Complex network connection edge importance evaluation method and device

Abstract

The invention provides a complex network connection edge importance evaluation method and device, and the method is characterized in that the method comprises the steps: obtaining connection edge property evaluation indexes in a complex network; constructing an edge connection importance evaluation index according to the edge connection property evaluation index; and evaluating the edge connection importance of the complex network through the edge connection importance evaluation index. According to the method, the degree value, betweenness and edge betweenness indexes of the nodes are comprehensively considered, two variable parameters are introduced to adjust the indexes, the edge connection importance evaluation indexes are comprehensively designed, and the edge connection importance can be effectively evaluated under the condition of different network topology structures.

Description

Technical Field

[0001] This document relates to the technical field of edge importance evaluation, and particularly to a method and device for evaluating the importance of edges in a complex network. Background Art

[0002] Currently, there are many algorithm studies on mining important nodes in a network, such as designing important node mining algorithms based on indicators such as betweenness, degree, k-core, information entropy, etc.; in a complex network, compared with adding or deleting nodes to optimize the network structure, the method of adding or deleting edges has a lower cost and is easier to implement. For example, to increase network connectivity, some edges can be directly added or some edges can be adjusted at key nodes; to control information dissemination, important edges can be deleted to avoid a significant decline in network connectivity after deleting important nodes. In a complex network, the main indicators for evaluating the nature of edges are edge betweenness and edge clustering coefficient, and the number of indicators is relatively small. Using a single indicator to evaluate the importance of edges will result in a large number of edge indicators being the same, thus causing the evaluation method to fail. At the same time, using a single indicator to measure the importance of edges is also relatively one-sided.

[0003] In the currently published literature, for the problem of edge importance, by combining indicators such as degree centrality, betweenness centrality, and clustering coefficient of nodes, edge importance evaluation indicators are designed, which can sort the edges in a specific network topology and obtain beneficial results. However, after the network topology changes, the performance of the method will decline. Summary of the Invention

[0004] The present invention provides a method and device for evaluating the importance of edges in a complex network, which can effectively evaluate the importance of edges under different network topology situations.

[0005] An embodiment of the present invention provides a method for evaluating the importance of edges in a complex network, including:

[0006] S1. Obtain the evaluation indicators for the nature of edges in the complex network;

[0007] S2. Construct an edge importance evaluation indicator according to the evaluation indicator for the nature of the edge;

[0008] S3. Implement the evaluation of the importance of edges in the complex network through the edge importance evaluation indicator.

[0009] An embodiment of the present invention provides a device for evaluating the importance of edges in a complex network, including:

[0010] An evaluation indicator acquisition module, which obtains the evaluation indicators for the nature of edges in the complex network;

[0011] The importance evaluation index acquisition module constructs the link importance evaluation index according to the link property evaluation index;

[0012] The evaluation module is used to evaluate the importance of links in a complex network through the link importance evaluation index.

[0013] By adopting the embodiment of the present invention, by comprehensively considering the degree value, betweenness, and edge betweenness indexes of nodes, and introducing two variable parameters to adjust the indexes, the link importance evaluation index is comprehensively designed, and the effective evaluation of the link importance can be realized under different network topological structures. Brief Description of the Drawings

[0014] In order to more clearly illustrate the technical solutions in one or more embodiments of this specification or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments recorded in this specification. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0015] Figure 1 It is a flowchart of the method for evaluating the importance of links in a complex network according to the embodiment of the present invention;

[0016] Figure 2 It is a schematic diagram of the device for evaluating the importance of links in a complex network according to the embodiment of the present invention;

[0017] Figure 3 It is a schematic diagram of the comparison of betweenness according to the embodiment of the present invention;

[0018] Figure 4 It is a schematic diagram of the network efficiency change curve;

[0019] Figure 5 It is a schematic diagram of the network efficiency change curve after changing the parameters;

[0020] Figure 6 It is a schematic diagram of the network efficiency change curve when α = β = 0.1 and α = β = 0.2;

[0021] Figure 7 It is a schematic diagram of the network efficiency change curve when α = β = 0.3 and α = β = 0.4;

[0022] Figure 8 It is a schematic diagram of the network efficiency change curve when α = β = 0.5 and α = β = 0.6;

[0023] Figure 9 It is a schematic diagram of the network efficiency change curve when α = β = 0.7 and α = β = 0.8;

[0024] Figure 10Schematic diagram of the network efficiency change curve for α = β = 0.05 and α = β = 0.08;

[0025] Figure 11 Schematic diagram for comparing network efficiency after the network scale increases. Detailed implementation manners

[0026] To enable those skilled in the art of this technology to better understand the technical solutions in one or more embodiments of this specification, the following will clearly and completely describe the technical solutions in one or more embodiments of this specification with reference to the accompanying drawings in one or more embodiments of this specification. Obviously, the described embodiments are only a part of the embodiments of this specification, rather than all the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of this document.

