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

Abstract

The application provides a network topology evolution-based edge attack matching robustness test method for a network, which comprises the following steps: constructing a network, constructing a matching energy distribution function, determining a matching energy matrix, setting an attack strategy and constructing an evaluation index. A network structure parameter is introduced, and a continuous evolution model of the network matching energy distribution from topology heterogeneity to random characteristics 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 characteristics is realized, and the influence of the network structure difference on the network matching robustness is explored. The method provides a reference for the design strategy of the resource-scarce matching network and the prevention of systematic collapse.

Description

TECHNICAL FIELD

[0001] The present application relates to network security and network decision technology, and particularly relates to a technology for detecting network matching robustness based on edge attack. BACKGROUND

[0002] Compared with traditional connectivity research, matching robustness extends the perspective to the dynamic equilibrium mechanism of network micro-interaction, focuses on the sustainability of global optimal allocation under resource constraints, and its core lies in exploring the dynamic influence of disturbance on the energy landscape of the system. Network matching robustness is crucial to guarantee the integrity of network functions, especially in scenarios such as logistics scheduling and power transmission. For example, in the shipping network, due to local regional conflicts, the shipping route is closed, which leads to the interruption of the optimal path, forcing the logistics system to rely on suboptimal path, resulting in a sharp increase in transportation costs; similarly, in the Internet, the communication efficiency is reduced due to the accidental cutting of optical fibers. The matching instability phenomenon caused by such edge failure reveals the limitations of traditional connectivity indicators in the evaluation of functional integrity. Even if the network remains connected, the energy consumption caused by suboptimal matching may still cause systemic risks.

[0003] Edges in the network represent the connection relationship between nodes, and the connection relationship can reflect communication links, resource allocation paths, dependency relationships, etc. Edge attack refers to an act of damaging, interfering or manipulating the availability, reliability or transmission capacity of edges, resulting in damage to network functions. After the network is subjected to edge attack, the system performance of the network after edge attack is obtained to evaluate and detect the network matching robustness, which has important value for designing anti-destroyed resource allocation network.

[0004] Existing network robustness detection mainly focuses on the change of network structure connectivity against attacks. The robustness is quantified by referring to the percolation theory in physics, and the integrity of structure matching is evaluated by monitoring the dynamic decay behavior of the size of giant connected component with the removal ratio of nodes. Existing network robustness testing is mainly based on simple graph networks, and the core goal is to evaluate the ability to maintain global connectivity when nodes or edges in the network fail. The topological characteristics of such networks are node homogeneity and full connection possibility, so the main indicators for testing network robustness include the proportion of the largest connected subgraph for measuring structural integrity, the network diameter reflecting information transmission efficiency, and the clustering coefficient representing local tightness, etc.

[0005] The network matching robustness test focuses on the bipartite network, and the core objective is to evaluate the ability of the network to maintain optimal matching when facing attacks. The topological characteristics of the bipartite network are that the nodes are divided into two categories and only allow the connection of nodes of different categories, which makes it impossible to directly evaluate the core function of the traditional connectivity index. For example, the bipartite network has two types of nodes, category A and category B. When a node i belonging to category A is selected as an individual, the node needs to be connected, that is, the potential matching object is selected, and only category B can be selected, that is, the nodes in category B are selected as the candidate of individual i.

[0006] In the network matching robustness test, random networks and scale-free networks are used as contrast models. The two types of networks have the same number of nodes and edges, but their topological structure characteristics are essentially different: the connection between the nodes of the random network is completely randomly generated, the degree of the random network usually obeys the Poisson distribution, the degree of most nodes is similar, there is a lack of hub nodes, and the network structure is uniform; a small number of hub nodes in the scale-free network are connected to a large number of edges, and the degree of most nodes is low, and the degree of the node obeys the power-law distribution. In network design, by strictly controlling the network size variable, the influence mechanism of the network structure characteristics on the robustness can be effectively separated, which provides an important insight for understanding the vulnerability of complex networks. However, the limitations of the above method mainly reflect in two aspects: first, this binary contrast framework ignores the fact that real networks often have mixed characteristics of randomness and scale-free characteristics; second, the fixed network structure parameters in the experimental design cannot reflect the characteristics of the dynamic evolution of real networks. These limitations make it difficult to effectively detect the network matching robustness of more complex network models. SUMMARY

[0007] The technical problem to be solved by the present application is to provide a detection scheme for measuring the influence of network structure differences on network matching robustness by introducing a continuously adjustable structure parameter to generate edge attacks based on the continuous evolution of network topology.

