix.

4. The method according to claim 1 or 3, wherein: The edge attack strategy is as follows: select a fully connected bipartite network as the initial state; the initial value of f is 0, and the attack ratio f is gradually increased from 0, 0≤f<1.

5. The method according to claim 4, wherein: The specific method for calculating the detection index of matching robustness based on the optimal matching solution set M obtained in step S8 is: (1) Calculate the average matching energy Among them, ∈ ij represents the matching energy between individual i and candidate j in the optimal solution set M, and |M| represents the number of matching pairs in the optimal solution set M; (2) Calculate the average matching retention rate p: Among them, |M max | is the number of matching pairs in the optimal matching solution set M corresponding to when the attack ratio f is zero.

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