[0027] Method embodiments

[0028] According to an embodiment of the present invention, a method for evaluating the importance of edges in a complex network is provided. Figure 1 Is the flowchart of the method for evaluating the importance of edges in a complex network according to an embodiment of the present invention. According to Figure 1 As shown, the method for evaluating the importance of edges in a complex network according to an embodiment of the present invention specifically includes:

[0029] S1. Obtain the evaluation indexes for the edge properties in the complex network; the evaluation indexes for the edge properties include: the betweenness of the edge, the betweenness of the nodes of the edge, and the degree value of the edge nodes.

[0030] Generally, in a network, the edge betweenness reflects the ability of a path to transmit and control a complex network. The larger the edge betweenness, the more times the shortest path of nodes passes through this edge, and the greater the ability to transmit and control the complex network, which to a certain extent indicates that this edge is more important. In addition, taking Figure 3 as an example, further considering, if the betweenness of a certain edge is very large, it means that there are more shortest distances between nodes in the network passing through this node. At the same time, if the degree value of this node is very large, it means that because the degree value of the node is large, there are more connections of the node, which leads to many edges passing through this node. Then, thinking from the opposite side, if an edge has a very small degree value and betweenness of its endpoints, but the betweenness value of this edge is very large, it can better illustrate that the position of this edge in the network is irreplaceable and this edge is more important.

[0031] The specific content of S1 includes:

[0032] Calculate the degree value k i of the node v i in the network;

[0033] Calculate the number of shortest paths between any two nodes in the network, and calculate the number of pairs of any nodes in the network passing through node v i Calculate the number of shortest paths between any two nodes passing through edge e ij Calculate the betweenness B of all nodes in the network i ;

[0034] Calculate the betweenness of edge e ij .

[0035] S2. Construct an edge importance evaluation index according to the edge property evaluation index; the specific content of S2 includes:

[0036] Obtain the edge importance evaluation index through Formula 1:

[0037]

[0038] where B ij is the edge between node v i and node v j , B i and B j are the betweenness of node v i and node v j , k i and k j are the degree values of two nodes, and α and β represent the adjustment parameters of the evaluation index.

[0039] S3. Implement the evaluation of the importance of edges in the complex network through the edge importance evaluation index. Select the edges with small betweenness and large degree values as the important edges of the network through the new index, and finally verify the effectiveness of the proposed index through simulation.

[0040] The method further includes:

[0041] Implement the evaluation of the importance of edges under different network topologies by adjusting the values of α and β.

[0042] To measure the effect of the present invention, different network structures are simulated by computer to verify the effect of the embodiments of the present invention. The edges sorted by the method proposed by the present invention are deleted by gradually increasing the proportion, and the change of network efficiency is observed. At the same time, the importance of edges in the network is evaluated and sorted by three indexes of edge betweenness, randomly selected edges and edge weights, and the network efficiency is observed after deleting the same proportion of the number of edges as a reference comparison.

[0043] First, construct small-world networks. Similarly, set up three WS small-world networks with the number of network nodes being NA = 500, NB = 400, and NC = 300 respectively. In each individual small-world network, initially each node is connected to one neighbor on each side. Set the probability of randomly reconnecting each edge to be 0.2. Since the small-world network belongs to a regular network and the properties of network nodes are roughly the same, the parameters α and β are set to 1 (empirical values). The edges connecting the two small-world networks are randomly connected, and the number of connecting edges is half of the number of nodes in the larger community. By using the method proposed in the embodiment of the present invention, the betweenness centrality, randomly selecting edges, and edge weight methods to rank the importance of the edges in the network, and comparing the network efficiency change curves obtained by sequentially deleting the edges, as Figure 4 shown.

[0044] Through Figure 4 it can be seen that as the proportion of deleted edges increases, the network efficiency of the four methods all shows a downward trend. This is because the deleted edges will cause the shortest distance between nodes in the network to increase, resulting in a decrease in network efficiency. In addition, the network efficiency curve of the method proposed in the embodiment of the present invention drops the fastest, indicating that the method in the embodiment of the present invention can better locate the key edges in the network than the betweenness centrality method and the edge weight method. Among the indicators proposed in the existing literature, most of the performances are approaching the betweenness centrality method, and the performance of the indicator proposed in the embodiment of the present invention is better than the betweenness centrality method, thanks to the unique indicator design idea.

