CN105471637A - Evaluation method and system for importance of node of complex network - Google Patents
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Abstract
The invention provides an evaluation method and system for importance of a node of a complex network. The method comprises: K nucleus decomposition is carried out on a given complex network and iteration information and each node Ks value during the decomposition process are kept; according to the iteration information and each node Ks value, a K nucleus iteration factor of each node is calculated; and according to the K nucleus iteration factors of the nodes, importance of a complex network is calculated. According to the invention, the iteration information during the K nucleus decomposition process is fully utilized and the importance of the complex network node can be evaluated accurately in detail. Moreover, the time complexity is low; the large-scale complex network can be evaluated rapidly; and the adaptability is high.
Description
Technical field
The invention belongs to Complex Networks Analysis technical field, relate to a kind of complex network node importance appraisal procedure and system, particularly relate to a kind of complex network node importance appraisal procedure based on K core iteration factor and system.
Background technology
The importance of accurate tolerance Node Contraction in Complex Networks for prevention network attack, prevent infectious disease popular and suppress there is very important meaning and function in the diffusion of rumor in society etc. in crowd.Node importance appraisal procedure roughly can be divided three classes: local approach, method of overall importance and the method based on random walk.Node degree is a kind of typical local approach.Local approach generally calculates simply, and complexity is low, but have ignored the global structure information of network, is difficult to embody node importance in the entire network.Network size is larger, and the defect of local approach is more obvious.Typical method of overall importance comprises characteristic vector, tightness and betweenness etc.Although method of overall importance can assess the importance of node exactly, due to information such as shortest paths between needs computing node, cause complexity very high, be not suitable for large-scale complex network.Typical random walk method comprises PageRank, LeaderRank and HITS etc., and these class methods are also assess from the importance of overall angle to complex network node, and complexity is higher, and mainly for directed networks.
The people such as Kitsak depend on its position in the entire network in article " Identificationofinfluentialspreadersincomplexnetworks " the middle finger egress importance being published in " NaturePhysics " periodical in 2010, and propose the complex network node importance appraisal procedure based on K nuclear decomposition.The method can rapid evaluation node importance, and complexity is low, goes for large scale network.But the maximum defect of the method is to give identical Ks value to a lot of node, cannot do further to distinguish to the importance of these nodes.
In recent years, many scholars expanded K nuclear decomposition method and improved, and make its range of application wider, accuracy is better.But so far, all improvement to K nuclear decomposition method all have ignored the iterative information produced in decomposable process, these information have a very important role and meaning to node importance assessment.Suppose that two nodes have identical Ks value, according to the theory of Kitsak, these two nodes have identical importance.Node importance depends on its position in the entire network.If they not with in an iteration deleted fall, illustrate that the position of two nodal distance network core nodes is different, they should have different importance.If make full use of the iterative information produced in K nuclear decomposition process, the importance of the node with identical Ks value just can be distinguished further.
Summary of the invention
The existing node importance appraisal procedure based on K nuclear decomposition ignores the shortcoming of iterative information in view of the above, the object of the present invention is to provide a kind of complex network node importance appraisal procedure and system, iterative information is ignored for solving the existing node importance appraisal procedure based on K nuclear decomposition, and the problem such as the importance effectively cannot distinguishing the node with identical Ks value.
For achieving the above object and other relevant objects, the invention provides a kind of complex network node importance appraisal procedure, described complex network node importance appraisal procedure comprises:
K nuclear decomposition is carried out to given complex network, the iterative information in preservation decomposable process and the Ks value of each node;
According to the Ks value of described iterative information and each node, calculate the K core iteration factor of each node;
According to described K core iteration factor, calculate the importance of each node.
Preferably, the computational methods of described node K core iteration factor comprise:
wherein,
for arbitrary node n in complex network
ik core iteration factor; K is K nuclear decomposition process interior joint n
ithe Ks value be endowed; M is that in K nuclear decomposition process, angle value is the total degree of the iterative operation of k; In this m time iterative operation, node n
ibe removed when n-th iteration, 1≤n≤m.
