A method and system for defining an edge initial load

Abstract

The present invention relates to a method for defining the initial load of edges in a command and control network cascading failure model. The method is as follows: according to the degree value of the node, an edge degree definition is given; based on the edge betweenness centrality, the network is divided into self-networks with each node as a unit, and the self-network edge betweenness definition is given; a new edge importance is defined by combining the important edge identification method of the improved bridging coefficient, the edge degree and the self-network edge betweenness; based on the hierarchy of the nodes in the network, a network edge hierarchy definition is given; based on the new edge importance and edge hierarchy, a method for defining the initial load of edges in a command and control network cascading failure model combining edge importance and edge hierarchy is designed. The present invention effectively suppresses the occurrence of cascading failure faults in the command and control network, enhances the network's anti-destruction capability, and provides a certain reference for improving the robustness of the command and control network.

Description

Technical Field

[0001] The present invention relates to the field of information technology, and in particular, to a method and system for defining the initial load of edges, and particularly to a method and system for defining the initial load of edges in a cascading failure model of a command and control network cascade. Background Art

[0002] In today's highly digital and network-connected world, command and control networks play a crucial and even decisive role in the military field. Command and control networks are responsible for integrating, transmitting, and processing information, providing real-time and accurate intelligence and instructions for decision-makers. However, with the increasing complexity of the network and the operator's dependence on it, command and control networks are facing more and more challenges. Among them, the most serious challenge is cascading failure caused by attacks. Relevant scholars have carried out extensive and in-depth research on this. However, most of these related studies are only about the cascading failure model of nodes. In a command and control network, edges play a crucial role. Edges carry various data instructions to support the communication and coordination between functional units. The connection method and layout of edges also directly affect the topological structure of the network. Well-designed edges can optimize the communication quality and response speed of the network. For this reason, relevant scholars have tried to study the cascading failure model of edges, but only construct the initial load of edges by simply adding or multiplying the degree values of nodes, without considering the global importance of edges. Some scholars have considered the importance and hierarchy of edges, but have not comprehensively considered the local and global importance of edges.

[0003] Based on this, the present invention gives the definition of edge degree by imitating the degree value of nodes; based on the edge betweenness centrality, divides the network into ego networks with each node as a unit to calculate the edge betweenness of ego networks; combines the improved edge importance recognition method of bridging coefficient, edge degree, and ego network edge betweenness to define a new edge importance; based on the hierarchy of nodes in the network, defines the hierarchy of edges in the network; based on the new edge importance and edge hierarchy, designs a method for defining the initial load of edges in a cascading failure model of a command and control network that combines edge importance and edge hierarchy. The present invention fully considers the local and global importance of edges in a command and control network, the topological structure of the network, and its information transmission ability, and designs a method for defining the initial load of edges in a cascading failure model of a command and control network that combines edge importance and edge hierarchy. The present invention effectively suppresses the occurrence of cascading failure faults in a command and control network, enhances the survivability of the network, and provides a certain reference value for enhancing the robustness of a command and control network.

[0004] In addition, on the one hand, there are differences in the understanding of those skilled in the art; on the other hand, when the applicant made this invention, a large number of documents and patents were studied, but due to space limitations, all details and content were not listed in detail. However, this does not mean that this invention does not possess the features of these prior arts. On the contrary, this invention already possesses all the features of the prior arts, and the applicant reserves the right to add relevant prior arts in the background art. Summary of the Invention

[0005] The object of the present invention is to provide a method for defining the initial load of edges in a command and control network cascade failure model. Considering that most of the existing methods are for defining the initial load of nodes, and most of the definitions of the initial load of edges do not combine the edge importance with the edge level, especially the edge importance does not take into account both the local and global importance of the edge. Therefore, the present invention gives a new method for defining edge importance by combining the improved bridging coefficient, edge degree, and self-network edge betweenness, and designs a method for defining the initial load of edges in a command and control network cascade failure model that takes into account both edge importance and edge level.

