A critical edge identification method for command and control network based on improved bridging coefficient

Abstract

The present invention discloses a method for identifying key edges of a command and control network based on an improved bridging coefficient, comprising obtaining information entropy of command and control network nodes according to the betweenness centrality of a self-network; defining information entropy of edges by the information entropy of the command and control network nodes; and obtaining the criticality of command and control network edges based on the improved bridging coefficient. Identification of key edges of a command and control network can not only improve the anti-destruction capability of one's own network, but also attack key edges of enemy networks at a lower cost and with higher benefits. The bridging coefficient can well identify bridge edges between communities in a command and control network, and plays an important role in maintaining the global connectivity of the network, while the information entropy defined based on the betweenness centrality characterizes the information transmission capability of edges. By improving the bridging coefficient in combination with information entropy, the network structure and network information transmission capability can be comprehensively considered.

Description

Technical Field

[0001] The present invention relates to the technical field of command and control network, and in particular to a command and control network key edge identification method based on an improved bridging coefficient. Background Art

[0002] In the field of research on key node (edge) identification in command and control networks, most studies focus on the identification of key nodes, and relatively few studies are conducted on the identification of key edges. However, in the process of information diffusion, it is often impractical to block all communications of a node. It is more practical to cut off some important communication links to prevent propagation. Therefore, research on key edge identification in command and control networks is also of great significance.

[0003] The existing key edge identification algorithms for command and control networks mainly include two types of methods: those based on network structure and those based on network information propagation. However, most of them only consider network structure or network information propagation unilaterally, and it is difficult to take into account the global connectivity and information transmission capabilities of the network. Summary of the invention

[0004] In view of the fact that the existing technology does not fully consider the impact of edge information transmission capability and network connectivity on key edges, the present invention combines the bridging coefficient and edge information entropy to propose a command and control network key edge identification method with improved bridging coefficient.

[0005] To achieve the above purpose, the technical solution of the present application is: a method for identifying key edges of a command and control network based on an improved bridging coefficient, comprising:

[0006] According to the betweenness centrality of the ego network, the information entropy of the command and control network nodes is obtained;

[0007] Defining edge entropy by the information entropy of the command and control network nodes;

[0008] The criticality of the command and control network edge is obtained based on the improved bridging coefficient.

[0009] Furthermore, the amount of information carried by the edge of the command and control network is related to its connection strength. Betweenness centrality is usually used to describe the edge connection strength during the information propagation process. However, betweenness centrality needs to calculate the shortest path of each pair of nodes, which has high complexity. Therefore, the betweenness centrality of the ego network is introduced. The ego network is a local network composed of any target node and its one-hop neighbor node in the network. The node information entropy is defined by the betweenness centrality of the ego network, which greatly reduces the time complexity of the betweenness centrality information entropy.

[0010] Therefore, according to the centrality of the self-network betweenness, the information entropy of the command and control network node i is obtained as:

[0011]

[0012] Where M represents the set of neighbor nodes of node i in the command and control network, |M| represents the number of neighbor nodes of node i; C EB (j) represents the ego-network betweenness centrality of node j’s neighbor nodes, and f represents the probability distribution function.

[0013] Furthermore, the self-network betweenness centrality C of the neighboring nodes of node j EB (j) and the probability distribution function f are defined as follows:

[0014]

[0015]

[0016] Among them, σ ij represents the number of shortest paths from node i to node j in the command and control network, σ ij (v) represents the number of shortest paths from node i to node j through node v in the command and control network; node i and node j are one-hop neighbors of node v, so there is only one path from node i to node j passing through node v, that is,

[0017] Furthermore, the information entropy of the edge is defined by the information entropy of the command and control network node, specifically: the node information entropy is distributed using the degree values ​​of the nodes at both ends of the edge as weights, and the expression is as follows:

[0018]

[0019] Among them, k i ,k j Represents the degree value of node i,j in the command and control network.

[0020] Furthermore, the criticality of the command and control network edge is obtained based on the improved bridging coefficient. Specifically, the improved bridging coefficient is defined as follows:

[0021]

[0022] Among them, X(i,j) represents the criticality of the command and control network edge, which is defined as follows:

[0023]

[0024] in, is the bridging coefficient of the command and control network edge; α is the adjustment coefficient; M, N are the neighbor node sets of nodes i and j respectively, |M|, |N| are the number of neighbor nodes of nodes i and j respectively; a m,n Indicates the connection relationship between nodes. If nodes m and n are connected, a m,n =1; otherwise a m,n=0; P represents the number of common neighbors of nodes i and j.