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

[0009] Step S1. Determine the total number of nodes of the bipartite network in the network, the total number of nodes of the first type is m, and the total number of nodes of the second type is n; the nodes of the first type are individuals, and the nodes of the second type are candidates; set the current structure parameter u, 0

[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 ith individual (i ∈ {1, 2, …, m}) is:

[0011]

[0012] wherein, represents the initial matching probability of the individual i and the candidate j under the current structure parameter u, ∈' j represents the initial matching energy value of the candidate j, ∈' k is the initial matching energy value of each candidate k in the candidate 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 a parameter for regulating the exponential decay rate;

[0013] Step S3. For each individual i, the candidate is extracted without replacement according to the individual matching probability updated at the last extraction, and the matching energy value of the individual i and the candidate is recorded, the matching energy value is negatively correlated with the extraction order, and finally a preference sequence composed of the matching energy values of the n candidates is obtained;

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

[0015]

[0016] wherein, is the matching probability of the individual i and the candidate at the tth extraction, and s is the current extraction number, s = 1, 2, …, t;

[0017] Step S4. The population preference matrix E is obtained by executing step S3 on the m individuals;

[0018] Step S5. The optimal matching solution set M is obtained by solving the matrix E using the existing minimum cost maximum flow algorithm, and the optimal matching solution set M contains all the matching pairs of subjects and candidates in the network that keep the edges;

[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 population preference matrix E to 0 or null to obtain the population preference matrix E after the attack a ;

[0021] Step S8. After completing a round of edge attack, the matrix E is solved using the existing minimum cost maximum flow algorithma solving is performed to update the optimal matching solution set M;

[0022] Step S9. Calculate the 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 needed, return to steps S6-S9; when the network topology needs to be adjusted, return to step S1.

[0024] Further, the attack strategy includes the selection of three attack types, the three attack types being minimum energy attack, random energy attack and maximum energy attack;

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

[0026] The beneficial effects of the present application are that by defining the continuously adjustable structure parameter u in the bipartite network composed of the group where the individual is located and the group where the candidate is located, introducing the energy concept in physics, the differentiated measurement of the network topology structure characteristics is realized, and the evaluation index is set to realize the quantitative evaluation of the network matching robustness under different network topology characteristics, so as to detect the influence of the network structure difference on the network matching robustness. BRIEF DESCRIPTION OF DRAWINGS

[0027] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0028] Figure 1 is a network schematic diagram based on network topology evolution of the embodiment.

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

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

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

[0032] Figure 5 is a result schematic diagram of the average matching energy change trend thermodynamic diagram provided by the embodiment of the present application.

[0033] Figure 6 is a result schematic diagram of the average matching retention rate change trend heat map provided by an embodiment of the present application. DETAILED DESCRIPTION

[0034] The matching energy is defined for the importance of the edge between two nodes, and 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 node.

[0036] The individual preference is the connection demand order of the candidate node of each node in the network which comprehensively considers the priority, state, resource demand and ability level. The group preference is the connection demand order of the candidate node of a type of node in the network.