[0006] To achieve the above object of the invention, as Figure 1 shown, the present invention designs a method for defining the initial load of edges. The definition method takes into account both edge importance and edge level, and the definition method includes the following steps:

[0007] (1) Imitating the node degree, give the definition of edge degree;

[0008] (2) Based on the edge betweenness centrality, divide the network into self-networks with each node as a unit, and give the definition of self-network edge betweenness;

[0009] (3) Combine the improved bridging coefficient edge importance identification method, edge degree, and self-network edge betweenness to define a new edge importance;

[0010] (4) Based on the levels of nodes in the network, give the definition of network edge level;

[0011] (5) Based on the new edge importance and edge level, design a method for defining the initial load of edges in a command and control network cascade failure model that combines edge importance and edge level.

[0012] According to a preferred embodiment, imitate the degree value of the node to give the definition of edge degree. The node degree is a typical index representing the local importance of the command and control network, which is expressed as the number of edges connected to the node or as the number of neighbor nodes of the node. Imitating the definition of node degree, define the edge degree in the network as the number of edges connected to the edge or as the number of neighbor nodes of the edge. The edge degree can well represent the local importance of the edge in the whole network. Therefore, imitate the node degree to give the definition of edge degree, as shown in the following formula:

[0013] k ij= k i + k j -2(1)

[0014] where k ij is the degree of edge u ij and k i and k j represent the degrees of nodes i and j respectively.

[0015] According to a preferred embodiment, based on edge betweenness centrality, the network is divided into ego-networks with each node as a unit, and the definition of ego-network edge betweenness is given. Edge betweenness centrality refers to the proportion of the number of shortest paths passing through a certain edge between any two nodes in the network to the total number of all shortest paths. Edge betweenness centrality can well characterize the global importance of an edge in the network. The definition formula of edge betweenness centrality is as follows:

[0016]

[0017] where C B (e) represents the betweenness centrality of edge e, σ ij represents the total number of shortest paths from node i to node j, and σ ij (e) represents the number of shortest paths from node i to node j passing through edge e, and N represents the number of nodes in the network.

[0018] Calculating edge betweenness centrality requires computing the shortest paths between every pair of nodes in the entire network, resulting in a high computational complexity. To reduce the computational complexity, the ego-network edge betweenness is introduced, and its definition formula is as follows:

[0019]

[0020] where C v (v, e) represents the betweenness centrality of edge e in the ego-network of the target node v; (i≠j)∈T(e) means that there is a shortest path from node i to j (i≠j) passing through edge e in the ego-network with v as the target node.

[0021] Traverse the entire network topology so that each node in the network serves as the target node once. The ego-network edge betweenness is the sum of the betweenness centralities of edges in the ego-networks of different target nodes, and the expression is as follows:

[0022]

[0023] where C SNB (e) represents the ego-network edge betweenness of edge e, and N represents the number of network nodes.

[0024] According to a preferred embodiment, the edge importance is defined by combining the improved bridging coefficient edge importance identification method, edge degree, and ego-network edge betweenness. The definition of the improved bridging coefficient is as follows:

[0025]

[0026] HQ ij To improve the bridging coefficient edge importance identification method, X(i,j) is the bridging coefficient edge importance identification method, where a mn indicates whether there is an edge between nodes m and n. If there is an edge, a mn = 1; otherwise, it is 0. M and N respectively represent the sets of neighbor nodes of nodes i and j.

[0027] H(i,j) is the edge information entropy, and the expression of H(i,j) is as follows:

[0028]

[0029] where the degrees of nodes i and j are k i and k j , and H(i) and H(j) are the information entropies of nodes i and j.

[0030] where M is the set of neighbor nodes of node i.

[0031] C EB (j) is the ego-network node betweenness of node j.

[0032] By combining the improved bridging coefficient, edge degree, and ego-network edge betweenness, a new definition of edge importance is obtained, and the expression is as follows:

[0033] Z(i,j) = HQ ij ×(k ij + C SNB (e)) (7)

[0034] where HQ ij is the improved bridging coefficient edge importance identification method, which comprehensively considers the network topology structure and information transmission ability; k ij is the degree of the edge, which reflects the local importance of the edge in the network; C SNB (e) is the ego-network edge betweenness, which reflects the global importance of the edge in the network. Combining the three can take into account both the local and global importance of the network on the basis of considering the network topology structure and information transmission ability, and can well represent the importance degree of the edge in the network.

