A graph attack method for suppressing graph disassembly and a graph structure protection system and device

Abstract

The present invention belongs to the field of big data analysis, and specifically relates to a graph attack method for suppressing graph disassembly, and a protection system and device for the graph structure of a network using this method. The graph attack method includes the following steps: S1: using a graph structure to characterize the network to be processed; S2: drawing the ANC curve of the graph structure under two disassembly strategies based on degree value and collective influence; S3: determining the target node set in the network based on the ANC curve; S4: constructing a loss function for evaluating the difference in disassembly sequences generated under a mixed attack strategy based on the target node sets of the two disassembly paths; S5: presetting constraints and iteration rounds, and then using the loss function to calculate the link gradient, and iteratively deleting the edges that meet the constraints with the link gradient as a guide to obtain an enhanced graph structure; the present invention overcomes the problem that various existing network systems have weak resistance to graph disassembly methods and are easily subject to network attacks.

Description

Technical Field

[0001] The present invention belongs to the field of big data analysis, and specifically relates to a graph attack method for suppressing graph disassembly, and a protection system and device for the graph structure of a network using the method. Background Art

[0002] The network is a medium for information dissemination and plays an important role in the dissemination of information. In a complex network, the connectivity between single nodes may have a huge impact on the information transmission performance of the entire network. Power systems and social platforms are both typical network structures. Therefore, problems such as cascading failures in power systems, virus transmission between individuals, and rumor propagation on social networks are all crucial to the structure of the network. Therefore, analyzing and processing the network structure has become a feasible solution to these problems. Based on this problem, many network disassembly methods have emerged. They can efficiently find key nodes in the network and remove nodes from the network, thereby greatly destroying the network structure and function.

[0003] However, any technology has two sides, and increasingly efficient network disassembly methods can also cause security problems. For example, key nodes in the network may be easily identified and attacked in efficient disassembly methods, eventually causing the collapse of the entire network. Therefore, in order to combat graph disassembly methods, we need to hide key nodes in the network. Considering that the premise of graph disassembly methods is the need to analyze the graph structure, this analysis needs to rely on the basic structure of the network and the large amount of relevant data contained in the network. Therefore, if the network can be made to have the performance to resist graph analysis tasks, it will have a good defensive effect against graph disassembly attacks.

[0004] Among them, graph adversarial attack is an effective method that can interfere with graph analysis tasks. This method changes the original graph structure by deleting edges, modifying node features, inserting nodes, etc., so as to achieve the corresponding purpose. For example, the graph neural network model can be deceived by adding and deleting edges and modifying node features, causing it to misclassify nodes. However, random graph attacks on the original graph structure may also affect the function of the original network and be quickly discovered and defended; therefore, how to find a graph attack method that can more efficiently resist graph disassembly and minimize the impact on the normal function of the network has become a technical problem that technicians in this field need to solve urgently. Summary of the invention

[0005] In order to overcome the problem that various existing network systems have weak resistance to graph analysis and graph disassembly methods and are easily vulnerable to network attacks, the present invention provides a graph attack method for suppressing graph disassembly, as well as a protection system and device for the graph structure of a network using this method.

[0006] The present invention is implemented by the following technical solutions:

[0007] A graph attack method for suppressing graph disassembly, which is used to perform graph attack processing on the original graph structure of the network on the basis of satisfying constraint conditions, and obtain an enhanced graph structure by deleting some edges; thereby hiding key information in the original graph structure and improving the network's defense capability against graph disassembly attacks.

[0008] The graph attack method of the present invention comprises the following steps:

[0009] S1: The network to be processed is represented by a graph structure G, wherein V represents the set of nodes in the network, and E represents the set of edges between nodes in the network.

[0010] S2: According to the changes in the connectivity of the remaining nodes after network disassembly, the corresponding ANC curves of the graph structure G are drawn under the two disassembly strategies based on degree value and collective influence.

[0011] S3: Based on the drawn ANC curves, the target node sets V1 and V2 that play a key role in network disassembly in the degree-based and collective influence-based disassembly strategies are determined respectively.

[0012] S4: Based on the target node sets V1 and V2 of the two disassembly paths, a loss function loss is constructed to evaluate the difference between the disassembly sequences generated by the original graph and the attacked graph under the mixed attack strategy. The loss function loss is as follows:

[0013]

[0014] In the above formula, HD G′ and CI G′ They refer to the node degree and collective influence value calculated based on the current graph structure after deleting the edges. i , v i+1 , …, v j} G represents the key node set corresponding to the degree-based disassembly strategy (HD strategy), namely: V1. j+1 , v j+2 , …, v N} G Includes all nodes sorted after the key node set; {v i′ , v i′+1 , …, v j′} represents the corresponding key node set in the collective influence-based disassembly strategy (CI strategy), namely V2. j′+1 , v j′+2 , …, v N′} GIncludes all nodes sorted after the critical node set; σ is a preset very small constant.

[0015] S5: Preset the constraints and iteration rounds k of the graph attack process, then use the loss function to calculate the link gradient, and use the link gradient as a guide to iteratively delete the edges that meet the constraints in the original graph structure G, and then obtain the enhanced graph structure G′ after the graph attack;

[0016] The iterative deletion process of each edge during graph attack is as follows:

[0017] S51: The test statistic ∧(G, G′) of the node degree distribution before and after the edge deletion is lower than the threshold τ as a preset constraint

[0018] conditions, namely:

[0019] ∧(G, G′)<τ;

[0020] S52: The number of edges to be deleted is used as the preset maximum iteration round k max .

