Complex structure-oriented network node importance dynamic evaluation method

Abstract

The invention discloses a complex structure-oriented network node importance degree dynamic evaluation method, relates to the technical field of dynamic node identification analysis methods, and particularly aims to overcome the defect that the existing KPDN method cannot completely cover important node identification in a dynamic environment in the background technology. The improved network constraint coefficient INCC is introduced, the defect of the KPDN method in the aspect of complex network dynamic important node identification is made up, the network structural measurement can be well kept in the dynamic node deletion process, the structural importance of the node in the remaining network can be effectively judged, and the dynamic network dynamic important node identification method has the advantages of high reliability and high reliability. And particularly, the method has a better recognition effect on a small-world network with a smaller random connectivity probability.

Description

Technical Field

[0001] The present invention belongs to the technical field of dynamic node identification and analysis methods and apparatuses, and in particular relates to a method for dynamically evaluating the importance of network nodes with complex structures. Background Art

[0002] For a networked target system, its network structure will change dynamically as the attack progresses. Therefore, the importance ranking of nodes in the network will also change at different attack stages and times. A single wave attack based on the static attack assumption is more suitable for saturated attack conditions with abundant resources. In a complex actual combat environment, attack resources are often constrained, and tasks need to be implemented in stages. Therefore, it is of practical significance to dynamically monitor the target network and evaluate and identify the timing changes of important nodes. It is also of great significance to realize the intelligence and dynamic nature of the system's attack and defense.

[0003] At present, there are two main directions for the research on important node identification based on dynamic complex networks: one is to use time series analysis to predict the dynamic changes of network topology based on edges. For example, Shi Yujing et al. used time synchronization control to prove that the dynamic network error system is stable in finite time. The second is to directly identify the important nodes that play a key role in the dynamic network. Since link prediction has been studied in depth, this paper intends to focus on the research on the identification of important nodes in dynamic networks.

[0004] At present, the research on identifying important nodes in the network is mainly focused on static networks. Various types of centrality such as degree centrality, closeness centrality, betweenness centrality indicators and their fusion methods are more suitable for stable topological structures in real physical environments. When the network structure changes dynamically, the difficulty of identifying key nodes increases greatly, especially in the fields of network protocols and network security. In response to this challenge, scholars have carried out some attempts. Fu Kai's team integrates multiple centrality indicators to improve recognition efficiency. Shao Hao's team uses local neighborhood priority asynchronous H operation to speed up convergence. Ruan Yirun's team constructs a two-step neighborhood model to evaluate node importance, which can be applied to large-scale dynamic networks. There is also dynamic network analysis based on heterogeneous nodes. In response to the problems existing in the current link prediction research, Tan Shiyin and others conducted research on link prediction algorithms on dynamic networks and heterogeneous networks, respectively, and constructed a model that can accurately predict network edge relationships; Zhao Danling and others proposed a combat ring-based weapon equipment system capability contribution rate evaluation method for combat missions and a system simulation-based weapon equipment system effectiveness contribution rate evaluation method for combat processes;

[0005] The problems with the above existing methods are as follows: (1) There are currently more studies on methods for identifying important nodes in static networks, but fewer on methods for identifying important nodes in dynamic networks; (2) Some methods have good global and local characteristics in the static network analysis process, but as network nodes are continuously deleted, the re-analysis of the remaining network may not still have good analysis results; (3) Some algorithms work better for networks that tend to be random in small-world networks, but cannot provide better resolution for networks with less randomness.

[0006] Therefore, it is urgent to design a dynamic evaluation method for the importance of network nodes with complex structures to solve the above problems. Summary of the invention

[0007] In view of the characteristics of structural changes of complex networks when they are attacked, the present invention provides a dynamic evaluation method for the importance of network nodes in complex structures. The method comprehensively considers the defect that the existing KPDN method cannot completely cover the identification of important nodes in a dynamic environment, and combines with the improved network constraint coefficient (INCC) to make up for the shortcomings of the KPDN method in the identification of dynamic important nodes in complex networks, especially for small-world networks with a small probability of random connectivity.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0009] A method for dynamically evaluating the importance of network nodes with complex structures: the steps include:

[0010] S1. Based on the degree of each node in the complex network, all nodes are sorted according to their degrees, and the nodes with fixed degrees and their edges are deleted according to the sorting results to obtain the k-shell layer corresponding to the node Ks value.