[0035] According to a preferred embodiment, a network edge hierarchy definition is given based on the hierarchy of nodes in the network. The hierarchical characteristics of the command and control network are obvious. Edges are composed of nodes of the same or different levels, and the hierarchy of edges can be constructed by the hierarchy of nodes, as shown below:

[0036]

[0037] Among them, d i and d j Respectively represent the level of nodes i and j, d ij Represents edge u ij The level, u ij represents the edge between nodes i and j. HC, CC and SC represent the hierarchical command, same-level command and cross-level (overstepping) command relationships respectively. ij The smaller the value, the higher the level of the edge and the more important the edge.

[0038] According to a preferred implementation, based on the new edge importance and edge level, a command and control network cascading failure model edge initial load definition method combining edge importance and edge level is designed. In view of the fact that the existing command and control network cascading failure model initial load definition is mostly based on nodes and lacks edge initial load definition, a command and control network edge initial load definition method that takes into account edge importance and edge level is proposed. ij (0) is a method for defining the initial load of a command and control network edge that takes into account both edge importance and edge hierarchy. The expression is as follows:

[0039] L ij (0)=α×Z(i,j)+(1-α)×(D+1-d ij ) 2 (9)

[0040] Among them, Z(i,j) is the new definition of edge importance proposed in this paper; D represents the number of network layers; d ij Represents edge u ij The layer in the network; α represents the adjustment parameter, which is used to adjust the importance of the first half of the edge and the weight of the second half of the edge layer.

[0041] The edge initial load is composed of edge importance and edge level. It takes into account the hierarchical characteristics of the command and control network on the basis of reflecting the edge importance. It can not only improve the accuracy and robustness of the model, but also more comprehensively reflect the complexity and diversity of the actual network.

[0042] The present invention also relates to a method system for defining an initial load of an edge. The system is configured as follows:

[0043] (1) Based on the node degree, the definition of edge degree is given;

[0044] (2) Based on betweenness centrality of edges, divide the network into ego networks with each node as a unit, and give the definition of betweenness of edges in ego networks;

[0045] (3) Combine the important edge recognition method with the improved bridging coefficient, edge degree, and betweenness of edges in ego networks to define the new edge importance;

[0046] (4) Based on the hierarchy of nodes in the network, give the definition of edge hierarchy in the network;

[0047] (5) Based on the new edge importance and edge hierarchy, design a method for defining the initial load of edges in the cascading failure model of the command and control network that combines edge importance and edge hierarchy.

[0048] The beneficial effects of the present invention compared with the prior art are as follows:

[0049] First, imitate the degree value of nodes to give the definition of edge degree; second, based on betweenness centrality of edges, divide the network into ego networks with each node as a unit, and give the definition of betweenness of edges in ego networks; third, combine the important edge recognition method with the improved bridging coefficient, edge degree, and betweenness of edges in ego networks to define the new edge importance; fourth, based on the hierarchy of nodes in the network, give the definition of edge hierarchy in the network; finally, based on the new edge importance and edge hierarchy, design a method for defining the initial load of edges in the cascading failure model of the command and control network that combines edge importance and edge hierarchy.

[0050] The present invention fully considers the local and global importance of edges in the command and control network, the topological structure of the network, and the information transmission ability, effectively inhibits the occurrence of cascading failure faults in the command and control network, enhances the network survivability, and has good guiding significance for improving the robustness of the command and control network. Description of the Drawings

[0051] Figure 1 is the flowchart of the method involved in this application;

[0052] Figure 2 is the comparison diagram of the change of edge initial load under different α values;

[0053] Figure 3 is the comparison diagram of the change of edge survival rate under different α values;

[0054] Figure 4 is the comparison diagram of the change of network connectivity coefficient under different α values;

[0055] Figure 5 is the comparison diagram of the change of edge survival rate under different definitions of initial load;

[0056] Figure 6 is the comparison diagram of the change of network connectivity coefficient under different definitions of initial load;

[0057] Figure 7The following is a comparison chart of the survival rate changes under different load distribution strategies;

[0058] Figure 8 This is a comparison chart of network connectivity coefficient changes under different load distribution strategies;

[0059] Figure 9 This is a comparison chart of the survival rate changes under different attack methods;

[0060] Figure 10 This is a comparison chart of network connectivity coefficient changes under different attack methods;

[0061] Figure 11 This is a comparison chart of the survival rate changes under different cascading failure models;

[0062] Figure 12 A comparison chart of the changes in network connectivity coefficients under different cascading failure models. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solution and advantages of the present invention clearer, the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. For those skilled in the art, the specific meanings of the terms in the present invention can be understood in specific circumstances.

