CN107943882A - Network-critical node recognition methods based on side diffusivity K truss decomposition methods - Google Patents
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Abstract
The invention discloses the network-critical node recognition methods based on side diffusivity K truss decomposition methods, including step 1：Support SD (the e of each edge in calculating network Gij) and diffusivity DD (e to informationij)；Step 2：According to while support and diffusivity redefine while support SDV(eij)；Step 3：Filter out SD in networkV(eijThe side of)=0, and the network after renewal is denoted as G' and is；Step 4：To network G ' carry out K truss decomposition；Step 5：To network G ' continue to execute step 4, until all sides in network meet SDV(eij)≥K‑2；Step 6：Repeat step 4 is to step 5, until all sides in network are all deleted, all nodes are all decomposed truss layers corresponding；Step 7：Bigger according to K, also more important rule is ranked up node to its node truss layers corresponding.The present invention reduces time complexity while improving the accuracy that influence power node is found.
Description
Technical Field
The invention relates to a network important node identification method based on a side diffusivity K-tress decomposition method, and belongs to the technical field of influence node discovery methods in complex networks.
Background
With the rapid development of information technology, human living environments are also more networked, such as online social networks, communication networks, and scientific research cooperation networks for people-to-people communication; the internet, traffic networks, power networks, which are closely related to life; metabolic networks, neural networks, etc. associated with the person himself. The nodes have very important functions as indispensable components of the network, and the identification and protection of the key nodes are beneficial to improving the robustness of the network, so that a high-efficiency system structure is designed. Specifically, after the importance of a node is accurately evaluated, certain objectives can be achieved by performing some operations on key nodes. On one hand, the reliability and the survivability of the network can be effectively improved by strengthening the protection of the key nodes. For example, if a navigable city is affected by an emergency and falls into paralysis, all airlines connected to the navigable city will be cancelled at the same time, which may cause an airline interruption between other navigable cities in the airline network. Therefore, the key navigation city in the aviation network is accurately identified and protected, large-area delay and even paralysis of the aviation network caused by external interference can be effectively reduced, and safe and efficient operation of aviation transportation is guaranteed. On the other hand, the purpose of destroying the whole network can be achieved by carrying out attack operation on key nodes in the network. Therefore, it is very important to effectively evaluate the key nodes in the network.
Many research achievements have been made in response to the identification of key nodes in complex networks. The identification algorithm of the key node is increasingly perfected from simple neighbor number calculation to complex machine learning and information transmission. The currently existing methods are divided into two main categories by nature: one is based on the network topological structure characteristics, and is commonly known as degree centrality, betweenness centrality, approach centrality, K-core decomposition, H index and the like; another is a method based on continuous iterative refining, such as: eigenvectors, pageRank, leaderRank, HITS, SALSA centrality, and the like. Analyzing the structural characteristic information of the network is an important method for measuring the importance of the nodes, malliaros et al think that the topological properties of the nodes in the network also play a decisive role and have important significance for understanding the propagation capacity of the nodes, and provide a K-tress decomposition algorithm based on the thought, and introduce the support degree of the node connecting edges to identify the key nodes in the complex network. By using the K-tress decomposition algorithm, finer and denser subgraphs can be extracted from the network, and key nodes in the network are identified through the subgraphs, so that the method is more accurate and has lower time complexity. However, the K-tress decomposition is affected by the local clustering structure in the network, so that the error of the ordering result of the node importance is greatly increased.
In the K-core and K-tress decomposition methods, the diffusivity of the edges in the network is ignored, so that when a large number of topological structures with close connection between the edges exist in the network, the decomposition methods can be disabled, that is, the most important node set obtained by decomposition is a close-connected local community structure, and the range of virus or information propagation can be more limited to the interior of the community by the nodes. Therefore, for these networks, the most important nodes obtained by the K-core and K-tress decomposition methods are inaccurate. Aiming at the situation that a pseudo core structure which influences key node identification exists in a network, the invention identifies the most influential node by considering the diffusivity of edges, namely, the information of the initial moment reaches one node through one connecting edge, and the number of the nodes of the information is obtained for the first time in the nodes which can be reached by the information at the next moment. The support and the diffusivity of the connecting edge have advantages and disadvantages when identifying the key nodes, and the invention further researches the identification of the key nodes.