[0011] Among them, after deleting nodes with fixed degrees and their edges each time, the remaining network is obtained;

[0012] S2. In the process of deleting fixed degree nodes to obtain k-shell, nodes with different degree values ​​in the same deletion order are formed into a set, and the nodes in the set are sorted according to their degree value proportion KPD i Perform secondary sorting;

[0013] S3. Based on the order of the second sorting, the relationship value S between the adjacent nodes of each node is calculated ij , and according to the relationship value S ij Perform three sortings;

[0014] S4. Based on the residual network in step S1, the INCC factor is used to capture the indirect impact factor INCC of the residual network on the nearest neighbor and the next nearest neighbor of each node i, and sort four times;

[0015] S5. KPD obtained based on the second sorting i , S obtained by the third sorting ij And the INCC obtained from the fourth sorting i Get the KPDN-INCC value and perform final sorting based on the KPDN-INCC value.

[0016] Preferably, in step S1, the process of obtaining the k-shell layer corresponding to the node Ks value includes:

[0017] S101. Based on the degree of each node in the complex network, all nodes are sorted according to their degrees;

[0018] S102. Delete nodes with degrees 1...n and their edges from the complex network in sequence to obtain a k-shell layer corresponding to the node Ks value;

[0019] When nodes of multiple k-shell layers are peeled off in sequence, the peeling order, layer number, and sequence number of the corresponding nodes are recorded simultaneously.

[0020] Preferably, in step S2, the node degree value ratio calculation formula is:

[0021]

[0022] Among them, ks i is the k-shell value of node i, k i is the degree of node i, k N(i)max is the maximum degree of the neighboring nodes of node i, l i For node i in the same ks i The order in which the shell is stripped under iterative stripping operation, l max For the same ks i The maximum number of peeling sequences under the layer; ks i|next are the adjacent nodes of node i.

[0023] Preferably, in step S3, the relationship value between adjacent nodes is calculated using the following formula:

[0024]

[0025] Where N(i)∩N(j) is the number of neighbor nodes shared by nodes i and j, and k i represents the degree value of node i, k j Represents the degree value of node j.

[0026] Preferably, in step S4, the INCC formula is as follows:

[0027]

[0028] in And Q j is the sum of the first-order neighbor degrees of node j, LR i is the sum of the second-order neighbor node degrees of node i; N w is the sum of the degree values ​​of the neighboring nodes of node j, Γ(j) represents the neighboring node set of node j, Γ(i) represents the neighboring node set of node i, INCC i refers to the structural hole factor, p′ ij Refers to the ratio of Q and LR, p' ik Refers to the ratio of Q and LR, p' kj It refers to the ratio of Q to LR, which is three, where n and k are natural numbers.

[0029] Preferably, in step S5, the formula of KPDN-INCC is as follows:

[0030]

[0031] Among them, N(i) refers to the first-order neighbor nodes of node i; k i Refers to the degree value of node i, KPD j Refers to the calculated kpd value of node i.

[0032] The second object of the present invention is to provide a complex structure-oriented network node importance dynamic evaluation system, characterized in that it includes:

[0033] The k-shell layer acquisition module sorts all nodes according to their degrees based on the degree of each node in the complex network, and deletes the nodes with fixed degrees and their edges according to the sorting results to obtain the k-shell layer corresponding to the node Ks value; each time the nodes with fixed degrees and their edges are deleted, the remaining network is obtained;

[0034] Sorting module 1: In the process of deleting fixed degree value nodes to obtain k-shell, nodes with different degree values ​​in the same deletion order are formed into a set, and the nodes in the set are sorted according to their degree value proportion KPD i Perform secondary sorting;

[0035] Sorting module 2, based on the order of the second sorting, calculates the relationship value S between the adjacent nodes of each node ij , and according to the relationship value S ij Perform three sortings;

[0036] Sorting module three, based on the residual network in step S1, uses the INCC factor to capture the indirect impact factor INCC of the residual network on the nearest neighbor and the next nearest neighbor of each nodei , and sort four times;

[0037] Node importance acquisition module, based on the KPD obtained from the second sorting i , S obtained by the third sorting ij And the INCC obtained from the fourth sorting i Get the KPDN-INCC value and perform final sorting based on the KPDN-INCC value.

[0038] The second object of the present invention is to provide a non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to enable the computer to execute a method for dynamically evaluating the importance of network nodes with complex structures.

[0039] The second object of the present invention is to provide an electronic device, comprising:

[0040] At least one processor and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can perform a method for dynamically evaluating the importance of network nodes with complex structures.