[0025] Furthermore, the number of common neighbors P of nodes i and j is defined as:

[0026]

[0027] Among them, a jm Indicates the connection relationship between nodes. If nodes j and m are connected, a jm =1; otherwise a jm =0; a ni Indicates the connection relationship between nodes. If nodes n and i are connected, a ni =1; otherwise a ni =0.

[0028] Identifying the key edges of command and control networks can not only improve the anti-destruction capability of one's own network, but also attack the key edges of enemy networks at a lower cost and with higher benefits. However, most current studies only consider the network structure or network information propagation unilaterally, and it is difficult to take into account the global connectivity and information transmission capabilities of the network. The bridging coefficient can well identify the bridge edges between communities in the command and control network, and plays an important role in maintaining the global connectivity of the network. The information entropy defined based on the betweenness centrality characterizes the information transmission capability of the edge. Improving the bridging coefficient in combination with the information entropy can comprehensively consider the network structure and the network information transmission capability. Based on this, a method for identifying the key edges of command and control networks based on the improved bridging coefficient is proposed.

[0029] By adopting the above technical scheme, the present invention can achieve the following technical effects: the present invention introduces the centrality of the self-network betweenness to construct the information entropy of the edge in the command and control network; combines the information entropy to improve the bridging coefficient, and proposes a command and control network key edge method based on the improved bridging coefficient. The recognition accuracy of the key edges in the network is improved, especially the recognition accuracy of the key edges within the community, which meets the needs of the key edge recognition of the command and control network. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The present invention has attached Figure 6 Size:

[0031] Figure 1 Simplified model diagram for command and control network;

[0032] Figure 2 This is a diagram of the command and control network model;

[0033] Figure 3 This is a graph showing the changes in average network efficiency under different attack strategies;

[0034] Figure 4 This is a graph showing the change in the average network efficiency drop rate of different recognition algorithms under deliberate attacks;

[0035] Figure 5 This is the trend graph of the network connectivity coefficient changing with the number of deleted edges;

[0036] Figure 6 This is a changing trend graph of the maximum connected subgraph ratio. DETAILED DESCRIPTION

[0037] In order to verify the feasibility and effectiveness of the above-mentioned command and control network key edge identification method based on the improved bridging coefficient, this embodiment conducted three experiments, namely, the importance ranking experiment of the simplified command and control network model, the network performance analysis experiment under different attack strategies, and the performance analysis of different key edge identification methods. The experimental data comes from the simplified command and control network model and the command and control network model established in the literature [Gao Xiu'e, Chen Xiaoshuang, Wang Yunming, Chen Bo. Command and control network bridge edge identification method based on bridging coefficient [J]. Computer Engineering, 2019, 45(07): 309-314.], the number of nodes in the simplified command and control network model is N = 10, the number of edges is L = 20; the number of nodes in the command and control network model is N = 121, the number of edges is L = 256, the number of failed nodes is controlled within 200, and the adjustment parameter of the bridging coefficient is α = 0.4.

[0038] (1) Experiment on importance ranking of simplified command and control network model

[0039] In order to verify the feasibility of the method proposed in this invention, the edge importance ranking results of the simplified model of the command and control network are first analyzed, as shown in Table 1. 3,10 The edge importance of is the largest, followed by edge e 4,6 , are all bridge edges between communities in the command and control network. Table 1 shows that the key edge identification method proposed in the present invention can effectively identify bridge edges in the command and control network.

[0040] Table 1

[0041]

[0042] (2) Network performance analysis experiments under different attack strategies