[0037] The structural parameter u introduced in the present application is used to continuously adjust the network topology characteristics, and 0 < u ≤ 1. As shown in the following formula, after setting the initial group preference, when the parameter u → 0, the network presents a completely homogeneous feature, the individual preference tends to be consistent with the initial preference, that is, the group preference presents a high similarity, and at this time, the minimum matching energy edge is completely concentrated in a few candidates, corresponding to the scale-free network feature. With the increase of u, the minimum matching energy distribution gradually transits from homogeneity to randomness, that is, the energy distribution presents a mixed feature; when u → 1, the network presents a typical random feature, at this time, the group preference presents complete randomness, and the minimum matching energy edge is evenly distributed, corresponding to the random network feature. Figure 1

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

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

[0040] Step S2. Initialize the individual matching energy distribution function. Given the initial matching energy ∈'j of the jth node in the candidate set, ∈'j = j / n, j ∈ {1, 2, …, n}. The matching energy distribution function is composed of the matching probability of each individual and other nodes in the network, and for the ith individual (i ∈ {1, 2, …, m}), the matching probability expression is as follows: j j Step S3. Calculate the individual preference. The individual preference is the connection demand order of the candidate node of each node in the network which comprehensively considers the priority, state, resource demand and ability level. The individual preference is calculated according to the following formula:​

[0041]

[0042] where, represents the initial matching probability of individual i with candidate j at parameter u, ∈' j represents the initial matching energy value of candidate j, ∈' k is the initial matching energy value of each candidate k in the candidate set, k = 1, 2, …, n, ln is the natural logarithm function with base e, exp is the exponential function with base e, and λ is a parameter that regulates the decay rate of the index. When u→0, ln(u)→∞, the steeper the exponential decay, the greater the difference in probability distribution, corresponding to the power-law distribution characteristics. When u→1, ln(u)→0, the slower the exponential decay, the more uniform the probability distribution, corresponding to the random characteristics.

[0043] Step S3. Generating individual preference sequence. To balance the certainty preference and randomness, the probability weight of the preference distribution is converted into a preference ranking by stepwise non-replacement sampling of the ranking selection model Plackett-Luce.

[0044] The specific process is as follows:

[0045] (1) Initialization: for each individual i, initialize its preference sequence E i to empty, and initialize the ranking number t = 1;

[0046] (2) t-th sampling: at the t-th step, according to the individual matching probability in the current probability distribution, the t-th preference candidate j t is sampled non-replacement;

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

[0048]

[0049] where t represents the preference ranking value of individual i for candidate j t , and n represents the number of all candidates. The matching energy value corresponds to the ranking in the preference list, the earlier the ranking, the smaller the matching energy value, meaning the more stable the matching;

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

[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 The middle row is deleted.

[0061] The complete connected bipartite network is used as the initial state to establish an ideal limit reference system, which eliminates the interference of initial topological heterogeneity and ensures that the result difference of the optimal matching solution set is completely derived from different edge attack strategies. The influence of three typical attack strategies on the optimal matching energy of the network is quantified by gradually increasing the attack ratio f from 0 to 1, i.e., 0≤f<1.

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

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

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

[0065] (1) Average matching energy

[0066]

[0067] wherein, represents the average matching energy of the group, ∈ ij represents the matching energy of the matching pair of 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, the higher the robustness of the network. The index By quantifying the system energy increment caused by matching conflicts, the dynamic influence of attacks on matching quality can be accurately reflected: when the optimal matching is destroyed, suboptimal matching will produce higher system energy, and this energy change directly represents the degree of degradation of matching quality. As shown in Figure 3 and Figure 5 .

[0068] (2) Average matching retention rate

[0069]

[0070] wherein |M max| is the number of matching pairs in the optimal matching solution set M corresponding to the attack ratio f of zero. The higher the value of p, the higher the robustness of the network. The index p measures the proportion of the network that remains matched after an attack. For example Figure 4 and Figure 6 as shown.

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

[0072] Step S10. If there is still a need to conduct the next round of edge attack matching robustness detection, the existing attack ratio f is updated by increasing, and returns to steps S6-S9. When it is necessary to adjust the network topology, return to step S1.

[0073] Through the above steps, the network topology with the best matching robustness can be determined, which provides 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 the 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 ∈ ij Represents the matching energy between individual i and candidate j in the optimal solution set M, and determines 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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