[0041] The beneficial effects of the present invention are as follows: the present invention discloses a complex network dynamic important node identification and analysis method based on the KPDN method. Compared with the prior art, the improvements of the present invention are as follows:

[0042] The invention proposes a dynamic evaluation method for the importance of network nodes facing complex structures, namely, a KPDN-INCC method (A K-Shell methods positioned with Degrees, Neighbors and INCC.), which comprehensively considers global and local characteristics, applies the K-shell method to stratify in the global range, and records the separation order in each K-shell stratification process as the basis for secondary sorting; then, the association relationship between the node and its adjacent nodes is judged according to the Solton index of each node, and the third sorting is performed; finally, based on the change of the remaining network after each node deletion operation, the INCC factor is introduced, and the fourth sorting is performed to distinguish the importance of dynamic nodes. Since the KPDN-INCC method does not contain free parameters, and the information of adjacent nodes can be recorded simultaneously when traversing and running each node degree value, most calculations are based on the operation between the node and its own neighbors, and the improved k-shell method also follows the record in the k-shell expansion process, so it has a lower calculation complexity; at the same time, due to the introduction of the INCC factor, the network structural measurement can be better maintained in the dynamic node deletion process, so the structural importance of the node in the remaining network can be effectively judged. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flowchart of the KPDN-INCC method of the present invention;

[0044] Figure 2 This is a flow chart of the KPDN-INCC method of the present invention;

[0045] Figure 3 This is a calculation example of the KPDN-INCC method of the present invention;

[0046] Figure 4 Comparison of static and dynamic important node identification results of the six methods of the present invention;

[0047] Figure 5 The network connectivity relationship of various nodes of the present invention;

[0048] Figure 6 The network structure actually generated by the present invention;

[0049] Figure 7 Comparison of subnet connectivity coefficients of the real network of the present invention;

[0050] Figure 8 Comparison of the remaining edge scales of subnets in the real network of the present invention;

[0051] Fig. 9 Comparison of subnet sensitivity of the real network of the present invention;

[0052] Fig.10 The maximum connected subgraph of the small-world network of the present invention under different attack strategies;

[0053] Fig.11 It is the maximum remaining edge graph of the small-world network of the present invention under different attack strategies;

[0054] Fig.12 It is a subnet sensitivity graph of the small-world network of the present invention under different attack strategies;

[0055] Fig.13 This is a comparative analysis of important nodes based on parameter 0 function chain of the present invention;

[0056] Fig.14 This is a comparative analysis of important nodes of the function chain based on parameter 1 of the present invention;

[0057] Fig.15 This is a comparative analysis of important nodes of the parameter 2 function chain of the present invention;

[0058] Fig.16 This is a comparative analysis of the important nodes of the parameter 3 function chain of the present invention;

[0059] Fig.17 This is a comparative analysis of the important nodes of the parameter 4 function chain of the present invention;

[0060] Fig.18 This is a comparative analysis of the important nodes of the parameter 5 function chain of the present invention;

[0061] Fig.19 This is a comparative analysis of the reduction in the number of function chains under 6 types of network attacks using the KPDNINCC method in the present invention;

[0062] Fig. 20 This is a comparative analysis of the reduction in the proportion of functional chains under six types of network attacks using the KPDNINCC method in the present invention;

[0063] Among them, Figure 6 In the figure, green represents class A nodes, orange represents class B nodes, blue represents class C nodes, and purple represents class D nodes. DETAILED DESCRIPTION

[0064] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0065] Embodiment 1:

[0066] Refer to the attached Figure 1-2 A method for dynamically evaluating the importance of network nodes with complex structures is shown, and the specific steps include:

[0067] S1. Based on the degree of each node in the complex network, all nodes are sorted according to their degrees, and the nodes with fixed degrees and their edges are deleted according to the sorting results to obtain the k-shell layer corresponding to the node Ks value. After deleting the nodes with fixed degrees and their edges each time, the remaining network is obtained. The specific process includes:

[0068] S101. Based on the degree of each node in the complex network, all nodes are sorted according to their degrees;

[0069] Assume that there is no isolated node with degree 0 in the complex network, determine the degree of each node, that is, the number of edges directly connected to the node; sort all nodes according to their degree, starting from the node with the highest degree.

[0070] S102. Delete nodes with degrees 1...n and their edges from the complex network in sequence to obtain the k-shell layer corresponding to the node Ks value; when the nodes of multiple k-shell layers are peeled off in sequence, the order, number of layers, and sequence number of the corresponding nodes are simultaneously recorded as the basis for the second sorting.

[0071] From the perspective of degree index, nodes with degree 1 are the least important nodes in a complex network. Therefore, the nodes with degree 1 and their edges are first deleted from the complex network. After the deletion operation, new nodes with degree 1 will appear in the complex network. Then delete these newly appeared nodes with degree 1 and their edges, and repeat the above operation until no new nodes with degree 1 appear in the complex network. At this time, all deleted nodes constitute the first layer, that is, the Ks value of the nodes in this layer of 1-shell is equal to 1, and the degree of each node in the remaining complex network is at least 2. Continue to repeat the above deletion operation to obtain the second layer with a Ks value of 2, that is, 2-shell, and so on, until all nodes in the network are assigned Ks values ​​and the k-shell layer corresponding to the Ks value.