[0021] S53: Update the loss function value loss corresponding to the graph structure G of the current round, and use the following formula to calculate the link gradient ga corresponding to each edge in the graph structure G:

[0022]

[0023] In the above formula, H a Represents edge e a The corresponding elements in the sparse matrix H are obtained by converting the graph structure G and are used to represent the edges in the network; that is, H∈{1} |1|×|E| .

[0024] S54: According to the link gradient g a The negative terms in the graph structure G correspond to the edge e i Arrange in ascending order to obtain an edge sequence A.

[0025] S55: Calculate the test statistic ∧(G, G′) of the node degree distribution of the original graph after each edge in the edge sequence A is deleted; and determine whether the test statistic ∧(G, G′) satisfies the constraint condition:

[0026] (1) When there is an item that satisfies the constraint, the edge that satisfies the constraint and is located at the front of the edge sequence A is deleted in the current round.

[0027] (2) When the test statistic ∧(G, G′) of the node degree distribution formed after deleting any edge in the edge sequence A does not meet the constraint conditions, the first item in the edge sequence A is taken as the edge to be deleted in the current round.

[0028] S56: After deleting each edge, the iteration round k is incremented, and then steps S53-S55 are repeated until the iteration round k reaches the preset maximum iteration round k. max , that is: the number of deleted edges reaches the preset value; at this time, the obtained graph structure is the required enhanced graph structure G′.

[0029] As a further improvement of the present invention, in step S1, in the original graph structure G=(V, E), V={v1, v2, ..., v N}, E = {e1, e2, ..., e M}; That is, the graph structure of the network contains N nodes and M edges;

[0030] The original graph structure G can be converted into the form of an adjacency matrix A, that is: A∈{0,1} |V|×|V| ;

[0031] The adjacency matrix A can be further converted into a sparse matrix H, that is: H∈{1} |1|×|E| .

[0032] As a further improvement of the present invention, in step S2, in the disassembly strategy based on degree value or collective influence, the method for drawing the ANC curve is as follows:

[0033] S21: Calculate the degree value or collective influence value of each node in the graph structure G, and then sort the nodes in descending order according to the degree value or collective influence value to generate a corresponding node sequence B or B′.

[0034] S22: According to the order of each node in the node sequence B or B′ in the previous step, delete each node in the graph structure G in turn, and calculate the connectivity of the remaining graph structure G′ after deleting one percent of the nodes.

[0035] S23: When all nodes in the graph structure G are disassembled, the corresponding metadata is obtained with the proportion of the number of removed nodes as the horizontal axis and the connectivity of the remaining graph structure G′ after deleting the nodes as the vertical axis. Then, a series of discrete metadata are fitted to draw the corresponding ANC curve.

[0036] As a further improvement of the present invention, in step S22, the calculation formula of the remaining node connectivity is as follows:

[0037]

[0038] In the above formula, connectivy(G\{v1,v2,…,v i} G ) means deleting {v1, v2, …, vi} G The connectivity of the remaining graph structure G′ after all nodes in N GCC (G\{v1, v2, …, v i} G ) means deleting the node set {v1, v2, ..., v i} G The number of nodes contained in the largest part of the interconnected structure in the post-graph; N G Represents the number of nodes in the original graph structure G.

[0039] As a further improvement of the present invention, in step S3, the process of obtaining the target node set V1 or V2 is as follows:

[0040] S31: Calculate each node v according to the ANC curve i The first-order derivative approximation corresponding to the metadata of slop i , the calculation formula is as follows:

[0041] slop i =connectivy(G\{v1, v2,…,v i+1} G )-connectivy(G\{v1, v2,…,v i} G ).

[0042] S32: Based on each node v i The corresponding first-order derivative approximation slop i Calculate each node v i The difference of the curve drop rate before and after slope_dif i ; The calculation formula is as follows:

[0043] slope_dif i =slop i+1 -slop i ,

[0044] S33: The slope_dif value of the slope rate difference before and after the node in the node sequence B or B′ is calculated. i The node v corresponding to the smallest data i As the left node of the target node set V1 or V2.

[0045] S34: The node v in each ANC curve that makes the function value satisfy connectivy<c0 for the first time j As the right node of the target node set V1 or V2; where c0 is the preset lower limit of network connectivity.

[0046] S35: Define the node set {v i , vi+1 , …, v j} is the target node set V1 or V2 that plays a key role in disassembly.

[0047] As a further improvement of the present invention, in step S34, the lower limit value c0 of connectivity is set to 0.02.

[0048] As a further improvement of the present invention, in step S51, the test statistic threshold τ is set to 0.004.

[0049] The present invention also includes a protection system for a graph structure of a network, which is used to delete some key edges in the original graph structure of the network to obtain an enhanced graph structure; thereby improving the network's defense capability against node removal-type graph disassembly. The protection system for the graph structure uses the aforementioned graph attack method for suppressing graph disassembly to perform edge deletion processing on the original graph structure. Specifically, the protection system for the graph structure includes a degree calculation module, a collective influence calculation module, an ANC curve generation module, a key node acquisition module, a link gradient update module, and an edge processing module.

