CN109728955A - Based on the network node sort method for improving k-shell - Google Patents
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Abstract
The invention belongs to complex network technical fields, are related to a kind of based on the network node sort method for improving k-shell.In the case where given network adjacent matrix, the present invention is based on the key node recognition methods that k-shell and node entropy propose a kind of optimization.This method considers the propagation effect of the neighbor node of network, and identical two nodes of former k core value can also distinguish significance level.The higher core value the more important between different stratum nucleares, passes through the significance level for considering neighbor node to it between identical stratum nucleare, and the bigger node of node entropy is more important.This method computation complexity is identical as k-shell, therefore can be adapted for catenet.The experimental results showed that this method performance in the node importance evaluation to live network USAir (US Airways network) is more preferable than degree centrality (DC), betweenness center (BC), degree of approach centrality (CC), method of the invention can efficiently identify out key node, algorithm is simple, works well.
Description
Technical field
The invention belongs to complex network technical fields, are related to a kind of based on the network node sort method for improving k-shell.
Background technique
In complex network key node identification be always an important subject, fight crime, information propagate etc.
Aspect has important application, therefore we need to find a kind of sort method of key node.For the sequence of nodes
Strategy, there are many methods at present.Based on local attribute's degree of having and degree centrality, had in betweenness and the degree of approach based on global property
Disposition, the method based on network site attribute have k- core method, degree of mixing decomposition method, and the method based on random walk attribute has
PageRank, LeaderRank, HITS method etc..The k- core (k-shell) that wherein Kitsak is proposed is a kind of simple and effective
Method, this method peel off the node of outer layer layer by layer, the influence power with higher of the node in internal layer.Detailed process are as follows:
If there is 1 degree of vertex in network, node and its even side removal these degree for 1, if still there is 1 degree of node in network,
Again by these 1 degree of knot-removal, this process is repeated until not having 1 degree of node in network.At this point, all nodes being stripped are called
1-shell.Then the node that searching degree is 2, the knot removal for being 2 remaining node degree continue if there are also degree for 2 node
It deletes, until there is no 2 degree of nodes in network.The node of this process removal is 2-shell.As procedure described above, continue to remove
Node, obtains 3-shell, and 4-shell ... has the k-shell layer of oneself until nodes all in network.K-shell is decomposed
Method computation complexity is low, however the method has many limitations:
(1) it can not be applied in many networks, such as binary tree, star network；
(2) node importance with identical nucleus number cannot be distinguished, because network node is divided into k layers by this method, often
One node layer k nucleus number is identical.Since k-shell index is without providing enough node topographical location information, so it is assumed that institute
There is the extended capability all having the same of the node with identical k-shell, research shows that this is inaccurate；
(3) this method thinks that key node is located at highest stratum nucleare, and actually outer node layer is it could also be possible that key node.
Although such as in Fig. 2 interior joint 23 in 3-shell, it is the only way which must be passed towards other 10 nodes, using original
K-shell method can only identify that the node 1,2,3,4 in 1-shell is key node, cannot select node 23.
It for above disadvantage, needs to improve former k-shell method, comprehensively considering position and neighbor node influences
The factors such as power, the importance of different nodes can be assessed by finding a kind of improved k-shell method.
Summary of the invention
Present invention aims at the deficiency for improving existing k-shell sort method, provide it is a kind of decomposed using k-shell and
The key node sort method of information of neighbor nodes, referred to as IKS method.It, can be than original k- by improved IKS method
Shell decomposition method is more accurate and efficient.
Provided technical solution comprises the following steps the present invention to solve above-mentioned technical problem.
Assuming that figure G=(V, E) is a undirected and unweighted network, including n node and m side, V={ v1,v2,……
vnRepresent node set, E={ e1,e2,……emRepresent line set.According to whether having Bian Xianglian, the adjoining of network G between node
Matrix A can indicate are as follows: A=[aij]n×n, wherein
Node viDegree be expressed as ki, it is defined as and node viThe number for the neighbor node being connected directly, is expressed mathematically as
In order to distinguish the importance of identical k core value node, the first concept of definition node entropy, by the sparse adjoining of network
Matrix A obtains the degree k of each nodeiAnd relative Link Importance Ii, whereinN is the number of nodes of network.Then net
The node entropy of network is defined asWherein j ∈ Γ (i) indicates node viNeighbor node collection.The calculating of above formula
Having measured surroundings nodes from the angle of the unordered degree of network is to keep propagating and the energy time of investment with the information of node.
The step of IKS method, is as follows:
1, the degree k of each node is calculated by the sparse adjacency matrix A of networkiAnd relative Link Importance Ii。
2, the node entropy of network is calculatedIt is what the node provided that node entropy, which characterizes neighbor node,
Transmission capacity.
3, the decomposition level of each node of network is obtained according to k-shell method.
4, since top (highest shell), the maximum node of this level interior joint entropy is chosen as first
Key node, then choose time high-rise maximum node of interior joint entropy as second key node ... and repeat this process until choosing
To the maximum node of 1-shell level interior joint entropy.At this point, first round iteration terminates.