[0072] S2. In the process of deleting fixed degree value nodes to obtain k-shell, nodes with different degree values ​​in the same deletion order are formed into a set, and the nodes in the set are sorted twice according to their degree value proportions, i.e., the second sorting; specifically, in the process of obtaining multiple k-shell layer peeling, the node peeling order of each k-shell layer is recorded, the nodes with the same peeling order are recorded and formed into a node collection, and then the nodes in the set are sorted twice according to their degree value proportions;

[0073] The calculation formula for the node degree ratio is:

[0074]

[0075] Among them, ks i is the k-shell value of node i, k i is the degree of node i, k N(i)max is the maximum degree of the neighboring nodes of node i, l i For node i in the same ks i The order in which the shell is stripped under iterative stripping operation, l max For the same ks i The maximum number of peeling sequences under the layer; ks i|next is the neighboring node of node i, especially to avoid the maximum ks i The layer cannot participate in the calculation. When the node is in the maximum k-shell layer, the ks i|next -ks i The value is set to 1.

[0076] S3. Based on the order of the second sorting, the relationship value (Solton index) between the adjacent nodes of each node is calculated, and three sortings are performed according to the relationship value, that is, the third sorting is completed; the relationship value calculation formula between adjacent nodes is:

[0077]

[0078] Where N(i)∩N(j) is the number of common neighbor nodes between nodes i and j. This value directly reflects the degree of direct connection between the two nodes in the network. The more common neighbors there are, the closer the connection between the nodes is. i represents the degree of node i, that is, the number of neighbors directly connected to node i, k j Represents the degree value of node j.

[0079] S4. Calculate the structural hole index of the entire network when the node is dynamically deleted. The hole index is an indicator for judging the structural stability in a complex network. Specifically, based on the residual network in step S1, the INCC factor is used to capture the indirect impact factor INCC of the residual network on the nearest neighbor and the next nearest neighbor of each node. i , and sorted four times; , thereby distinguishing the importance of dynamic nodes in the remaining network.

[0080] The INCC factor calculation formula is as follows:

[0081]

[0082] in And Q j is the sum of the first-order neighbor degrees of node j, LR i is the sum of the second-order neighbor node degrees of node i; N wis the sum of the degree values ​​of the neighboring nodes of node j, Γ(j) represents the neighboring node set of node j, Γ(i) represents the neighboring node set of node i, INCC i refers to the structural hole factor, p′ ij Refers to the ratio of Q and LR, p' ik Refers to the ratio of Q and LR, p' kj It refers to the ratio of Q to LR, n and k are natural numbers not equal to 0;

[0083] S5. KPD obtained based on the second sorting i , S obtained by the third sorting ij And the INCC obtained from the fourth sorting i , we get KPDN-INCC, whose formula is as follows:

[0084]

[0085] Among them, N(i) refers to the first-order neighbor nodes of node i, k i Refers to the degree value of node i, KPD j Refers to the calculated value of kpd of node i;

[0086] The ranking result of KPDN-INCC is the final important node identification result.

[0087] The present invention also provides a complex structure-oriented network node importance dynamic evaluation system, comprising:

[0088] The k-shell layer acquisition module sorts all nodes according to their degrees based on the degree of each node in the complex network, and deletes the nodes with fixed degrees and their edges according to the sorting results to obtain the k-shell layer corresponding to the node Ks value; each time the nodes with fixed degrees and their edges are deleted, the remaining network is obtained;

[0089] Sorting module 1: In the process of deleting fixed degree value nodes to obtain k-shell, nodes with different degree values ​​in the same deletion order are formed into a set, and the nodes in the set are sorted according to their degree value proportion KPD i Perform secondary sorting;

[0090] Sorting module 2, based on the order of the second sorting, calculates the relationship value S between the adjacent nodes of each node ij , and according to the relationship value S ij Perform three sortings;

[0091] Sorting module three, based on the residual network in step S1, uses the INCC factor to capture the indirect impact factor INCC of the residual network on the nearest neighbor and the next nearest neighbor of each node i , and sort four times;

[0092] Node importance acquisition module, based on the KPD obtained from the second sorting i , S obtained by the third sorting ij And the INCC obtained from the fourth sorting i Get the KPDN-INCC value and perform final sorting based on the KPDN-INCC value.

[0093] The present invention also provides a non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to enable the computer to execute a method for dynamically evaluating the importance of network nodes with complex structures.

[0094] The present invention also provides an electronic device, comprising: at least one processor, and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute a dynamic evaluation method for the importance of network nodes with complex structures.