[0050] Among them, the degree calculation module is used to calculate the degree value corresponding to each node in the graph structure to be processed; the collective influence calculation module is used to calculate the collective influence value corresponding to each node in the graph structure to be processed.

[0051] The ANC curve generation module includes two independent inputs and outputs, one of which is used to generate a corresponding ANC curve according to the degree value of each node in the graph structure, and the other is used to generate a corresponding ANC curve according to the collective influence value of each node in the graph structure.

[0052] The key node acquisition module is used to obtain the target node set that plays a key role in network disassembly in the graph structure according to the ANC curve. The target node set is the original nodes arranged in descending order according to the degree value or collective influence value, and the sequence corresponds to the "inflection point" in the ANC curve and all the nodes between the critical nodes. Among them, the inflection point is the slope_dif i The critical point is the node where the connectivity in the ANC curve drops below the lower limit for the first time.

[0053] The link gradient update module is used to calculate the loss function value of the original graph structure after deleting each node according to a preset loss function; and calculate the link gradient of each edge based on the loss function value. When the number of edges in the graph structure changes, the link gradient update module dynamically updates the link gradient of the remaining edges.

[0054] The edge processing module is used to iteratively delete each edge based on the link gradient of each edge in the graph structure, until the number of deleted edges reaches a preset value.

[0055] As a further improvement of the present invention, the working process of the edge processing module is as follows: first, the test statistic ∧(G, G′) of the node degree distribution before and after the edge is deleted is lower than the threshold τ as a preset constraint condition, and the number of edges to be deleted is used as the preset maximum iteration round k max . Secondly, update the loss function value loss corresponding to the graph structure G of the current round, and calculate the link gradient g corresponding to each edge in the graph structure G a Then, according to the negative terms in the link gradient, the corresponding edge e in the graph structure G is i Arrange in ascending order to obtain an edge sequence A. Next, calculate the test statistic τ of the node degree distribution before and after the deletion of each edge in the edge sequence A; and determine whether the test statistic ∧(G, G′) satisfies the constraint condition: if yes, the edge that satisfies the constraint condition and is located at the front item in the edge sequence A is used as the edge deleted in the current round; otherwise, the first item in the edge sequence A is used as the edge deleted in the current round. Finally, after each edge is deleted, the iteration round k is incremented, and then the aforementioned edge deletion steps are repeated until the iteration round k reaches the preset maximum iteration round k max .

[0056] The present invention also includes a protection device for a graph structure of a network, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the graph attack method for suppressing graph disassembly are implemented, and then the graph structure of the original network is subjected to graph attack processing to obtain a new graph structure with enhanced resistance to node disassembly.

[0057] The technical solution provided by the present invention has the following beneficial effects:

[0058] In order to achieve the purpose of enhancing the network's performance in resisting graph disassembly attacks, the present invention preprocesses the graph structure of the network in a graph counterattack manner. The preprocessing process mainly performs the operation of deleting some edges. At the same time, in the processing process of the present invention, constraints are added to make the executed graph attack operations more concealed. At the same time, in order to make the gradient-based graph attack method adaptable to the purpose of graph disassembly, the present invention also specially designs an optimization target based on the degree of confusion of the node disassembly order. Finally, on the basis of satisfying the constraints and optimization targets, the edges of the original graph structure are iteratively deleted. Compared with the original graph structure, the graph structure with some edges deleted has a smaller difference in network performance, but has a stronger performance in resisting node disassembly. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0060] Figure 1 This is a flowchart of the steps of a graph attack method for suppressing graph disassembly provided in Example 1 of the present invention.

[0061] Figure 2 This is a method for drawing the corresponding ANC curve during the removal of each node of the graph structure based on degree value or collective influence in Example 1 of the present invention.

[0062] Figure 3 It is a flowchart of the target node set acquisition process under different disassembly strategies in Example 1 of the present invention.

[0063] Figure 4 This is a flow chart of iteratively deleting edges in a graph structure when performing a graph attack using the method of Embodiment 1 of the present invention.

[0064] Figure 5 In the test experiment of Example 1 of the present invention, when the edge removal rate is set to 0.1, the corresponding connectivity curve when the graph structure enhanced by each group of graph attack methods adopts the HD strategy for graph decomposition.

[0065] Figure 6 In the test experiment of Example 1 of the present invention, when the edge removal rate is set to 0.1, the corresponding connectivity curve when the graph structure enhanced by each group of graph attack methods is decomposed using the CI strategy.

[0066] Figure 7 In the test experiment of Example 1 of the present invention, when the edge removal rate is set to 0.1, the corresponding connectivity curve when the graph structure enhanced by each group of graph attack methods is decomposed using the HDA strategy.

[0067] Figure 8 In the test experiment of Example 1 of the present invention, when the edge removal rate is set to 0.2, the corresponding connectivity curve when the graph structure enhanced by each group of graph attack methods adopts the HD strategy for graph decomposition.

[0068] Fig. 9 In the test experiment of Example 1 of the present invention, when the edge removal rate is set to 0.2, the corresponding connectivity curve when the graph structure enhanced by each group of graph attack methods is decomposed using the CI strategy.

[0069] Fig.10 In the test experiment of Example 1 of the present invention, when the edge removal rate is set to 0.2, the corresponding connectivity curve when the graph structure enhanced by each group of graph attack methods is decomposed using the HDA strategy.