[0045] Further change the parameters, set p = 0.4, K = 2 and p = 0.4, K = 4, and the network efficiency curves are as Figure 5 shown. Similarly, as the proportion of deleted edges on both sides increases, the network efficiency curves of the four methods all decrease, and the method proposed in the embodiment of the present invention can locate the key edges in the network faster and more accurately than the other three methods.

[0046] Further change the network type, change the three small-world networks into three scale-free networks with the number of nodes being NA = 500, NB = 400, and NC = 300. The formation process is as follows:

[0047] In the initial state, the network is a globally coupled network with the number of nodes being m0;

[0048] Add a new node to the network every unit time. The new node is connected to m nodes in the network, and the connection probability is proportional to the degree value of the node.

[0049] The connections between the three networks are randomly connected, and the number of connecting edges is half of the number of nodes in the larger community among the interconnected communities.

[0050] First, set \(m = 2\), \(m_0 = 2\). A scale-free network is a type of non-uniform network. In the network, there are fewer nodes with high degrees and more nodes with low degrees. The two terms on the right side of the formula for the evaluation index of edge importance can be used as auxiliary parameters. First, set the parameters \(\alpha\) and \(\beta\) to 0.1 here.

[0051] As can be seen from Figures 6 - 10 , in all simulation results, the network efficiency curves of the four methods all continuously decline as the proportion of deleted edges increases. This is because the important edges in the network decrease, and the shortest distance between network nodes continuously increases. In a scale-free network, the parameters \(\alpha\) and \(\beta\) have a greater impact on the algorithm proposed in the embodiments of the present invention. This is due to the non-uniformity of the scale-free network. In a scale-free network, by adjusting the parameters \(\alpha\) and \(\beta\), a better effect of locating important edges can be achieved compared with the edge weight method, the edge betweenness method, and the method of randomly selecting edges. When the parameters \(\alpha\) and \(\beta\) are less than or equal to 0.5, the method proposed in the embodiments of the present invention can achieve the fastest decline in network efficiency, indicating that the method proposed in the embodiments of the present invention can locate the key edges in the network more accurately than the other three methods. In addition, it is worth noting that when the parameters \(\alpha\) and \(\beta\) are less than or equal to 0.5, the closer the value of the parameter is to 0.1, the more the efficiency curve of the algorithm proposed in the embodiments of the present invention declines compared with the other three methods. When the parameters \(\alpha\) and \(\beta\) are less than or equal to 0.1, the performance of the network curve is not further improved, and the change in the network efficiency curve is not significant. From the last two simulation result figures, it can be seen that when the parameter is less than 0.1, the performance of the proposed method is weaker than when the parameters \(\alpha\) and \(\beta\) are equal to 0.1. Therefore, for a scale-free network, the optimal solution is greater than 0.05 and less than 0.5.

[0052] When the parameters \(\alpha\) and \(\beta\) are set to 0.1 and 0.2, increase the number of network nodes. Set the number of network nodes in three communities to \(N_A = 1000\), \(N_B = 800\), \(N_C = 600\). The simulation diagram is as shown in Figure 11 . Obviously, after the network scale increases, the network efficiency curve obtained by the method proposed in the embodiments of the present invention is the optimal.

[0053] In a complex network, there are a large number of nodes, each node is connected to at least one edge, and the number of edges is even more massive. How to measure the importance of edges to optimize the network structure has always been a research hotspot. In the embodiments of the present invention, aiming at the problem of measuring the importance of edges in a complex network, an edge importance measurement index combining degree value and betweenness centrality index is proposed. This method comprehensively considers the degree value, betweenness, and edge betweenness of nodes, and introduces two variable parameters to adjust the index, and comprehensively designs an edge importance evaluation index, which can effectively evaluate the importance of edges under different network topologies. Finally, taking network efficiency as a measurement index, through simulation, it is proved that the index proposed in this paper can obtain a lower network efficiency than the edge betweenness method, edge weight method, and random edge selection method when deleting the same proportion of nodes, proving the effectiveness of the index proposed in this paper.

[0054] By adopting the embodiments of the present invention, the following beneficial effects are achieved:

[0055] The present invention conducts research on the problem of evaluating the importance of edges in a complex network. Based on three indicators: edge betweenness, the betweenness and degree values of the two end nodes of the edge, and two variables are introduced to design an edge importance evaluation method. In the present invention, the variables can be adjusted to adapt to changes in different network topologies. Finally, through simulation, taking the small-world network and scale-free network as examples, and using the edge weight method, edge betweenness method, and random edge selection method as comparison methods, it is verified that the present invention can more accurately locate the key edges in the network.