[0095] Embodiment 2:

[0096] Example 2 is a simulation experiment using the method of Example 1, and the specific process is as follows:

[0097] 1. Collect different network data;

[0098] The following seven networks are selected for the experiment: Facebook_1912, Aves-wildbird-network, US-airports, Soc-hamsterster, Fb-pages-tvshow, P2p-Gnutella08 and Fb-pages-government. The detailed information is shown in Table 3.

[0099] Table 3 Specific parameters of real networks with scale 10^3-10^4

[0100]

[0101] These seven datasets depict complex networks in different fields, as follows: The Facebook_1912 dataset describes a movie topic subscription social network on Facebook, where nodes represent users and edges represent friend relationships. The Aves-wildbird-network dataset depicts the food web of North American wild birds, where nodes represent birds and edges represent food chain relationships. The US-airports dataset shows the route network between airports in the United States, where nodes are airports and edges are routes. The Soc-hamsterster dataset is a user social network of the Hamsterster website. The Fb-pages-tvshow dataset gives the network of TV program pages on Facebook, where nodes are TV program pages and edges are hyperlinks between pages. The P2p-Gnutella08 dataset describes the topological structure of the Gnutella peer-to-peer file sharing network, where nodes are hosts and edges are connections between hosts. The Fb-pages-government dataset constructs a network of government agency pages on Facebook, where nodes are government pages and edges are links between pages. These seven network datasets cover social, biological, and technical fields and can be used for complex network analysis and model research.

[0102] Furthermore, in order to verify the extensibility of the proposed method, combined with the actual force composition of a certain unit, an unweighted and undirected heterogeneous network with four types of nodes of similar structure was designed. The four types of nodes are A, B, C, and D as shown in Table 4. Among them, the probability of A-type nodes is 20% to interconnect with each other, the probability of B-type nodes is 25%, the probability of C-type nodes is 5%, and the probability of D-type nodes is 25%; at the same time, the probability of A-type nodes is 15% to interconnect with B-type nodes, and the probability of C-type nodes is 5%, the probability of BC nodes is 15%, and the probability of D nodes is 15% to interconnect with A-type nodes and C-type nodes, respectively. The total number of nodes is 60, and the total number of edges is 80;

[0103] Table 4 Relationships between various nodes in heterogeneous networks

[0104]

[0105]

[0106] The network connectivity relationship of various nodes is roughly as follows Figure 5 As shown, the actual generated network structure is as follows Figure 6As shown. At the same time, 8 function chains are defined, namely ABC, AABC, ABBC, ABCC, AABBC, AABCC, ABBCC, and ABCD, to express 8 types of actual functions in real scenarios. The function chain here is a generalized function chain, which does not consider the order of nodes, but only considers whether different functions are connected. For example, the ABC chain is the same as the BCA chain.

[0107] From the perspective of the overall network configuration, there are random connections between nodes of the same type and relatively regular connections between nodes of different types. Therefore, the overall network structure also belongs to a small-world network. In terms of attack methods, the focus is on comparing the number of remaining functional chains after different attacks, and giving different heterogeneous network optimization model suggestions.

[0108] 2. Experimental results analysis

[0109] In this experiment, the experimental results of the above 7 real network data sets, 1 artificial small-world network data set and a heterogeneous network data set under six parameters are used as examples to verify the performance of the algorithm proposed in the present invention compared with other 8 types of classical algorithms and a random algorithm. The important identification process of dynamic network nodes, especially the accuracy of the evaluation results of homogeneous networks, and the effectiveness of the results of the heterogeneous network carrying function chain capability are verified. Finally, the scope of use suitable for artificial small-world networks is given.

[0110] 2.1 Analysis of results using real network datasets

[0111] The performance of the proposed method and other existing methods in the above 7 real network data sets is compared, focusing on the node recognition effect in a dynamic environment. Figure 6 (a)-(g) in the figure are the recognition results of the above 7 real network datasets, among which (a) Facebook_1912,

[0112] (b)Aves-wildbird-network, (c)US-airports, (d)Soc-hamsterster, (e)Fb-pages-tvsho, (f)P2p-Gnutella08, (g)Fb-pages-government; Figure 5 The robustness of the network after gradually removing nodes is studied. Figure 7 Figures (a) and (b) show that the method of the present invention is very effective in dynamic node identification. Figure 7(c) to (g) are comparisons between the method of the present invention and the KPDN method. The results show that the KPDN method can attack vulnerable nodes more quickly in the early stage, causing the network to be rapidly eroded. However, these nodes found in the early stage are relatively easy to attack, and the effect will decrease in the later stage. Therefore, when attacking dynamic important nodes, the KPDN method is more suitable for scenarios that require rapid disintegration of half the scale of the network. Although the KPDN-INCC method is slightly slower in the early stage, it can achieve a devastating effect with the least node removal steps as a whole. It is more suitable for applications that require rapid and complete destruction of the network. After all, any form of attack is generally a consumption of resources. Even the speed of network attacks is a very important constraint. Different strategies need to be used in different network environments and attack requirements to maximize the effect.