[0070] Fig.11 In the test experiment of Example 1 of the present invention, when the edge removal rate is set to 0.3, the corresponding connectivity curve when the graph structure enhanced by each group of graph attack methods adopts the HD strategy for graph decomposition.

[0071] Fig.12 In the test experiment of Example 1 of the present invention, when the edge removal rate is set to 0.3, the corresponding connectivity curve when the graph structure enhanced by each group of graph attack methods is decomposed using the CI strategy.

[0072] Fig.13 In the test experiment of Example 1 of the present invention, when the edge removal rate is set to 0.3, the corresponding connectivity curve when the HDA strategy is used to decompose the graph structure enhanced by each group of graph attack methods.

[0073] Fig.14 This is a diagram showing the operating principles of a network graph structure protection system provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0075] Example 1

[0076] This embodiment provides a graph attack method for suppressing graph disassembly, which is used to perform graph attack processing on the original graph structure of the network on the basis of satisfying constraint conditions, and obtain an enhanced graph structure by deleting some edges; thereby hiding key information in the original graph structure and improving the network's defense capability against graph disassembly attack behaviors.

[0077] like Figure 1 As shown, the graph attack method provided in this embodiment includes the following steps:

[0078] S1: The network to be processed is represented by a graph structure G, where V represents the set of nodes in the network and E represents the set of edges between nodes in the network. In the original graph structure G = (V, E), V = {v1, v2, ..., v N}, E = {e1, e2, ..., e M}; That is, the graph structure of the network contains N nodes and M edges;

[0079] In particular, the original graph structure G can be converted into the form of an adjacency matrix A, that is: A∈{0,1} |V|×|V| ; The adjacency matrix A can be further converted into a sparse matrix H, that is: H∈{1} |1|×|E| In the sparse matrix H, each element 1 represents that there is an edge between the corresponding nodes of the row-column feature; converting the graph structure G into a sparse matrix can facilitate the deletion of edges in the graph structure G in the subsequent process. Deleting an edge corresponds to changing the element 1 at the corresponding position to 0 in the sparse matrix.

[0080] S2: According to the changes in the connectivity of the remaining nodes after network disassembly, the corresponding ANC curves of the graph structure G are drawn under the two disassembly strategies based on degree value and collective influence.

[0081] like Figure 2 As shown in the figure, in the disassembly strategy based on degree value or collective influence, the ANC curve is drawn as follows:

[0082] S21: Calculate the degree value or collective influence value of each node in the graph structure G, and then sort the nodes in descending order according to the degree value or collective influence value to generate a corresponding node sequence B or B′.

[0083] S22: According to the order of each node in the node sequence B or B′ in the previous step, delete each node in the graph structure G in turn, and calculate the connectivity of the remaining graph structure G′ after deleting one percent of the nodes.

[0084] The calculation formula for the remaining node connectivity is as follows:

[0085]

[0086] In the above formula, connectivy(G\{v1,v2,…,v i} G ) means deleting {v1, v2, …, v i} G The connectivity of the remaining graph structure G′ after all nodes in N GCC (G\{v1, v2, …, v i} G ) means deleting the node set {v1, v2, ..., v i} G The number of nodes contained in the largest part of the interconnected structure in the post-graph; N G Represents the number of nodes in the original graph structure G.

[0087] S23: When all nodes in the graph structure G are disassembled, the corresponding metadata is obtained with the proportion of the number of removed nodes as the horizontal axis and the connectivity of the remaining graph structure G′ after deleting the nodes as the vertical axis. Then, a series of discrete metadata are fitted to draw the corresponding ANC curve.

[0088] S3: Based on the drawn ANC curves, the target node sets V1 and V2 that play a key role in network disassembly in the degree-based and collective influence-based disassembly strategies are determined respectively.

[0089] like Figure 3As shown, the process of obtaining the target node set V1 or V2 is as follows:

[0090] S31: Calculate each node v according to the ANC curve i The first-order derivative approximation corresponding to the metadata of slop i , the calculation formula is as follows:

[0091] slop i =connectivy(G\{v1, v2,…,v i+1} G )-connectivy(G\{v1, v2,…,v i} G ).

[0092] S32: Based on each node v i The corresponding first-order derivative approximation slop i Calculate each node v i The difference of the falling rate of the curve before and after slope_dif i ; The calculation formula is as follows:

[0093] slope_dif i =slop i+1 -slop i ,

[0094] S33: The slope_dif value of the slope rate difference before and after the node in the node sequence B or B′ is calculated. i The node v corresponding to the smallest data i As the left node of the target node set V1 or V2. In this embodiment, the node v is defined as i This is the “inflection point” of the ANC curve.

[0095] S34: The node v in each ANC curve that makes the function value satisfy connectivy<c0 for the first time j As the right node of the target node set V1 or V2; where c0 is the preset lower limit of network connectivity. In this embodiment, the node v is defined j It is the “critical point” of the ANC curve.

[0096] S35: Define the node set {v i , v i+1 , …, v j} G That is, the target node set V1 or V2 that plays a key role in the disassembly.