Disclosure of Invention
In order to solve the existing problems, the invention discloses a network important node identification method based on a side-diffusive K-tress decomposition method, which comprises the following specific technical scheme:
the network important node identification method based on the edge diffusivity K-tress decomposition method comprises the following steps:
step 1: calculating the support SD (e) of each edge in the network G ij ) And diffusion capability DD (e) for information ij ) Initialization parameter K =2, where K ∈ [2,K ∈ max ],K max Denoted as the largest tress layer;
and 2, step: redefining edge support according to edge support and diffusion capability
And 3, step 3: filtering out of the networkAnd marking the updated network as G';
and 4, step 4: performing K-tress decomposition on the network G', and firstly selecting the network with weight value satisfying Then delete the edge and form the other two sides of the triangle with the edgeCorrespondingly subtracting 1, and updating the network G';
and 5: step 4 is continued for the network G' until all edges in the network are satisfiedAdding the newly stripped isolated node of the current layer into a tress layer corresponding to the current K, and then updating K = K +1;
and 6: repeating the step 4 to the step 5 until all the connecting edges in the network are deleted and all the nodes are decomposed in the corresponding tress layers;
and 7: and sorting the nodes according to a rule that the more K is, the more important the nodes of the corresponding tress layer are.
SD (e) in said step 1 ij ) And DD (e) ij ) The calculation method of the transition probability comprises the following steps:
SD(e ij )＝|{Δ uvw ：Δ uvw ∈Δ G }| (1)
DD(e ij )＝d i→j +d j→i (2)
wherein in the formula (1), Δ uvw Representing a vertex of u, v, w triangle, Δ G Denotes the set of all triangles in the network G, SD (e) ij ) Represented in the network with edge e ij The number of the triangles forming different triangles is increased,
in the formula (2), d i→j The number of nodes except the common neighbor node of the node i and the node j in the neighbor nodes of the node j is shown after the information is spread from the node i at one end of the edge to the node j at the other end of the edge, and the same principle is that d j→i Indicating the ability of the information to diffuse from the opposite direction.
Redefining the support degree of the edge according to the support degree and the diffusion capacity of the edge in the step 2The specific formula of (A) is as follows:
SD(e ij )＝0.5*(k i +k j -2-DD(e ij )) (4)
wherein (3), alpha represents a relative importance factor between the support and the diffusivity of the measuring edge,
(4) Is represented byThe relationship between the support of edges and the ability of edges to spread information, k i Degree, k, representing node i j Which represents the degree of the node j,
(5) The expression is a relationship between the newly defined support degree and the initial support degree derived from the expressions (3) and (4).
Calculated according to step 2Selecting a side with a value of 0, and when the support or diffusion ability of one side is 0Namely 0, a large number of unimportant nodes and connecting edges in the network can be deleted through the step, and the time complexity of the algorithm is greatly reduced.
The specific process of performing K-tress decomposition on the network G' in the step 4 is as follows: firstly, a parameter initial value K =2 is carried out, then an edge with the support degree smaller than K-2 in the network is deleted, the support degrees of the other two edges forming a triangle with the edge are correspondingly reduced by 1, then the topology of the network is updated, the edge with the support degree smaller than K-2 is continuously deleted until the support degrees of all the edges in the network are larger than or equal to K-2, the currently stripped isolated node is added into a corresponding tress layer, at the moment, K is added with 1, and the edge with the support degree smaller than K-2 in the network is continuously deleted until the whole network is completely decomposed.
The beneficial effects of the invention are:
the invention can decompose the false core in the network, namely the network topology structure which influences the close connection of the identification important node, and identify the node which really has the most influence, thereby improving the identification accuracy. Meanwhile, when the method is used for identifying the most important node, relevant parameters do not need to be considered, and the parameters do not need to be adjusted along with different networks. Moreover, the method has stability and has better identification effect on various networks. Finally, in time complexity, the method utilizes local information of the network and adds an edge filtering strategy, so that the speed of identifying the most important node is relatively high.