[0043] In order to verify the effectiveness of the method of the present invention, the average network efficiency reduction rate of the method of the present invention under random attack and deliberate attack strategies is analyzed respectively. Figure 3 Then the contrast product, Jaccard coefficient, edge betweenness, bridging coefficient and the average network efficiency change trend of the five key edge identification methods of the present invention under deliberate attack are shown as follows: Figure 4 As shown. Figure 3 It can be seen that the average network efficiency decrease rate under deliberate attack is significantly higher than that under random attack, which indicates that the deliberate attack strategy has a greater impact on network performance; Figure 4 It shows that the average network efficiency decrease rate of the method of the present invention is higher than that of the three methods of degree product, edge betweenness and Jaccard coefficient. In the early stage of deleting important edges, the average network efficiency decrease rate is slightly lower than that of the bridging coefficient method; but in the later stage of deleting important edges, it is higher than that of the bridging coefficient method. The reason for this phenomenon is that the method proposed by the present invention combines the bridging coefficient with the information entropy. The bridging coefficient has a higher accuracy in identifying the connecting edges between communities in the command and control network; while the information entropy is defined based on the centrality of the self-network betweenness of the node, which is a local information indicator and cannot accurately identify the bridging edges. Therefore, when identifying the connecting edges between communities in the command and control network in the early stage of important edge identification, the identification accuracy is slightly inferior to the bridging coefficient. After the identification of the bridging edges in the network is completed, the method of the present invention is better than the bridging coefficient for identifying important edges within the community. It can be seen that the bridging coefficient is slightly inferior to the recognition accuracy of the key edges within the community, and the method of combining information entropy with the bridging coefficient of the present invention can effectively improve the recognition accuracy of the key edges within the command and control network community.

[0044] (3) Performance analysis of different key edge identification methods

[0045] In order to further verify the effectiveness of the method of the present invention compared with the other four methods, the network connectivity and the maximum connected subgraph ratio of the five methods are analyzed respectively. Figure 5 and Figure 6 As shown. It can be seen that as the number of deleted edges increases, the network connectivity coefficient and the ratio of the number of edges of the largest connected subgraph in the network to the total number of edges both show a downward trend, and the method proposed in the present invention decreases the fastest, with the proportion of the largest number of connected edges first dropping to 10% of the total number of edges in the initial network, indicating the effectiveness of the key edge identification method proposed in the present invention. Figure 6 and Figure 4 The trends shown are similar. In the early stage of edge deletion, the effect of reducing the proportion of the maximum connected subgraph edges of the method of the present invention is basically consistent with that of the bridging coefficient method, but in the later stage of edge deletion, the effect of the method of the present invention is better than that of the bridging coefficient method.

[0046] In summary, the key edge identification method of command and control network based on improved bridging coefficient proposed in the present invention can effectively identify the key edges in command and control network, especially the key edges within the community in command and control network. This shows that the method of the present invention has great potential in the identification of key edges in command and control network, and provides a certain reference for the research on key edge identification method of command and control network.

[0047] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. It should be pointed out that ordinary technicians in this technical field can make several improvements and modifications without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for identifying key edges in a command and control network based on an improved bridging coefficient, characterized in that: include: According to the betweenness centrality of the self-network, the information entropy of the command and control network nodes is obtained: Where M represents the set of neighbor nodes of node i in the command and control network, |M| represents the number of neighbor nodes of node i; C EB (j) represents the ego-network betweenness centrality of the neighboring nodes of node j, and f represents the probability distribution function; the ego-network betweenness centrality C of the neighboring nodes of node j EB (j) and the probability distribution function f are defined as follows: Among them, σ ij represents the number of shortest paths from node i to node j in the command and control network, σ ij (v) represents the number of shortest paths from node i to node j through node v in the command and control network; node i and node j are one-hop neighbors of node v, so there is only one path from node i to node j passing through node v, that is, The information entropy of the edge is defined by the information entropy of the command and control network node. Specifically, the node information entropy is distributed using the degree values ​​of the nodes at both ends of the edge as weights. The expression is as follows: Among them, k i ,k j represents the degree value of node i,j in the command and control network; The criticality of the command and control network edge is obtained based on the improved bridging coefficient. Specifically, the improved bridging coefficient is defined as follows: Among them, X(i,j) represents the criticality of the command and control network edge, which is defined as follows: in, is the bridging coefficient of the command and control network edge; α is the adjustment coefficient; M, N are the neighbor node sets of nodes i and j respectively, |M|, |N| are the number of neighbor nodes of nodes i and j respectively; a m,n Indicates the connection relationship between nodes. If nodes m and n are connected, a m,n =1; otherwise a m,n =0; P represents the number of common neighbors of nodes i and j.

2. According to claim 1, a command and control network key edge identification method based on improved bridging coefficient is characterized in that: The number of common neighbors P of nodes i and j is defined as: Among them, a jm Indicates the connection relationship between nodes. If nodes j and m are connected, a jm =1; otherwise a jm =0; a ni Indicates the connection relationship between nodes. If nodes n and i are connected, a ni =1; otherwise a ni =0.

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