[0097] S4: Based on the target node sets V1 and V2 of the two disassembly paths, a loss function loss is constructed to evaluate the sequence differences of disassembly nodes in different disassembly strategies. The loss function loss is as follows:

[0098]

[0099] In the above formula, HD G′ and CI G′ They refer to the degree and collective influence of the nodes calculated based on the current graph structure after deleting the edges. i , v i+1 , …, v j} G Represents the key node set corresponding to the degree-based decomposition strategy. j+1 , v j+2 , …, v N} G Includes all nodes sorted after the key node set. Node set V2 = {v i′ , v i′+1 , …, v j′} G represents the key node set corresponding to the disassembly strategy based on collective influence. j′+1 , v j′+２ , …, v N′} G Includes all nodes sorted after the key node set. σ is a preset very small constant.

[0100] S5: Preset the constraints and iteration rounds k of the graph attack process, then use the loss function to calculate the link gradient, and use the link gradient as a guide to iteratively delete the edges that meet the constraints in the original graph structure G, and then obtain the enhanced graph structure G′ after the graph attack;

[0101] like Figure 4 As shown in Figure 2, the iterative deletion process of each edge during graph attack is as follows:

[0102] S51: The test statistic ∧(G,G') of the node degree distribution before and after edge deletion is lower than the threshold τ as a preset constraint condition, that is:

[0103] ∧(G,G')<τ.

[0104] S52: The number of edges to be deleted is used as the preset maximum iteration round k max .

[0105] S53: Update the loss function value loss corresponding to the graph structure G of the current round, and use the following formula to calculate the link gradient g corresponding to each edge in the graph structure G a :

[0106]

[0107] In the above formula, Ha Represents edge e a The corresponding elements in the sparse matrix H are obtained by converting the graph structure G and are used to represent the edges in the network; that is, H∈{1} |1|×|E| .

[0108] It should be emphasized that during the processing, the process of solving the collective influence value (CI) of all nodes is dynamic, which makes it easier to find the link gradient g a The process is difficult to carry out; therefore, in this embodiment, the CI value of each node obtained statically for the first time is approximated to the required CI value of each node to simplify the calculation process.

[0109] S54: According to the link gradient g a The negative terms of the corresponding edge e in the graph structure G i Arrange in ascending order to obtain an edge sequence A.

[0110] S55: Calculate the test statistic ∧(G, G') of the node degree distribution of the graph after each edge in the edge sequence A is deleted and the original graph; and determine whether the test statistic ∧(G, G') satisfies the constraint condition:

[0111] (1) When there is an item that satisfies the constraint, the edge that satisfies the constraint and is located at the front of the edge sequence A is deleted in the current round.

[0112] (2) When the test statistic ∧(G,G') of the node degree distribution formed after deleting any edge in the edge sequence A does not meet the constraint conditions, the first item in the edge sequence A is taken as the edge to be deleted in the current round.

[0113] S56: After deleting each edge, the iteration round k is incremented, and then steps S53-S55 are repeated until the iteration round k reaches the preset maximum iteration round k. max , that is: the number of deleted edges reaches the preset value; at this time, the obtained graph structure is the required enhanced graph structure G′.

[0114] In the embodiment, the lower limit value c0 of connectivity in step S34 is set to 0.02. In step S51, the test statistic threshold τ is set to 0.004.

[0115] In order to achieve the purpose of enhancing the network's performance in resisting graph disassembly attacks, this embodiment pre-processes the graph structure of the network in a graph counter-attack manner. The pre-processing process mainly performs the operation of deleting some edges. At the same time, in the processing process of the present invention, constraints are added to make the executed graph attack operations more concealed. At the same time, in order to make the gradient-based graph attack method adaptable to the purpose of graph disassembly, the present invention also specially designs an optimization goal based on the degree of chaos in the node disassembly order. Finally, on the basis of satisfying the constraints and optimization goals, the edges of the original graph structure are iteratively deleted. Compared with the original graph structure, the graph structure with some edges deleted has a smaller difference in network performance, but has a stronger performance in resisting node disassembly.

[0116] Verification test

[0117] In order to test the feasibility of the graph attack method provided by this embodiment, this embodiment also formulates relevant performance control experiments. In the control experiment, the graph attack method provided by this embodiment is used as the test group, and the random edge reduction method (random) and the attack method of dynamically deleting the edge with the largest product of the degree of the nodes at both ends of the edge (degree mul ) and the attack method of dynamically deleting the edge with the largest product of the collective influence values ​​of the nodes at both ends of the edge (CI mul ) as the control group.

[0118] Each group of graph attack methods is used to enhance the same graph structure. The enhanced graph structure is then disassembled using the HD method, CL method, and HDA (a variant of the HD method, which dynamically deletes nodes based on node degrees) method. The effectiveness of the graph structure enhanced by different graph attack methods in resisting various graph disassembly methods is verified.

[0119] In addition, during the test process of this embodiment, comparisons were made with edge removal ratios of 0.1, 0.2, and 0.3, respectively, to verify the enhancement effects of each method at different edge removal ratios.

[0120] In the performance test, the connectivity curves of the graph structures enhanced by different methods under different graph disassembly strategies are plotted based on the test results. When the ratio of edge deletion is 0.1, the connectivity curves of the enhanced graph structures obtained by the four attack methods and the original graph structure (start) under the three disassembly strategies of HD, CI, and HDA are shown as follows: Figure 5-7 When the ratio of edge deletion is 0.2, the connectivity curves of the enhanced graph structure obtained by the four attack methods and the original graph structure under the three disassembly strategies of HD, CI, and HDA are shown as follows: Figure 8-10When the ratio of deleted edges is 0.3, the connectivity curves of the enhanced graph structure obtained by the four attack methods and the original graph structure under the three disassembly strategies of HD, CI, and HDA are shown as follows: Figure 11-13 shown.