Drawings
FIG. 1 is a simple network topology;
FIG. 2 is a flow chart of a method of the present invention;
FIG. 3-a is a comparison diagram of the influence function of each centrality index in a Dophins real network,
FIG. 3-b is a comparative diagram of the influence function of each centrality index in Polbooks real network,
FIG. 3-c is a comparative diagram of the influence function of each centrality index in a Football real network,
FIG. 3-d is a comparative diagram of the influence function of each centrality index in an Email real network,
FIG. 3-e is a comparative diagram of the influence function of each centrality index in a Netsccience real network,
FIG. 3-f is a comparative diagram of the influence function of each centrality index in a Geom real network.
Detailed Description
The invention is further elucidated with reference to the drawings and the detailed description. It should be understood that the following detailed description is illustrative of the invention only and is not intended to limit the scope of the invention.
The network important node identification method based on the edge diffusivity K-tress decomposition method comprises the following steps:
step 1: calculating the support SD (e) of each edge in the network G ij ) And diffusion capability DD (e) for information ij ) Initialization parameter K =2, where K ∈ [2,K max ],K max Denoted as the largest tress layer;
SD(e ij ) And DD (e) ij ) The calculation method of the transition probability comprises the following steps:
SD(e ij )＝|{Δ uvw ：Δ uvw ∈Δ G }| (1)
DD(e ij )＝d i→j +d j→i (2)
wherein in the formula (1), Δ uvw Representing a vertex of u, v, w triangle, Δ G Denotes the set of all triangles in the network G, SD (e) ij ) Represented in the network with edge e ij The number of the triangles forming different triangles is increased,
in the formula (2), d i→j The number of nodes except the common neighbor node of the node i and the node j in the neighbor nodes of the node j is shown after the information is spread from the node i at one end of the edge to the node j at the other end of the edge, and the same principle is that d j→i Indicating the ability of the information to diffuse from the opposite direction.
See FIG. 1, edge e 14 In two different triangles, thus SD (e) 14 ) And (5) =2. When information is propagated from node 1 to node 4, d 1→4 =1, propagation from node 4 to node 1 d 4→1 =0, therefore DD (e) 14 )＝1。
Step 2: redefining edge support according to edge support and diffusion capability
Redefining edge support according to edge support and diffusion capabilityThe specific formula of (A) is as follows:
SD(e ij )＝0.5*(k i +k j -2-DD(e ij )) (4)
wherein, in the formula (3), alpha represents a relative importance degree factor between the support and the diffusivity of the measurement edge,
(4) The expression represents the relationship between the support of the edge and the information diffusion capability of the edge, k i Degree, k, representing node i j Which represents the degree of the node t,
(5) The formula is a relationship between the newly defined support degree and the initial support degree derived from the formulas (3) and (4).
According to edge e 14 Support and diffusion of (2), defineWhen a =1, the signal is transmitted,where α =1 indicates that the support of the edge is as important as the diffusion capability.
And step 3: filtering out of the networkAnd marking the updated network as G';
calculated according to the previous stepSelecting a connection edge with a value of 0, and when the support or diffusion capability value of one edge is 0, thenNamely 0, a large number of unimportant nodes and connecting edges in the network can be deleted through the step, and the time complexity of the algorithm is greatly reduced.
And 4, step 4: performing K-tress decomposition on the network G', and firstly selecting the network with the weight value satisfying Then delete the edge and compare it withThe one side forming the other two sides of the triangleCorrespondingly subtracting 1, and updating the network G';
the K-tress decomposition process is that firstly, a parameter initial value K =2 is carried out, then an edge with the support degree smaller than K-2 in the network is deleted, the support degrees of the other two edges forming a triangle with the edge are correspondingly reduced by 1, then the topology of the network is updated, the edge with the support degree smaller than K-2 is continuously deleted until the support degrees of all the edges in the network are larger than or equal to K-2, and the currently stripped isolated node is added into a corresponding tress layer. At this time, K adds 1, and continues to delete the edge with the support degree smaller than K-2 in the network until the whole network is completely decomposed.
Table 1:
table 1 shows the results obtained by decomposing the network topology of fig. 1 by three different decomposition methods, K-shell, K-tress, and K-SD, where K-SD is the algorithm proposed by the present invention. From the decomposition result, it can be found that when the most important node is identified, the relatively unimportant node 1 can be removed from the most important node set {2,3,4}, and the identification result is more finely divided.