5, the second wheel iteration is successively chosen, according to the process of the 4th step until 1-shell level.If in a certain level
It is available without node, then it skips.IKS method process terminates until nodes all in network have all selected.
Improved IKS method is on the basis of former k-shell, in conjunction with the concept of node entropy, takes node in each layer choosing
The big point of entropy is as key node.Node entropy considers the influence of neighbor node, and the information relative to only consideration node itself is more
Add sufficiently.The key node that IKS method is selected can make propagation information more dispersed, to assess calculation side than the Kitsak k proposed
Method is more acurrate.This method is not only able to the importance of correct evaluation node in a network, can also be transmission of pathogen, community network
Important node is found in equal networks.
Beneficial effects of the present invention:
In the case where given network adjacent matrix, the present invention is based on the passes that k-shell and node entropy propose a kind of optimization
Key node recognition methods.This method considers the propagation effect of the neighbor node of network, identical two nodes of former k core value
Significance level can be distinguished.The higher core value the more important between different stratum nucleares, by considering neighbor node pair between identical stratum nucleare
Its significance level, the bigger node of node entropy are more important.This method computation complexity is identical as k-shell, therefore can be applicable in
In catenet.The experimental results showed that this method is evaluated in the node importance to live network USAir (US Airways network)
More preferably than degree centrality (DC), betweenness center (BC), degree of approach centrality (CC), method of the invention can be effective for middle performance
Ground identifies key node, and algorithm is simple, works well.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is that IKS method calculates schematic diagram；
Fig. 3 is two methods schematic illustration, and (a) is k-shell method, (b) is IKS method；
Fig. 4 is USAir network topology structure；
Fig. 5 is the SIR emulation of infection rate at any time on USAir network；
Fig. 6 is that infection rate is emulated with the SIR of primary infection node on USAir network.
Specific embodiment
The present invention will be described in detail with simulated example with reference to the accompanying drawing, so that those skilled in the art can be more
Understand the present invention well.
The present invention is based on key node sort method IKS in the complex network of the optimization of k-shell and node entropy include with
Lower step:
Input: the adjacency matrix A=[a of networkij]n×n, whereinAccording to
The topological structure of Fig. 2 exemplary network obtains the adjacency matrix of the network are as follows:
Step 1: according to the definition of network moderateThe degree for obtaining node is
K=[5 844422411111131211111812 1]；
Step 2: the degree as obtained in step 1 calculates the relative Link Importance I of each nodei, whereinN is net
The number of nodes of network；
Step 3: calculating the node entropy of networkWherein j ∈ Γ (i) indicates node viNeighbor node
Collection.
Calculated result is shown in Table 1；
Step 4: 1 degree of node gradually being removed by k-shell method, 2 degree of nodes obtain 3 stratum nucleares of Fig. 2 network, each
Level has marked in Fig. 2；
Step 5: node selection strategy: it is maximum in the node entropy of 3-shell interior joint 2, therefore node 2 is chosen first, in 2-
It is node 5 that it is maximum that node entropy is chosen in shell, node 23 is chosen in 1-shell, then first round iterative process terminates.
Table 1k core and node entropy calculated result
Step 6: according to step 5, successively iteration chooses remaining node.Second wheel iteration, chooses node 1 in 3-shell,
Node 8 is chosen in 2-shell, and node 17 is chosen in 1-shell.Then the second wheel iteration terminates.This process is repeated, if should
Stratum nucleare node has all been chosen, then skips the stratum nucleare.The key node ranking results that last Fig. 2 network obtains be 2,5,23,
1,8,17,4,6,11,3,7,12,16,18,19,20,21,22,15,25,9,10,26,13,14,24}。
From fig. 2 it can be seen that if all nodes only have 3 kinds of different weights in network with the method for original k-shell
The property wanted, and this far from meets the requirements.After improving k-shell method, all nodes all have different weights
The property wanted meets our requirement.In addition, can see from result, preceding 4 key nodes that IKS is obtained are 2,5,23,1 distributions
Relatively disperse, avoid the overlapping of propagation effect, propagation effect can be made to maximize.
The ranking results and conventional method degree centrality (DC), degree of approach centrality (CC), betweenness that this patent method obtains
The ranking results that centrality (BC), k-shell method obtain make comparisons and (take preceding 10 nodes), as a result as shown in the table.
The ranking results of 2 five kinds of methods of table
By comparing to network node top ten list ranking results in table 2, discovery ranking has little bit different, main cause
It is every kind of Method And Principle difference.Improved k-shell method main purpose is to avoid the overlapping of propagation effect herein, expands shadow
It rings, schematic diagram is as shown in Figure 3.Assuming that using first four node in Fig. 2 exemplary network as key node, grayed-out nodes in Fig. 3
It indicates key node (as the source of infection in SIR), propagation effect ability of the red circle as infection node, left figure k-
Propagation effect of the shell method interior joint 1,2,3,4 as key node, right figure are 2,5,23,1 conduct of IKS method interior joint
The propagation effect of key node, the node in red area are infected.It can be seen that the infection section that k-shell method is newly-increased
Point is 5,6,7,8, and IKS newly-increased infection node is 3,4,6,16,17,18,19,20,22.Therefore IKS infection node is more, sense
Dye source relative distribution can be to avoid the overlapping of transmission capacity.