[0064] This embodiment provides a method for defining the initial load of the edge of the command and control network cascading failure model. In order to verify the feasibility, applicability and effectiveness of the present invention, simulation analysis is designed from five aspects. The embodiment analyzes the following five aspects respectively: edge initial load adjustment parameters; different edge initial load definition methods; different load distribution strategies; different attack methods; network edge survival rate and network connectivity coefficient of different cascading failure models.

[0065] The initial parameters are set as follows: the network model contains 1 first-level node, the span is 3, there are 5 levels in total, the total number of nodes is 121, the total number of edges is 256, of which there are 118 collaborative edges and 18 leapfrog edges; during random attacks, 10 experiments are taken to calculate the average.

[0066] (1) Simulation analysis of adjustment parameter α

[0067] In order to verify that the initial load in this paper can meet the hierarchical characteristics of the command and control network, a comparative analysis of the initial load under different α values ​​is carried out, such as Figure 2 shown.

[0068] Depend on Figure 2 It can be seen that when α = 0, the initial load of the edge depends entirely on the edge level, and the level characteristics are very obvious, but the initial loads in the second and third levels are very different.

[0069] When α=1, the initial edge load depends only on the edge importance and does not reflect the hierarchical characteristics, which is inconsistent with the command and control network.

[0070] When 0.25 ≤ α ≤ 0.75, the initial load of the edge combines edge importance and edge hierarchy, showing obvious hierarchy while reducing the differences within the layer.

[0071] Then, the attack method in this paper is adopted to observe the changes in edge survival rate and network connectivity coefficient under different α values. β and γ are the adjustment parameters in the edge initial load-capacity model, and η is the adjustment parameter in the edge load distribution strategy. When β = 0.15, γ = 1.15, and η = 0.7, the simulation results are as Figure 3 and Figure 4 shown. From Figure 3 and Figure 4 it can be seen that with different α values, the decline rates of evaluation indicators are different. When α = 0 and α = 1, the decline rates of evaluation indicators are relatively fast, and the anti-destruction ability of the model is poor; when α = 0.5, the decline rates of all evaluation indicators are the slowest, and the anti-destruction ability of the model is the strongest, which fully demonstrates the necessity of combining edge hierarchy and edge importance. The optimal value of α here is 0.5.

[0072] (2) Simulation analysis of different definitions of edge initial load

[0073] To observe the influence of different initial loads on the anti-destruction ability of the model, the edge survival rate and network connectivity coefficient of the initial load in this paper and several other common initial loads are compared and analyzed, as Figure 5 and Figure 6 shown. The adjustment parameter α takes the optimal value of 0.5.

[0074] From Figure 5 and Figure 6 it can be seen that the anti-destruction abilities of the initial load definition methods of edge degree, improved structural hole and information entropy combination (XIJ), product of edge degree and ego-network edge betweenness, and ego-network edge betweenness and edge betweenness are significantly worse than that of the method in this paper.

[0075] Although the method in this paper is slightly worse than the improved structural hole method in the early stage, the method in this paper is superior to the improved structural hole method in the later stage. In summary, the initial load definition method in this paper has obvious advantages.

[0076] (3) Simulation analysis of different load distribution strategies

[0077] Under the above values of β and γ, the capacity is relatively sufficient, but the cascade failure is not very obvious. To clearly observe the cascade failure process, the values of β and γ are taken smaller (i.e., the edge capacity is taken smaller). Here, both β and γ are set to 0.3. As the number of deleted edges increases, the changes in edge survival rate and network connectivity coefficient under different load distribution strategies are as Figure 7 and Figure 8 shown.

[0078] From Figure 7 andFigure 8 It can be seen that, compared with the other four load redistribution strategies, the indicators of the strategy in this paper decrease at the slowest rate with the increase in the number of deleted edges, indicating that the load redistribution strategy in this paper can well match the characteristics of the command and control network and can also greatly improve the network's survivability.