[0113] In order to better evaluate the comparison results of the models, we not only make an intuitive comparison of the maximum connected subgraph size of the remaining subgraphs, but also introduce a subgraph sensitivity index to supplement it. Figure 8 It can be observed from (a) to (g) that the method of the present invention has a significant effect on the change of the subgraph edge residual rate index. Of course, this index is the best under the dynamic attack strategy, so this index does not have an absolute advantage overall. However, it can be seen from the figure that even if it is not the optimal residual edge attack strategy, it can still maintain a relatively fast residual edge strategy when the maximum connected subgraph of the network is quickly reduced;

[0114] The threshold set in the experiment is 100% of the original network size. When the sensitivity index reaches a peak after removing a certain proportion of nodes, it means that each method has disassembled the original network into fragments below the threshold size to the maximum extent. Then, as the fragments are further reduced, the sensitivity enters a downward phase. As can be seen from the figure, for Fig. 9 (b) Of course, this indicator works best under the dynamic attack strategy. Therefore, this indicator does not have an absolute advantage overall, but it can be seen from the figure that even if it is not the optimal residual edge attack strategy, it can still maintain a relatively fast residual edge strategy when the maximum connected subgraph of the network is quickly reduced.

[0115] Here we also remind you that the fastest result of the largest connected subgraph of a network attack may be a trade-off among other indicators. The fastest way to obtain the largest connected subgraph may not necessarily be to attack the node with the largest degree. The specific attack requirements should also be selected according to the actual situation.

[0116] 2.2 Analysis of results using the small-world network dataset

[0117] At the same time, the network with small-world effect is also compared. The network with small-world effect consists of three parts, namely the number of nodes, the average degree of each node, and the average random connectivity probability of the network. The number of nodes and the average degree of nodes affect the speed at which all methods appear the rapid collapse turning point, which is reflected in the image that the main body of the image change is biased towards the lower right or upper left. Figures (a) to (i) represent small-world networks under the conditions of the same number of nodes, the same average degree of nodes, and different average random connectivity probabilities of the network. The random connectivity probabilities are (a) 10%, (b) 20%, (c) 30%, (d) 40%, (e) 50%, (f) 60%, (g) 70%, (h) 80%, and (i) 90%. The results are shown in Figure 10-12 shown.

[0118] like Fig.10 As shown in the figure, as the probability of random connectivity increases in the small-world network, the small-world network gradually transitions from a regular network to a random network. From Figures (a) to (d), it can be seen that the KPDN-INCC method has an obvious effect in the attack on the maximum connected subgraph; at the same time, from Figures (e) to (i), there are also certain gratifying results. The KPD method as an intermediate calculation parameter can also slightly supplement the effect of the KPDN method that cannot completely destroy the coverage attack when the random connectivity probability is greater than 40%.

[0119] like Fig.11 As shown in the figure, as the probability of random connectivity increases in the small-world network, the small-world network gradually transitions from a regular network to a random network. From Figures (a) to (i), it can be seen that the KPDN-INCC method also performs well in the maximum residual edge indicator.

[0120] Fig.12 This is the subnet sensitivity graph of the small-world network. From it, we can see that for the highest point of the image of each method, it can be clearly seen that the KPDN and KPDN-INCC methods have more obvious results. From the figure, we can see that the KPDN-INCC method and the KPDN method are more efficient in removing network nodes. (The highest point of the subnet sensitivity represents the maximum disruption of the network by the attack method, and the horizontal axis represents the proportion of nodes that need to be attacked or removed during the disruption. Therefore, when the highest point is reached, the smaller the corresponding horizontal axis value, the faster the network disintegrates and the better the effect.) It can be clearly seen in the figure that the KPDN-INCC method can quickly disintegrate the network with the small-world effect.

[0121] In general, if the goal is to completely destroy the complex network, the dynamic KPDN-INCC method is preferred. In actual attacks, it is necessary to select and combine different attack strategies based on the judgment of the network topology and the purpose of the attack to maximize the attack effect. Figure 13-20(a)-(h) correspond to the results of 8 functional chains respectively, (a) is ABC chain, (b) is AABC chain, (c) is ABBC chain, (d) is ABCC chain, (e) is AABBC chain, (f) is AABCC chain, (g) is ABBCC chain, and (h) is ABCD chain.