And 5: continuing to perform step 4 for network G' until all edges in the network are satisfiedAdding the newly stripped isolated node of the current layer into a tress layer corresponding to the current K, and then updating K = K +1;
and 6: repeating the steps 4 to 5 until all the connecting edges in the network are deleted and all the nodes are decomposed in the corresponding tress layers;
and 7: and sorting the nodes according to a rule that the more K is, the more important the nodes of the corresponding tress layer are.
In order to illustrate the superiority of the algorithm in the aspect of finding the influence nodes, the K-SD algorithm is compared with various classic algorithm Degree Centrality (DC), betweenness Centrality (BC), MDD, K-shell and K-reus.
Using the classical virus propagation model, the SIR propagation model measures the node propagation range. In the SIR model, users are generally divided into vulnerable nodes (S-state), infected nodes (propagation nodes, I-state) and immune nodes (R-state), and the propagation mechanism is as follows
If the S state individual is in the I state, the contact of the S state individual is infected into the I state with the probability lambda, and the infection node I recovers into the immune node R with the probability mu due to the self or external healing capacity and is not infected any more. When the system is stable in the SIR model, the network tends to have no I-state nodes, namely the I-state nodes are finally R-state nodes. The invention carries out 1000 SIR transmissions on each node in the network and measures the most real transmission influence of each node.
And (3) measuring the advantages and disadvantages of the centrality algorithms by introducing an influence function epsilon (p), wherein the expression of the influence function is as follows:
wherein p is the proportion of the selected nodes in the whole network nodes, M (p) represents the average influence of the first p x N nodes of the sequencing result obtained by each centrality algorithm, and N is the number of the nodes of the network. M ef (p) represents the mean of the true influence of the first p x N nodes. The smaller epsilon (p) indicates the more accurate the algorithm is in identifying the most important nodes.
Through simulation verification in six real networks, the parameters of each network are as follows:
table 2:
where N is the number of network nodes, E is the number of network edges,<K> is the network average, K max Is the maximum degree, C is the network average clustering coefficient,<d>, is the average shortest path of the network,is the propagation threshold.
In fig. 3, by analyzing the influence function of each different centrality index in six real networks, it can be found that the K-SD algorithm of the present invention has relatively stable performance in each network as a whole, and the closer the value of the influence function is to 0, the more consistent the ranking result obtained by the method of the present invention is with the ranking result of the real influence of the node. In Polboots and Email networks, the DC, MDD and K-SD algorithms have close performance, and the most important nodes can be better identified. Whereas in dopins, football, netscience and Geom networks, K-SD has the lowest impact function value when p ranges from 0 to 0.2, and especially in Netscience and Geom networks, the impact function epsilon (p) approaches 0, and the advantages of the algorithm of the present invention are more apparent. Therefore, the method has the characteristics of high accuracy in identifying the most important node, relatively stable performance and low time complexity for each network.
The technical means disclosed by the scheme of the invention are not limited to the technical means disclosed by the technical means, and the technical means also comprises the technical scheme formed by any combination of the technical features.
In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.
Claims (5)
1. The network important node identification method based on the edge diffusivity K-tress decomposition method is characterized by comprising the following steps of:
step 1: calculating the support degree SD (e) of each edge in the network G ij ) And diffusion capability DD (e) for information ij ) Initialization parameter K =2, where K ∈ [2,K ∈ max ],K max Denoted as the largest tress layer;
step 2: redefining edge support according to edge support and diffusion capability
And step 3: filtering out of the networkAnd marking the updated network as G';
and 4, step 4: performing K-tress decomposition on the network G', and firstly selecting the network with the weight value satisfying Then delete the edge and form the other two sides of the triangle with the edgeCorrespondingly subtracting 1, and updating the network G';
and 5: continuing to perform step 4 for network G' until all edges in the network are satisfiedAdding the newly stripped isolated node of the current layer into a tress layer corresponding to the current K, and then updating K = K +1;
and 6: repeating the step 4 to the step 5 until all the connecting edges in the network are deleted and all the nodes are decomposed in the corresponding tress layers;
and 7: and sequencing the nodes according to the rule that the more K, the more important the nodes of the corresponding tress layer are.