In addition, verifying on live network USAir to the method for the present invention, and mould is carried out using SIR Epidemic Model
Quasi- analysis.USAir network is US Airways network, and topological structure is shown in Fig. 4, shares 332 airports as network node, airport it
Between 2461 flight routes as side, obtain corresponding adjacency matrix.Before being obtained using ranking results 2% node as infection
Source draws infection rate versus time curve such as Fig. 5 on network.Change primary infection number of nodes, propagates sense when stablizing
Dye rate is as shown in Figure 6 with the change curve of primary infection node.It can be seen that, methods herein is when each from the above figure
It carves, finally the infection rate at stable moment is above other methods, it was demonstrated that effectiveness of the invention.
Claims (1)
1. based on the network node sort method for improving k-shell, definition figure G=(V, E) is a undirected and unweighted network, wherein
Including n node and m side, V={ v1,v2,……vnRepresent node set, E={ e1,e2,……emRepresent line set；Root
According to whether there is Bian Xianglian between node, the adjacency matrix A of network G is indicated are as follows: A=[aij]n×n, wherein
Node viDegree be expressed as ki, it is defined as and node viThe number for the neighbor node being connected directly, is expressed mathematically as
Definition node entropy is used to distinguish the importance of identical k core value node: obtaining each section by the sparse adjacency matrix A of network
The degree k of pointiAnd relative Link Importance Ii, whereinN is the number of nodes of network, then the node entropy of network is defined asWherein j ∈ Γ (i) indicates node viNeighbor node collection；It is characterized in that, the sort method includes
Following steps:
S1, the degree k that each node is calculated by the sparse adjacency matrix A of networkiAnd relative Link Importance Ii；
S2, the node entropy for calculating networkIt is the propagation that the node provides that node entropy, which characterizes neighbor node,
Ability；
S3, the decomposition level of each node of network is obtained according to k-shell method；
S4, node selection: it is maximum to choose this level interior joint entropy since top for the network layer obtained according to step S3
Node as first key node, then choose time the high-rise maximum node of interior joint entropy as second key node ...
This process is repeated until choosing the maximum node of 1-shell level interior joint entropy；At this point, first round iteration terminates；
S5, the second wheel iteration is carried out according to the method for step S4, remaining node is successively chosen, until 1-shell level；If certain
It is available without node in one level, then it skips；The step is repeated until all nodes have all selected in network.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111428323A (en) * | 2020-04-16 | 2020-07-17 | 太原理工大学 | Method for identifying group of key nodes by using generalized discount degree and k-shell in complex network |
| CN111934915A (en) * | 2020-07-17 | 2020-11-13 | 合肥本源量子计算科技有限责任公司 | Network node sequencing display method and device |
| CN112087488A (en) * | 2020-08-03 | 2020-12-15 | 济南浪潮高新科技投资发展有限公司 | Method, device, equipment and medium for determining important cloud robot nodes |
| CN113780436A (en) * | 2021-09-15 | 2021-12-10 | 中国民航大学 | Complex network key node identification method based on integration degree |
| CN115643179A (en) * | 2022-12-23 | 2023-01-24 | 上海蜜度信息技术有限公司 | Block chain node propagation influence measuring method and system, storage medium and terminal |
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2019
- 2019-01-04 CN CN201910007600.3A patent/CN109728955A/en active Pending
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| AHMAD ZAREIE 等: "Influential nodes ranking in complex networks: An entropy-based approach", 《CHAOS, SOLITONS & FRACTALS》 * |
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111428323A (en) * | 2020-04-16 | 2020-07-17 | 太原理工大学 | Method for identifying group of key nodes by using generalized discount degree and k-shell in complex network |
| CN111428323B (en) * | 2020-04-16 | 2023-06-23 | 太原理工大学 | Method for identifying a group of key nodes in complex network by using generalized discount degree and k-shell |
| CN111934915A (en) * | 2020-07-17 | 2020-11-13 | 合肥本源量子计算科技有限责任公司 | Network node sequencing display method and device |
| CN112087488A (en) * | 2020-08-03 | 2020-12-15 | 济南浪潮高新科技投资发展有限公司 | Method, device, equipment and medium for determining important cloud robot nodes |
| CN112087488B (en) * | 2020-08-03 | 2023-08-25 | 山东浪潮科学研究院有限公司 | Method, device, equipment and medium for determining important cloud robot nodes |
| CN113780436A (en) * | 2021-09-15 | 2021-12-10 | 中国民航大学 | Complex network key node identification method based on integration degree |
| CN113780436B (en) * | 2021-09-15 | 2024-03-05 | 中国民航大学 | Complex network key node identification method based on comprehensive degree |
| CN115643179A (en) * | 2022-12-23 | 2023-01-24 | 上海蜜度信息技术有限公司 | Block chain node propagation influence measuring method and system, storage medium and terminal |
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Application publication date: 20190507 |