[0122] (1) Analysis of the results of applying heterogeneous networks

[0123] from Figures 13 to 18 The results show that in the experiment of attacking the function chain nodes in heterogeneous networks, the depth-first strategy (DFS) was used to traverse the key nodes carrying more function chains. PageRank, degree, HC and the KPDNINCC method proposed in this paper were also compared. The results show that the proposed method Fig.13 , 15 The performance of 1 to 18 is better. Therefore, for this experiment, the dynamic attack based on network structure is better than the attack based on function chain analysis in most cases.

[0124] pass Fig.19 and 20 It can be seen from the results that when the probability that the number of edges contained in the network structure and the number of edges in the functional chain account for the total number of edges in the network is similar, the KPDN-INCC method proposed in this patent is more applicable. Because the network is constructed based on the probability of edge connection, different networks may have different preferences for functional chains. However, when the probability of edges involved in the functional chain is similar to the probability of main edges in the network, this indicates that the degree of matching between the internal structure of the network and the structure of the functional chain is related. The more consistent the distribution of edges between the two, the more obvious the destructive effect of the key nodes identified by the KPDN-INCC method proposed in this patent on the functional chain. This also provides a way of thinking for further optimization, that is, when determining the functional chain, the internal structure of the network should be considered and links that match the network structure should be selected.

[0125] Embodiment 3:

[0126] Example 2 compares the method of Example 1 with the classic algorithm and the better dynamic node evaluation method in recent years. The comparison results show that the method of the present invention has better performance;

[0127] A randomly generated demo example Figure 3 , KPD method, KPDN method, Degree method, K-shell method and KPDN-INCC method of the present invention are selected, and numerical calculations are performed according to the corresponding formulas, and the results are shown in Table 1;

[0128] Table 1 Calculation results of different methods for demonstration cases

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[0131] From the data in Table 1, we can see that the KPD method is based on a certain improvement of the K-shel method, and the node differentiation is significantly improved; the most influential node of the KPDN method is node 207; the best node of the Degree method is node 7; the K-shell method is not so effective in this case, and a large number of nodes are at the same higher level of Ks=5, which is not conducive to the final identification of the importance of high-order nodes; the most influential node identified by the INCC method is node 203; and the most influential node proposed by the KPDN-INCC method proposed by the invention is node 5. INCC method, improved network constraint coefficient, here the INCC method proposes that the optimal node is node 203, and the number of triangles formed by node 203 can be counted as: Δ 203,204,7 , Δ 203,204,200 , Δ 203,204,6 , Δ 203,204,202 , Δ 203,204,201 , Δ 203,7,200 , Δ 203,200,206 , Δ 203,200,201 , Δ 203,6,202 , Δ 203,6,201 , a total of 10 triangles, so this method can better identify the number of adjacent triangles involved in each node in the original network. Of course, Table 1 is the result diagram used only once. The subsequent process re-evaluates the existing network at each step, and finally collects the first value in each evaluation. The dynamic attack node order table obtained by multiple dynamic attacks, the results of various methods are shown in Table 2. In order to have a more intuitive display of the final dynamic attack effect, the remaining network status after attacking 13 nodes under various methods is displayed, as shown in Figure 4 shown.

[0132] Table 2 Figure 2 Demonstration network dynamic important node sorting results

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[0135] Since nodes 301, 303, and 304 did not participate in the overall connection of the network in the initial state of the network, and the results of each method in the final dynamic node ranking were still 0, it means that the importance of these three nodes is too low. Therefore, they were not included in the ranking process of each method in Table 2.

[0136] At the same time, in order to have a more intuitive feeling for the proposed method and other existing methods, the results of the dynamic important nodes of the above six methods are respectively taken as the remaining situation of the network after deleting 9 nodes and the remaining situation of the network after deleting 13 nodes, as shown in the figure. Figure 4 shown.