[0121] The corresponding ANC value can be calculated based on the connectivity curve. The ANC value can be used to characterize the defensive performance of the enhanced graph structure against various graph decomposition methods. Figure 5-13 The ANC values ​​of various graph attack methods used in the test experiment for different graph disassembly strategies are shown in Table 1 below:

[0122] Table 1: Statistics of ANC values ​​of graph structures enhanced by different graph attack methods under different graph disassembly strategies:

[0123]

[0124] Analysis of the data in Table 1 shows that: along the horizontal comparison, compared with random, degree mul , CI mul Among the three existing graph attack methods, the graph attack method provided by this embodiment has a higher ANC value under any edge removal ratio (rate) condition. That is, the enhanced graph structure of this embodiment has a better ability to resist graph disassembly than the existing graph attack methods.

[0125] In vertical comparison, when the edge removal ratio is 0.1, the method of this embodiment has the best defense performance against the HD disassembly method, the ability to resist HDA disassembly is second, and the effect of resisting CI disassembly is the worst. When the edge removal ratio is 0.2 or 0.3, the method of this embodiment has the best defense performance against the HD disassembly method, the ability to resist CI disassembly is second, and the effect of resisting HDA disassembly is the worst. It can be seen that the graph attack method provided in this embodiment is particularly suitable for enhancing the defense capability of the graph structure against the HD graph disassembly method.

[0126] Example 2

[0127] On the basis of Example 1, this embodiment further provides a network graph structure protection system, which is used to delete some key edges in the original graph structure of the network to obtain an enhanced graph structure, thereby improving the network's defense capability against node removal graph disassembly. The graph structure protection system uses the graph attack method for suppressing graph disassembly as in Example 1 to perform edge deletion processing on the original graph structure.

[0128] like Fig.14 As shown, the graph structure protection system provided by this embodiment includes a degree calculation module, a collective influence calculation module, an ANC curve generation module, a key node acquisition module, a link gradient update module, and an edge processing module.

[0129] Among them, the degree calculation module is used to calculate the degree value corresponding to each node in the graph structure to be processed; the collective influence calculation module is used to calculate the collective influence value corresponding to each node in the graph structure to be processed.

[0130] The ANC curve generation module includes two independent inputs and outputs, one of which is used to generate a corresponding ANC curve according to the degree value of each node in the graph structure, and the other is used to generate a corresponding ANC curve according to the collective influence value of each node in the graph structure.

[0131] The key node acquisition module is used to obtain the target node set that plays a key role in network disassembly in the graph structure according to the ANC curve. The target node set is the original nodes arranged in descending order according to the degree value or collective influence value, and all the nodes in the sequence corresponding to the inflection point in the ANC curve and between the critical nodes. Among them, the inflection point is the slope_dif i The critical point is the node where the connectivity in the ANC curve drops below the lower limit for the first time.

[0132] The link gradient update module is used to calculate the loss function value of the original graph structure after deleting each node according to a preset loss function; and calculate the link gradient of each edge based on the loss function value. When the number of edges in the graph structure changes, the link gradient update module dynamically updates the link gradient of the remaining edges.

[0133] The edge processing module is used to iteratively delete each edge based on the link gradient of each edge in the graph structure, until the number of deleted edges reaches a preset value.

[0134] Specifically, the working process of the edge processing module is as follows: Figure 4 As shown, the method includes the following steps: first, the test statistic τ of the node degree distribution before and after the edge is deleted is lower than the threshold τ0 as a preset constraint condition, and the number of edges to be deleted is used as the preset maximum iteration round k max . Secondly, update the loss function value loss corresponding to the graph structure G of the current round, and calculate the link gradient g corresponding to each edge in the graph structure G a Then, according to the link gradient g a For each edge e in the graph structure G iArrange in ascending order to obtain an edge sequence A. Next, calculate the test statistic τ of the node degree distribution before and after the deletion of each edge in the edge sequence A; and determine whether the test statistic τ satisfies the constraint condition: if so, the edge that satisfies the constraint condition and is located at the front item in the edge sequence A is used as the edge deleted in the current round; otherwise, the first item in the edge sequence A is used as the edge deleted in the current round. Finally, after each edge is deleted, the iteration round k is incremented, and then the aforementioned edge deletion steps are repeated until the iteration round k reaches the preset maximum iteration round k max .

[0135] Example 3

[0136] On the basis of Example 1, this embodiment further provides a protection device for a graph structure of a network, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the graph attack method for suppressing graph disassembly as described above are implemented, and then the graph structure of the original network is subjected to graph attack processing to obtain a new graph structure with enhanced resistance to node disassembly.

[0137] In the actual deployment of the apparatus, the computer device may be a smart phone, tablet computer, laptop computer, desktop computer, rack server, blade server, tower server or cabinet server (including an independent server or a server cluster composed of multiple servers) that can execute programs. The computer device of this embodiment includes at least but is not limited to: a memory and a processor that can be interconnected through a system bus.