[0056] Device embodiments

[0057] According to the embodiments of the present invention, an apparatus for evaluating the importance of edges in a complex network is provided. Figure 2 For the schematic diagram of the apparatus for evaluating the importance of edges in a complex network according to the embodiments of the present invention, according to Figure 2 As shown, the apparatus for evaluating the importance of edges in a complex network according to the embodiments of the present invention specifically includes:

[0058] An evaluation index acquisition module 20, which acquires evaluation indexes for the nature of edges in a complex network;

[0059] The evaluation indexes for the nature of edges acquired by the evaluation index acquisition module include: the betweenness of the edge, the betweenness of the nodes of the edge, and the degree value of the edge nodes.

[0060] The evaluation index acquisition module 20 is specifically used for:

[0061] Calculating the degree value k of node v in the network i ; i ;

[0062] Calculating the number of shortest paths between any nodes in the network, and calculating the number of times that any node pair passes through node v iThe number of shortest paths between any pair of nodes passing through the connecting edge e ij The number of betweenness centrality B of all nodes in the network i ;

[0063] Calculate the connecting edge e ij Betweenness centrality of

[0064] The importance evaluation index acquisition module 22 constructs a connecting edge importance evaluation index according to the connecting edge property evaluation index;

[0065] The importance evaluation index acquisition module 22 is specifically used for:

[0066] Obtain the connecting edge importance evaluation index through Formula 1:

[0067]

[0068] Among them, B ij Is the connecting edge between node v i And node v j Between, B i And B j Is the betweenness centrality of node v i And node v j , k i And k j Are the degree values of two nodes, and α and β represent the adjustment parameters of the evaluation index.

[0069] The evaluation module 24 is used to evaluate the importance of the connecting edges in the complex network through the connecting edge importance evaluation index.

[0070] The importance evaluation index acquisition module 22 realizes the evaluation of the importance of connecting edges under different network topologies by adjusting the values of α and β.

[0071] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A complex network edge importance evaluation method, characterized by include: S1. Obtaining edge property evaluation indicators in complex networks; S2. constructing an edge importance evaluation index according to the edge property evaluation index; S3. The edge importance evaluation index is used to evaluate the edge importance of the complex network.

2. The method according to claim 1, characterized in that The edge property evaluation index includes: the betweenness of the edge, the betweenness of the edge nodes, and the degree of the edge nodes.

3. The method according to claim 1, characterized in that The S1 specifically includes: Calculate the node v in the network i The degree value k i ; Calculate the number of shortest paths between any nodes in the network, and calculate the number of shortest paths between any node pair in the network through node v i The number of nodes is calculated by the shortest path between any pair of nodes through the edge e ij , calculate the betweenness B of all nodes in the network i ; Calculate the edge e ij The betweenness of .

4. The method according to claim 1, characterized in that: The S2 specifically includes: The edge importance evaluation index is obtained through formula 1: Among them, B ij For node v i and node v j The edge between them, B i and B j is node v i and node v j The betweenness, k i and k j are the degree values ​​of the two nodes, and α and β represent the adjustment parameters of the evaluation index.

5. The method according to claim 4, characterized in that The method further comprises: By adjusting the values ​​of α and β, the importance of edges under different network topologies can be evaluated.

6. A complex network edge importance evaluation device, characterized in that: include: Evaluation index acquisition module, which obtains the evaluation index of edge properties in complex networks; An importance evaluation index acquisition module is used to construct an edge importance evaluation index according to the edge property evaluation index; An evaluation module is used to evaluate the importance of complex network edges through the edge importance evaluation index.

7. The device according to claim 6, characterized in that The edge property evaluation indicators acquired by the evaluation indicator acquisition module include: the betweenness of the edge, the betweenness of the edge nodes, and the degree values ​​of the edge nodes.

8. The device according to claim 6, characterized in that The evaluation index acquisition module is specifically used for: Calculate the node v in the network i The degree value k i ; Calculate the number of shortest paths between any nodes in the network, and calculate the number of shortest paths between any node pair in the network through node v i The number of nodes is calculated by the shortest path between any pair of nodes through the edge e ij , calculate the betweenness B of all nodes in the network i ; Calculate the edge e ij The betweenness of .

9. The device according to claim 6, characterized in that The importance evaluation index acquisition module is specifically used for: The edge importance evaluation index is obtained through formula 1: Among them, B ij For node v i and node v j The edge between them, B i and B j is node v i and node v j The betweenness, k i and k j is the degree value of the two nodes, α represents , and β represents .

10. The device according to claim 9, characterized in that The importance evaluation index acquisition module realizes edge importance evaluation under different network topologies by adjusting the values ​​of α and β.

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