2. The method for identifying important nodes in network based on edge-diffusivity K-tress decomposition method as claimed in claim 1, wherein SD (e) in step 1 ij ) And DD (e) ij ) The calculation method of the transition probability comprises the following steps:
SD(e ij )＝|Δ uvw ：Δ uvw ∈Δ G }|(1)
DD(e ij )＝d i→j +d j→i (2)
wherein in the formula (1), Δ uvw Representing a vertex of u, v, w triangle, Δ G Denotes the set of all triangles in the network G, SD (e) ij ) Represented in the network with edge e ij The number of the triangles forming the triangle is different,
in the formula (2), d i→j Indicating the number of nodes except the common neighbor node of the node i and the node j in the neighbor nodes of the node j after the information is spread from the node i at one end of the edge to the node j at the other end of the edge, and the same principle is that d j→i Indicating the ability of the information to diffuse from the opposite direction.
3. The method for identifying important nodes in a network based on the edge diffusivity K-tress decomposition method as claimed in claim 1, wherein the step 2 redefines the support degree of the edge according to the support degree and diffusivity of the edgeThe specific formula of (A) is as follows:
SD(e ij )＝0.5*(k i +k j -2-DD(e ij ))(4)
wherein (3), alpha represents a relative importance factor between the support and the diffusivity of the measuring edge,
(4) The expression represents the relationship between the support of the edge and the information diffusion capability of the edge, k i Degree, k, representing node i j Which represents the degree of the node j and,
(5) The expression is a relationship between the newly defined support degree and the initial support degree derived from the expressions (3) and (4).
4. The method for identifying important nodes in network based on edge diffusivity K-tress decomposition method as claimed in claim 1, wherein the important nodes are calculated according to step 2Selecting a connection edge with a value of 0, and when the support or diffusion capability value of one edge is 0, thenNamely 0, a large number of unimportant nodes and connecting edges in the network can be deleted through the step, and the time complexity of the algorithm is greatly reduced.
5. The method for identifying important nodes in a network based on the edge diffusion K-tress decomposition method according to claim 1, wherein the specific process of performing K-tress decomposition on the network G' in the step 4 is as follows: firstly, a parameter initial value K =2 is carried out, then an edge with the support degree smaller than K-2 in the network is deleted, the support degrees of the other two edges forming a triangle with the edge are correspondingly reduced by 1, then the topology of the network is updated, the edge with the support degree smaller than K-2 is continuously deleted until the support degrees of all the edges in the network are larger than or equal to K-2, the currently stripped isolated node is added into a corresponding tress layer, at the moment, K is added with 1, and the edge with the support degree smaller than K-2 in the network is continuously deleted until the whole network is completely decomposed.
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| CN109995593A (en) * | 2019-04-09 | 2019-07-09 | 重庆邮电大学 | The setting of IOBT key node and diffusance equalization methods |
| CN110826003A (en) * | 2019-11-01 | 2020-02-21 | 陕西师范大学 | Illegal or harmful network information propagation control method based on edge deletion cluster |
| CN112950451A (en) * | 2021-03-26 | 2021-06-11 | 北京理工大学 | GPU-based maximum k-tress discovery algorithm |
| WO2021208238A1 (en) * | 2020-04-14 | 2021-10-21 | 中山大学 | K-truss graph-based storage system cache prefetching method, system, and medium |
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| CN109995593A (en) * | 2019-04-09 | 2019-07-09 | 重庆邮电大学 | The setting of IOBT key node and diffusance equalization methods |
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| CN110826003A (en) * | 2019-11-01 | 2020-02-21 | 陕西师范大学 | Illegal or harmful network information propagation control method based on edge deletion cluster |
| CN110826003B (en) * | 2019-11-01 | 2022-05-17 | 陕西师范大学 | Illegal or harmful network information propagation control method based on edge deletion cluster |
| WO2021208238A1 (en) * | 2020-04-14 | 2021-10-21 | 中山大学 | K-truss graph-based storage system cache prefetching method, system, and medium |
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