[0079] (4) Simulation analysis of different attack methods

[0080] To observe the influence of different attack methods on the survivability of the model, the changes in the survival rate of edges and the network connectivity coefficient after attacking the network using the method in this paper and several other attack methods were compared and analyzed, as Figure 9 and Figure 10 shown.

[0081] From Figure 9 and Figure 10 it can be seen that, compared with the other six methods, after attacking a certain number of edges using the attack method in this paper, the values of each evaluation index gradually become the smallest. The results show that the attack method in this paper can accurately identify and strike important edges, demonstrating the strength of this attack method and at the same time showing that this model has strong anti-interference ability against the outside world.

[0082] (5) Simulation analysis of different cascade failure models

[0083] To verify that the method proposed in this paper can improve the robustness of the cascade failure model, several other common cascade failure models were compared and analyzed. The comparison diagrams of the edge survival rate and the network connectivity coefficient of several different cascade failure models are as Figure 11 and Figure 12 shown.

[0084] From Figure 11 and Figure 12 it can be seen that with the increase in the number of deleted edges, the decline rate of each index of the cascade failure model in this paper is slower than that of other models, indicating that the cascade failure model involved in the method proposed in this paper has stronger resistance and better survivability when suffering from external attacks.

[0085] In summary, a method for defining the initial load of edges in a cascade failure model of a command and control network proposed by the present invention has a higher edge survival rate and network connectivity coefficient compared with other methods under different initial edge load definitions, different load distribution strategies, different attack methods, and different cascade failure models. It ensures the robustness of the network while meeting the characteristics of the command and control network. This shows that the method of the present invention has certain advantages in suppressing cascade failures and provides certain reference for the construction of command and control network models.

[0086] It should be noted that the above specific embodiments are exemplary. Those skilled in the art can come up with various solutions inspired by the disclosure of the present invention, and these solutions also fall within the scope of the disclosure of the present invention and within the protection scope of the present invention. Those skilled in the art should understand that the description and drawings of the present invention are illustrative and do not constitute a limitation on the claims. The protection scope of the present invention is defined by the claims and their equivalents. The description of the present invention contains multiple inventive concepts. For example, "according to a preferred embodiment" indicates that the corresponding paragraph discloses an independent concept. The applicant reserves the right to file divisional applications based on each inventive concept. Throughout the text, the features guided by "preferably" are only optional and should not be understood as being required to be provided. Therefore, the applicant reserves the right to waive or delete the relevant preferred features at any time.

Claims

1. A method for defining the initial load of an edge, characterized in that: It includes the following steps: (1) Based on the node degree, the definition of edge degree is given; (2) Based on the edge betweenness centrality, the network is divided into ego networks with each node as the unit, and the definition of the edge betweenness of the ego network is given; (3) Combining the important edge identification method of the improved bridging coefficient, edge degree and self-network edge betweenness, a new edge importance is defined, and the definition of the improved bridging coefficient is as follows: HQ ij To improve the identification method of the importance of the bridging coefficient edge; X(i,j) is the identification method of the importance of the bridging coefficient edge, where a mn Indicates whether there is an edge between nodes m and n. If there is an edge a mn =1, otherwise 0; M and N represent the neighbor node sets of nodes i and j respectively; H(i,j) is the edge information entropy; The expression of H(i,j) is as follows: The degree of node i is k i , the degree of node j is k j ; H(i) is the information entropy of node i, H(j) is the information entropy of node j, where M is the set of neighbor nodes of node i, C EB (j) is the node betweenness of the ego network of node j; Combining the improved bridging coefficient, edge degree and self-network edge betweenness, we get a new definition of edge importance Z(i, j), which is expressed as follows: Z(i,j)=HQ ij ×(k ij +C SNB (e)) (7) Among them, HQ ij To improve the edge importance identification method of the bridging coefficient; k ij is the degree of the edge; C SNB (e) is the edge betweenness of the self-network; (4) Based on the hierarchy of nodes in the network, a definition of the network edge hierarchy is given; (5) Based on the new edge importance and edge hierarchy, a method for defining the edge initial load of the command and control network cascading failure model combining edge importance and edge hierarchy is designed. The expression is as follows: L ij (0)=α×Z(i,j)+(1-α)×(D+1-d ij ) 2 (9) Among them, Z(i,j) is the new definition of edge importance proposed in this paper; D represents the number of network layers; d ij Represents edge u ij The layer in the network; α represents the adjustment parameter, which is used to adjust the importance of the first half of the edge and the weight of the second half of the edge layer.