Preferably, the computational methods of described node importance comprise:
wherein,
for arbitrary node n in complex network
iimportance;
for node n
ik core iteration factor;
for node n
iangle value; N
ifor node n
ineighbor node set; n
jfor node n
ineighbor node, n
j∈ N
i;
for node n
jk core iteration factor;
for node n
jangle value.
The present invention also provides a kind of complex network node importance evaluating system, and described complex network node importance evaluating system comprises:
K nuclear decomposition module, carries out K nuclear decomposition to given complex network, and the Ks value of the iterative information preserved in decomposable process and each node;
Node K core iteration factor computing module, is connected with described K nuclear decomposition module, and the iterative information produced according to K nuclear decomposition and the Ks value of each node, calculate the K core iteration factor of each node;
Node importance computing module, is connected with described node K core iteration factor computing module, according to described K core iteration factor, calculates the importance of each node.
Preferably, the computing function of described node K core iteration factor computing module is:
wherein,
for arbitrary node n in complex network
ik core iteration factor; K is K nuclear decomposition process interior joint n
ithe Ks value be endowed; M is that in K nuclear decomposition process, angle value is the total degree of the iterative operation of k; In this m time iterative operation, node n
ibe removed when n-th iteration, 1≤n≤m.
Preferably, the computing function of described node importance computing module is:
wherein,
for arbitrary node n in complex network
iimportance;
for node n
ik core iteration factor;
for node n
iangle value; N
ifor node n
ineighbor node set; n
jfor node n
ineighbor node, n
j∈ N
i;
for node n
jk core iteration factor;
for node n
jangle value.
As mentioned above, complex network node importance appraisal procedure of the present invention and system, have following beneficial effect:
The present invention makes full use of the iterative information in K nuclear decomposition process, effectively can distinguish the importance of the node with identical Ks value.Node K core iteration factor is an index of overall importance, and node degree is a local parameter, and the present invention considers this two factors simultaneously, can assess node importance more exactly.The present invention has lower time complexity, can fast and effeciently process large-scale complex network data, have very strong adaptability.
Accompanying drawing explanation
Fig. 1 is the schematic flow sheet of complex network node importance appraisal procedure of the present invention.
Fig. 2 is the structural representation of complex network node importance evaluating system of the present invention.
Fig. 3 is a simple examples topology of networks schematic diagram.
The CCDF CCDF schematic diagram that Fig. 4 is network shown in Fig. 3.
Fig. 5 is the CCDF CCDF schematic diagram of Karateclub network.
Fig. 6 is the CCDF CCDF schematic diagram of Dolphin network.
Fig. 7 is the CCDF CCDF schematic diagram of NetScience network.
The discrimination index change schematic diagram of different node importance appraisal procedure when Fig. 8 is the n Parameters variation of LFR network generator.
The discrimination index change schematic diagram of different node importance appraisal procedure when Fig. 9 is the μ Parameters variation of LFR network generator.
The discrimination index change schematic diagram of different node importance appraisal procedure when Figure 10 is the k Parameters variation of LFR network generator.
The discrimination index change schematic diagram of different node importance appraisal procedure when Figure 11 is the γ Parameters variation of LFR network generator.
Element numbers explanation
S1 ~ S3 step
200 node importance evaluating systems
210K nuclear decomposition module
220 node K core iteration factor computing modules
230 node importance computing modules
Embodiment
Below by way of specific instantiation, embodiments of the present invention are described, those skilled in the art the content disclosed by this specification can understand other advantages of the present invention and effect easily.The present invention can also be implemented or be applied by embodiments different in addition, and the every details in this specification also can based on different viewpoints and application, carries out various modification or change not deviating under spirit of the present invention.
Refer to accompanying drawing.It should be noted that, the diagram provided in the present embodiment only illustrates basic conception of the present invention in a schematic way, then only the assembly relevant with the present invention is shown in graphic but not component count, shape and size when implementing according to reality is drawn, it is actual when implementing, and the kenel of each assembly, quantity and ratio can be a kind of change arbitrarily, and its assembly layout kenel also may be more complicated.