[0138] In this embodiment, the memory (i.e., readable storage medium) includes flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory, etc.), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the memory may be an internal storage unit of a computer device, such as a hard disk or memory of the computer device. In other embodiments, the memory may also be an external storage device of a computer device, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), etc. equipped on the computer device. Of course, the memory may also include both the internal storage unit of the computer device and its external storage device. In this embodiment, the memory is generally used to store an operating system and various application software installed on the computer device. In addition, the memory may also be used to temporarily store various types of data that have been output or are to be output.

[0139] In some embodiments, the processor may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip. The processor is generally used to control the overall operation of a computer device. In this embodiment, the processor is used to run the program code stored in the memory or process data. When the processor executes the computer program, the steps of the graph attack method for suppressing graph disassembly as in Example 1 are implemented, and then the network structure graph G representing the user relationship graph is adjusted to obtain a new graph G′ that meets the constraints and optimization goals; the new graph G′ has a smaller overall functional difference in the network than the original graph structure G, but it does have a stronger ability to resist node disassembly.

[0140] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A graph attack method for suppressing graph disassembly, characterized in that: It is used to perform graph attack processing on the original graph structure of the network on the basis of satisfying the constraint conditions, and obtain an enhanced graph structure by deleting some edges; thereby hiding the key information in the original graph structure and improving the network's defense capability against graph disassembly attacks; The graph attack method comprises the following steps: S1: The network to be processed is represented by a graph structure G, where V represents the set of nodes in the network and E represents the set of edges between nodes in the network; S2: According to the changes in the connectivity of the remaining nodes after network disassembly, the corresponding ANC curves of the graph structure G under the two disassembly strategies based on degree value and collective influence are drawn; S3: Based on the drawn ANC curve, the target node sets V1 and V2 that play a key role in network disassembly in the degree-based and collective influence-based disassembly strategies are determined respectively; S4: Based on the target node sets V1 and V2 of the two disassembly paths, a loss function loss is constructed to evaluate the difference between the disassembly sequences generated by the original graph and the attacked graph under the mixed attack strategy. The loss function loss is as follows: In the above formula, HD G′ and CI G′ They refer to the degree value and collective influence value of the node calculated according to the current graph structure after deleting the edge; the node set V 1＝ {v i ,v i+1 ,…,v j } G Represents the key node set corresponding to the degree-based decomposition strategy; the node set {v j+1 ,v j+2 ,…,v N } G Includes all nodes sorted after the key node set; node set V2 = {v i′ ,v i′+1 ,…,v j′ } G represents the corresponding key node set in the disassembly strategy based on collective influence; the node set {v j′+1 ,v j′+2 ,…,v N′ } G Includes all nodes sorted after the key node set; σ is a preset very small constant; S5: Preset the constraints and iteration rounds k of the graph attack process, then use the loss function to calculate the link gradient, and use the link gradient as a guide to iteratively delete the edges that meet the constraints in the original graph structure G, and then obtain the enhanced graph structure G′ after the graph attack; The iterative deletion process of each edge during graph attack is as follows: S51: The test statistic ∧(G,G′) of the node degree distribution of the graph after edge deletion and the original graph is lower than the threshold τ as a preset constraint condition, that is: ∧(G,G′)<τ; S52: The number of edges to be deleted is used as the preset maximum iteration round k max ; S53: Update the loss function value loss corresponding to the graph structure G of the current round, and use the following formula to calculate the link gradient g corresponding to each edge in the graph structure G a : In the above formula, H a Represents edge e a The corresponding elements in the sparse matrix H are obtained by converting the graph structure G and are used to represent the edges in the network; that is, H∈{1} |1|×|E| ; S54: According to the link gradient g a The negative terms in the graph structure G correspond to the edges e i Arrange in ascending order to obtain an edge sequence A; S55: Calculate the test statistic ∧(G, G′) of the node degree distribution of the graph after each edge in the edge sequence A is deleted and the original graph; and determine whether the test statistic ∧(G, G′) satisfies the constraint condition: (1) When there is an item that satisfies the constraint, the edge that satisfies the constraint and is located at the front of the edge sequence A is deleted in the current round; (2) When the test statistic ∧(G,G′) of the node degree distribution formed after deleting any edge in the edge sequence A does not meet the constraint conditions, the first item in the edge sequence A is taken as the edge to be deleted in the current round; S56: After deleting each edge, the iteration round k is incremented, and then steps S53-S55 are repeated until the iteration round k reaches the preset maximum iteration round k. max ; The graph structure obtained at this time is the required enhanced graph structure G′.

2. The graph attack method for suppressing graph disassembly as claimed in claim 1, characterized in that: In step S1, in the original graph structure G = (V, E), V = {v1, v2, ..., v N }, E={e1,e2,…,e M }; That is, the graph structure of the network contains N nodes and M edges; The original graph structure G can be converted into the form of an adjacency matrix A, that is: A∈{0,1} |V|×|V| ; The adjacency matrix A can be further converted into a sparse matrix H, that is: H∈{1} |1|×|E| .

3. The graph attack method for suppressing graph disassembly as claimed in claim 2, characterized in that: In step S2, in the disassembly strategy based on degree value or collective influence, the method of drawing the ANC curve is as follows: S21: Calculate the degree value or collective influence value of each node in the graph structure G, and then sort the nodes in descending order according to the degree value or collective influence value to generate a corresponding node sequence B or B′; S22: according to the order of each node in the node sequence B or B′ in the previous step, delete each node in the graph structure G in turn, and calculate the connectivity of the remaining graph structure G′ after deleting one percent of the nodes; S23: When all nodes in the graph structure G are disassembled, the corresponding metadata is obtained with the proportion of the number of removed nodes as the horizontal axis and the connectivity of the remaining graph structure G′ after deleting the nodes as the vertical axis. Then, a series of discrete metadata are fitted to draw the corresponding ANC curve.