2. The initial load definition method according to claim 1, characterized in that: Based on the node degree, the edge degree definition is given as shown below: k ij =k i +k j -2 (1) where k ij For edge u ij The degree, k i and k j denote the degrees of nodes i and j respectively.

3. The initial load definition method according to claim 2, characterized in that: Based on edge betweenness centrality, the network is divided into ego networks with each node as the unit, and the definition of ego network edge betweenness is given. The definition of edge betweenness centrality is as follows: Among them, C B (e) represents the betweenness centrality of edge e, σ ij represents the total number of shortest paths from node i to node j, σ ij (e) represents the number of shortest paths from node i to node j through edge e, and N represents the number of nodes in the network.

4. The initial load definition method according to claim 3, characterized in that: In order to reduce the computational complexity, the self-network edge betweenness is used. The definition of the self-network edge betweenness is as follows: Among them, C v (v,e) represents the betweenness centrality through edge e in the ego network of target node v; (i≠j)∈T(e) represents that there is a shortest path from node i to j (i≠j) through edge e in the ego network with v as the target node, where the edge betweenness of the ego network is the sum of the edge betweenness centralities in the ego networks of different target nodes, and the expression is as follows: Among them, C SNB (e) represents the ego-network edge betweenness of edge e, and N represents the number of network nodes.

5. The initial load definition method according to claim 4, characterized in that: Based on the hierarchy of nodes in the network, the network edge hierarchy definition is given. Edges are composed of nodes of the same or different levels, and the edge hierarchy can be constructed through the node hierarchy. The expression is as follows: Among them, d i and d j Respectively represent the level of nodes i and j, d ij Represents edge u ij The level, u ij represents the edge between nodes i and j, HC, CC and SC represent the hierarchical command, same-level command and cross-level command relationships respectively.

6. A method system for defining initial load of an edge, characterized in that: The system is configured to: (1) Based on the node degree, the definition of edge degree is given; (2) Based on the edge betweenness centrality, the network is divided into ego networks with each node as the unit, and the definition of the edge betweenness of the ego network is given; (3) Combining the important edge identification method of the improved bridging coefficient, edge degree and self-network edge betweenness, a new edge importance is defined, and the definition of the improved bridging coefficient is as follows: HQ ij To improve the identification method of the importance of the bridging coefficient edge; X(i,j) is the identification method of the importance of the bridging coefficient edge, where a mn Indicates whether there is an edge between nodes m and n. If there is an edge a mn =1, otherwise 0; M and N represent the neighbor node sets of nodes i and j respectively; H(i,j) is the edge information entropy; The expression of H(i,j) is as follows: The degree of node i is k i , the degree of node j is k j ; H(i) is the information entropy of node i, H(j) is the information entropy of node j, where M is the set of neighbor nodes of node i, C EB (j) is the node betweenness of the ego network of node j; Combining the improved bridging coefficient, edge degree and self-network edge betweenness, we get a new definition of edge importance Z(i, j), which is expressed as follows: Z(i,j)=HQ ij ×(k ij +C SNB (e)) (7) Among them, HQ ij To improve the edge importance identification method of the bridging coefficient; k ij is the degree of the edge; C SNB (e) is the edge betweenness of the self-network; (4) Based on the hierarchy of nodes in the network, a definition of the network edge hierarchy is given; (5) Based on the new edge importance and edge hierarchy, a method for defining the edge initial load of the command and control network cascading failure model combining edge importance and edge hierarchy is designed. The expression is as follows: L ij (0)=α×Z(i,j)+(1-α)×(D+1-d ij ) 2 (9) Among them, Z(i,j) is the new definition of edge importance proposed in this paper; D represents the number of network layers; d ij Represents edge u ij The layer in the network; α represents the adjustment parameter, which is used to adjust the importance of the first half of the edge and the weight of the second half of the edge layer.

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