Below in conjunction with accompanying drawing, the present invention is described in detail.
The invention provides a kind of complex network node importance appraisal procedure, as shown in Figure 1, described complex network node importance appraisal procedure comprises:
S1, carries out K nuclear decomposition to given complex network, the iterative information in preservation decomposable process and the Ks value of each node.
S2, according to the Ks value of described iterative information and each node, calculates the K core iteration factor of each node.
Further, the computational methods of described node K core iteration factor comprise:
wherein,
for arbitrary node n in complex network
ik core iteration factor; K is K nuclear decomposition process interior joint n
ithe Ks value be endowed; M is that in K nuclear decomposition process, angle value is the total degree of the iterative operation of k; In this m time iterative operation, node n
ibe removed when n-th iteration, 1≤n≤m.Wherein, described angle value refers to nodes the most adjacent around each node.
S3, according to described K core iteration factor, calculates the importance of each node.
Further, the computational methods of described node importance comprise:
wherein,
for arbitrary node n in complex network
iimportance;
for node n
ik core iteration factor;
for node n
iangle value; N
ifor node n
ineighbor node set; n
jfor node n
ineighbor node, n
j∈ N
i;
for node n
jk core iteration factor;
for node n
jangle value.
Protection scope of the present invention is not limited to the described step execution sequence based on the complex network node importance appraisal procedure of K core iteration factor, and the node importance appraisal procedure after every principle according to the present invention makes the distortion of any form is all included in protection scope of the present invention.
The present invention also provides a kind of complex network node importance evaluating system, this system can realize complex network node importance appraisal procedure of the present invention, but the implement device of complex network node importance appraisal procedure of the present invention includes but not limited to complex network node importance evaluating system of the present invention.
As shown in Figure 2, described complex network node importance evaluating system 200 comprises: K nuclear decomposition module 210, node K core iteration factor computing module 220, node importance computing module 230.
Described K nuclear decomposition module 210 carries out K nuclear decomposition to input complex network, and the Ks value of the iterative information preserved in decomposable process and each node.
Described node K core iteration factor computing module 220 is connected with described K nuclear decomposition module 210, and the iterative information produced according to K nuclear decomposition and the Ks value of each node, calculate the K core iteration factor of each node.Further, the computing function of described node K core iteration factor computing module is:
Wherein,
for arbitrary node n in complex network
ik core iteration factor; K is K nuclear decomposition process interior joint n
ithe Ks value be endowed; M is that in K nuclear decomposition process, angle value is the total degree of the iterative operation of k; In this m time iterative operation, node n
ibe removed when n-th iteration, 1≤n≤m.
Described node importance computing module 230 is connected with described node K core iteration factor computing module 220, according to the K core iteration factor of described node, calculates the importance of each node.Further, the computing function of described node importance computing module is:
Wherein,
for arbitrary node n in complex network
iimportance;
for node n
ik core iteration factor;
for node n
iangle value; N
ifor node n
ineighbor node set; n
jfor node n
ineighbor node, n
j∈ N
i;
for node n
jk core iteration factor;
for node n
jangle value.
The present invention ignores the shortcoming of iterative information in view of the node importance assessment technology based on K nuclear decomposition, provide a kind of complex network node importance appraisal procedure and system, iterative information is ignored for solving the existing node importance appraisal procedure based on K nuclear decomposition, and the problem such as the importance effectively cannot distinguishing the node with identical Ks value.The present invention makes full use of the iterative information in K nuclear decomposition process, effectively can distinguish the importance of the node with identical Ks value.Node K core iteration factor is an index of overall importance, and node degree is a local parameter, and the present invention considers this two factors simultaneously, can assess node importance more exactly.The present invention has lower time complexity, can fast and effeciently process large-scale complex network data, have very strong adaptability.
Below in conjunction with embodiment and accompanying drawing, the present invention is further described in detail.