4. The graph attack method for suppressing graph disassembly as claimed in claim 2, characterized in that: In step S22, the calculation formula of the remaining node connectivity is as follows: In the above formula, connectivy(G\{v1,v2,…,v i } G ) means deleting {v1, v2, …, v i } G The connectivity of the remaining graph structure G′ after all nodes in N GCC (G\{v1, v2, …, v i } G ) means deleting the node set {v1, v2, ..., v i } G The number of nodes contained in the largest part of the interconnected structure in the post-graph; N G Represents the number of nodes in the original graph structure G.

5. The graph attack method for suppressing graph disassembly as claimed in claim 4, characterized in that: In step S3, the process of obtaining the target node set V1 or V2 is as follows: S31: Calculate each node v according to the ANC curve i The first-order derivative approximation corresponding to the metadata of slop i , the calculation formula is as follows: slop i =connectivy(G\{v1,v2,…,v i+1 } G )-connectivy(G\{v1,v2,…,v i } G ) S32: Based on each node v i The corresponding first-order derivative approximation slop i Calculate each node v i The difference of the curve drop rate before and after slope_dif i ; The calculation formula is as follows: slope_dif i =slop i+1 -slop i , S33: The slope_dif value of the slope rate difference before and after the node in the node sequence B or B′ is calculated. i The node v corresponding to the smallest data i As the left node of the target node set V1 or V2; S34: The node v in each ANC curve that makes the function value satisfy connectivy<c0 for the first time j As the right node of the target node set V1 or V2; Wherein, c0 is the preset lower limit of network connectivity; S35: Define the node set {v i , v i+1 , …, v j } is the target node set V1 or V2 that plays a key role in disassembly.

6. The graph attack method for suppressing graph disassembly as claimed in claim 5, characterized in that: In step S34, the connectivity lower limit value c0 is set to 0.

02.

7. The graph attack method for suppressing graph disassembly as claimed in claim 1, characterized in that: In step S51, the test statistic threshold τ is set to 0.

004.

8. A network graph structure protection system, which is used to delete some key edges in the original graph structure of the network to obtain an enhanced graph structure; thereby improving the network's defense capability against node removal graph disassembly; characterized in that: The graph structure protection system uses the graph attack method for suppressing graph disassembly as described in any one of claims 1 to 7 to perform edge deletion processing on the original graph structure; the graph structure protection system includes: A degree calculation module, which is used to calculate the degree value corresponding to each node in the graph structure to be processed; A collective influence calculation module, which is used to calculate the collective influence value corresponding to each node in the graph structure to be processed; An ANC curve generation module includes two independent inputs and outputs, one of which is used to generate a corresponding ANC curve according to the degree value of each node in the graph structure, and the other is used to generate a corresponding ANC curve according to the collective influence value of each node in the graph structure; The key node acquisition module is used to obtain the target node set that plays a key role in network disassembly in the graph structure according to the ANC curve; the target node set is the "inflection point" in the ANC curve and all the nodes between the critical nodes in the sequence after the original nodes are arranged in descending order according to the degree value or collective influence value; wherein the "inflection point" is the slope_difference on the ANC curve. i The node corresponding to the minimum point, the critical node is the node where the connectivity in the ANC curve drops below the lower limit for the first time; A link gradient update module, which is used to calculate the loss function value of the original graph structure after deleting each node according to a preset loss function; and calculate the link gradient of each edge based on the loss function value; when the number of edges in the graph structure changes, the link gradient update module dynamically updates the link gradient of the remaining edges; The edge processing module is used to iteratively delete each edge based on the link gradient of each edge in the graph structure, until the number of deleted edges reaches a preset value.

9. The network graph structure protection system according to claim 8, characterized in that: The working process of the edge processing module is as follows: First, the test statistic ∧(G,G′) of the node degree distribution before and after the edge is deleted is lower than the threshold τ as a preset constraint condition, and the number of edges to be deleted is used as the preset maximum iteration round k max ; Secondly, update the loss function value loss corresponding to the graph structure G of the current round, and calculate the link gradient g corresponding to each edge in the graph structure G a :Then, according to the link gradient g a The negative terms in the graph structure G correspond to the edge e i Arrange them in ascending order to obtain an edge sequence A; then, calculate the test statistic ∧(G,G′) of the node degree distribution before and after the deletion of each edge in the edge sequence A; and determine whether the test statistic ∧(G,G′) satisfies the constraint condition: if so, the edge that satisfies the constraint condition and is located at the front item in the edge sequence A is used as the edge deleted in the current round; otherwise, the first item in the edge sequence A is used as the edge deleted in the current round; finally, after each edge is deleted, the iteration round k is incremented, and then the aforementioned edge deletion steps are repeated until the iteration round k reaches the preset maximum iteration round k max .

10. A protection device for a graph structure of a network, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the graph attack method for suppressing graph disassembly are implemented as described in any one of claims 1 to 7, and then the graph structure of the original network is subjected to graph attack processing to obtain a new graph structure with enhanced resistance to node disassembly.

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