[0137] from Figure 4 It can be seen that the KPDN-INCC method proposed in the present invention has a more obvious effect. When 9 nodes are deleted, the effect may be general, and basically no significant changes can be seen. However, when 13 nodes are deleted, it is obvious that the remaining network size obtained by the KPDN-INCC method is only 5. At the same time, by comparing the static and dynamic results of each method, it is found that under normal circumstances, the method of dynamic important node identification is better than the static important node identification method, but whether to use a dynamic method or a static method, it is also necessary to further verify it according to the actual network situation. The above shows and describes the basic principles, main features and advantages of the present invention. The technicians in this industry should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions only illustrate the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements fall within the scope of the invention to be protected. The scope of protection claimed by the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for dynamic evaluation of the importance of network nodes with complex structures: the steps include: S1. Based on the degree of each node in the complex network, all nodes are sorted according to their degrees, and the nodes with fixed degrees and their edges are deleted according to the sorting results to obtain the k-shell layer corresponding to the node Ks value. Among them, after deleting nodes with fixed degrees and their edges each time, the remaining network is obtained; S2. In the process of deleting fixed degree nodes to obtain k-shell, nodes with different degree values ​​in the same deletion order are formed into a set, and the nodes in the set are sorted according to their degree value proportion KPD i Perform secondary sorting; S3. Based on the order of the second sorting, the relationship value S between the adjacent nodes of each node is calculated ij , and according to the relationship value S ij Perform three sortings; S4. Based on the residual network in step S1, the INCC factor is used to capture the indirect impact factor INCC of the residual network on the nearest neighbor and the next nearest neighbor of each node i , and sort four times; S5. KPD obtained based on the second sorting i , S obtained by the third sorting ij And the INCC obtained from the fourth sorting i Get the KPDN-INCC value and perform final sorting based on the KPDN-INCC value.

2. According to claim 1, a complex structure-oriented network node importance dynamic evaluation method is characterized by: In step S1, the process of obtaining the k-shell layer corresponding to the node Ks value includes: S101. Based on the degree of each node in the complex network, all nodes are sorted according to their degrees; S102. Delete nodes with degrees 1…n and their edges from the complex network in sequence to obtain a k-shell layer corresponding to the node Ks value; When nodes of multiple k-shell layers are peeled off in sequence, the peeling order, layer number, and sequence number of the corresponding nodes are recorded simultaneously.

3. The method for dynamic evaluation of importance of network nodes with complex structures according to claim 1, characterized in that: In step S2, the node degree ratio calculation formula is: Among them, ks i is the k-shell value of node i, k i is the degree of node i, k N(i)max is the maximum degree of the neighboring nodes of node i, l i For node i in the same ks i The order in which the shell is stripped under iterative stripping operation, l max For the same ks i The maximum number of peeling sequences under the layer; ks i|next are the adjacent nodes of node i.

4. The method for dynamic evaluation of importance of network nodes with complex structures according to claim 1 is characterized by: In step S3, the relationship value between adjacent nodes is calculated as follows: Where N(i)∩N(j) is the number of neighbor nodes shared by nodes i and j, and k i represents the degree value of node i, k j Represents the degree value of node j.

5. The method for dynamic evaluation of importance of network nodes with complex structures according to claim 1 is characterized by: In step S4, the INCC formula is as follows: in And Q j is the sum of the first-order neighbor degrees of node j, LR i is the sum of the second-order neighbor node degrees of node i; N w is the sum of the degree values ​​of the neighboring nodes of node j, Γ(j) represents the neighboring node set of node j, Γ(i) represents the neighboring node set of node i, INCC i refers to the structural hole factor, p′ ij Refers to the ratio of Q and LR, p' ik Refers to the ratio of Q and LR, p' kj It refers to the ratio of Q to LR, which is three, where n and k are natural numbers.

6. The method for dynamic evaluation of importance of network nodes with complex structures according to claim 1, characterized in that: In step S5, the formula of KPDN-INCC is as follows: Among them, N(i) refers to the first-order neighbor nodes of node i; k i Refers to the degree value of node i, KPD j Refers to the calculated kpd value of node i.

7. A dynamic evaluation system for the importance of network nodes with complex structures, characterized by: include: The k-shell layer acquisition module sorts all nodes according to their degrees based on the degree of each node in the complex network, and deletes the nodes with fixed degrees and their edges according to the sorting results to obtain the k-shell layer corresponding to the node Ks value; each time the nodes with fixed degrees and their edges are deleted, the remaining network is obtained; Sorting module 1: In the process of deleting fixed degree value nodes to obtain k-shell, nodes with different degree values ​​in the same deletion order are formed into a set, and the nodes in the set are sorted according to their degree value proportion KPD i Perform secondary sorting; Sorting module 2, based on the order of the second sorting, calculates the relationship value S between the adjacent nodes of each node ij , and according to the relationship value S ij Perform three sortings; Sorting module three, based on the residual network in step S1, uses the INCC factor to capture the indirect impact factor INCC of the residual network on the nearest neighbor and the next nearest neighbor of each node i , and sort four times; Node importance acquisition module, based on the KPD obtained from the second sorting i , S obtained by the third sorting ij And the INCC obtained from the fourth sorting i Get the KPDN-INCC value and perform final sorting based on the KPDN-INCC value.

8. A non-transitory computer-readable storage medium storing computer instructions, wherein: The computer instructions are used to cause the computer to execute the method according to any one of claims 1-6.

9. An electronic device, comprising: At least one processor, and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the method according to any one of claims 1 to 6.

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