Embodiment one
The present embodiment for a simple examples network, by the importance of complex network node importance appraisal procedure provided by the invention for assessment of this network node.The topological structure of example network as shown in Figure 3, comprises 17 nodes.The present embodiment utilizes described complex network node importance appraisal procedure to carry out node importance assessment to the example network shown in Fig. 3, specifically comprises the following steps:
1) K nuclear decomposition is carried out to given example network, the iterative information in preservation decomposable process and the Ks value of each node.The K nuclear decomposition information of example network is in table 1.
Table 1: the K nuclear decomposition information of example network
| Angle value | Iteration number | Remove node | Node Ks value |
| 1 | 1 | 1,2,3,5,9,14,17 | 1 |
| 1 | 2 | 4,16 | 1 |
| 2 | 1 | 6 | 2 |
| 2 | 2 | 7,8,15 | 2 |
| 3 | 1 | 10,11,12,13 | 3 |
2) according to the iterative information of K nuclear decomposition generation and the Ks value of each node, the K core iteration factor of each node is calculated.According to K core iteration factor computational methods of the present invention, the K core iteration factor of the example network node calculated is in table 2.
Table 2: the K core iteration factor of example network node
| Node serial number | K core iteration factor | Node serial number | K core iteration factor |
| 1 | 1.5 | 10 | 6.0 |
| 2 | 1.5 | 11 | 6.0 |
| 3 | 1.5 | 12 | 6.0 |
| 4 | 2.0 | 13 | 6.0 |
| 5 | 1.5 | 14 | 1.5 |
| 6 | 3.0 | 15 | 4.0 |
| 7 | 4.0 | 16 | 2.0 |
| 8 | 4.0 | 17 | 1.5 |
| 9 | 1.5 |
3) according to the K core iteration factor of node, the importance of each node is calculated.According to node importance computational methods of the present invention, the importance of the example network node calculated is in table 3.
Table 3: the importance of example network node
| Node serial number | Importance | Node serial number | Importance |
| 1 | 9.3333 | 10 | 127.3333 |
| 2 | 6.3333 | 11 | 102.0000 |
| 3 | 6.3333 | 12 | 114.0000 |
| 4 | 15.6667 | 13 | 114.0000 |
| 5 | 9.3333 | 14 | 37.3333 |
| 6 | 27.6667 | 15 | 63.3333 |
| 7 | 68.0000 | 16 | 16.6667 |
| 8 | 61.3333 | 17 | 4.6667 |
| 9 | 13.3333 |
Can be found by table 3, nearly all example network node has all been endowed different importance.Well the importance of example network node can be distinguished by complex network node importance appraisal procedure of the present invention, demonstrate validity of the present invention thus.
Embodiment two
Described complex network node importance appraisal procedure provided by the invention, for example network, live network and artificial network, is used for the node importance assessment of above-mentioned network, and compares with other typical node importance appraisal procedures by the present embodiment.The typical method chosen comprises: node degree method (degreecentrality, be called for short d), tradition K nuclear decomposition method (traditionalk-shelldecomposition, be called for short KS), degree of mixing decomposition method (mixeddegreedecomposition, be called for short MDD), minimum K core method (minimumk-shellmethod, be called for short min-KS), knearest neighbour method (shortestdistancetohighestKsvaluenode, be called for short KS-k) and expansion neighbours kernel approach (extendedneighborhoodcorenesscentralitymeasur, be called for short C
nc+).The method of the invention is referred to as KS-IF.In order to evaluate the performance of various importance appraisal procedure better, introduce discrimination index M herein.Discrimination index definition is as follows:
Wherein, R is the ranking vector of network node importance, and n is total number of degrees of vectorial R, n
rit is the number of nodes in r grade.If all nodes are in same importance rate, the value of discrimination index M is 0, and corresponding appraisal procedure cannot distinguish the importance of each node.If only comprise 1 node in each importance rate, the value of discrimination index M is 1, and corresponding appraisal procedure can distinguish the importance of each node effectively, has the strongest separating capacity.
First, choose the example network shown in Fig. 3, adopt described 7 kinds of methods to assess example network node importance, and sort to node according to importance, ranking results is as shown in table 4.The corresponding a kind of importance appraisal procedure of each row of table 4, the node of same grade has identical importance, and " other " represents remaining all nodes.As can be seen from Table 4, compared with other 6 kinds of typical methods described, method of the present invention (KS-IF) can accurately, the importance of diffServ network node meticulously, the number of nodes of each importance rate mostly is 2 most.
Table 4: the ranking results of example network node importance
In order to further illustrate the performance of the inventive method, choose the live network of 8 different scales, the discrimination index M of 7 kinds of importance appraisal procedures described in com-parison and analysis.These 8 live networks comprise: Karateclub network, Dolphin network, Jazz network, NetScience network, E-mail network, Blogs network, PGP network and Enron network.Table 5 shows described 7 kinds of importance appraisal procedures to the separating capacity of described 8 live network node importances.Can find out: for described 8 live networks, method of the present invention (KS-IF) can both obtain maximum differentiation angle value.Illustrate than other 6 kinds of node importance appraisal procedures, the method for the invention more can importance that is careful, identification live network node exactly.
Table 5: different importance appraisal procedure is to the separating capacity of live network node importance
In order to further illustrate the performance of the inventive method, show by the result of CCDF CCDF his-and-hers watches 5.Fig. 4 ~ Fig. 7 respectively illustrates the CCDF of 4 networks, i.e. example network, Karateclub network, Dolphin network and NetScience network.According to the principle of CCDF, if the number of nodes being positioned at same importance rate is more, CCDF declines faster, otherwise CCDF then slowly can decline along clinodiagonal.As can be seen from Fig. 4 ~ Fig. 7, the CCDF of the method for the invention (KS-IF) slowly declines along clinodiagonal, illustrates that the difference of importance between network node can make a distinction by the method for the invention well.
In order to further illustrate the performance of the inventive method, generating artificial complex network by LFR network generator, utilizing artificial complex network to assess the method for the invention.LFR network generator has 4 important parameters, node scale n (numberofnodes) respectively, average node degree k (averagedegreeofnodes), community structure hybrid parameter μ (mixingparameterofcommunitystructure) and degree power-law distribution γ (power-lawofdegreedistribution).The change of described 4 parameters is by the topological structure of the artificial complex network of impact.Fig. 8 ~ Figure 11 respectively illustrates described 4 parameters at maintenance 1 Parameters variation, during all the other 3 parameter constants, and the situation of change of different node importance appraisal procedure discrimination index M.Can find out: for described artificial complex network, method of the present invention (KS-IF) can obtain maximum differentiation angle value.Illustrate than other 3 kinds of node importance appraisal procedures, the method for the invention more can identify the node importance of artificial complex network careful, exactly.
In conjunction with particular content of the present invention and embodiment one and embodiment two visible, the present invention carries out K nuclear decomposition to given complex network, preserves the Ks value of iterative information in decomposable process and each node; According to the Ks value of described iterative information and each node, calculate the K core iteration factor of each node; According to the K core iteration factor of node, the importance of calculation of complex network node.
The present invention makes full use of the iterative information in K nuclear decomposition process, effectively can distinguish the importance of the node with identical Ks value.The present invention considers index of overall importance and local parameter simultaneously, carries out assessing to node importance based on the K core iteration factor of node and degree information comprehensively, objectively.The present invention has lower time complexity, can fast and effeciently process large-scale complex network data, have very strong adaptability.
In sum, the present invention effectively overcomes various shortcoming of the prior art and tool high industrial utilization.
Above-described embodiment is illustrative principle of the present invention and effect thereof only, but not for limiting the present invention.Any person skilled in the art scholar all without prejudice under spirit of the present invention and category, can modify above-described embodiment or changes.Therefore, such as have in art usually know the knowledgeable do not depart from complete under disclosed spirit and technological thought all equivalence modify or change, must be contained by claim of the present invention.
Claims (6)
1. a complex network node importance appraisal procedure, is characterized in that, described complex network node importance appraisal procedure comprises:
K nuclear decomposition is carried out to given complex network, the iterative information in preservation decomposable process and the Ks value of each node;
According to the Ks value of described iterative information and each node, calculate the K core iteration factor of each node;
According to described K core iteration factor, calculate the importance of each node.
2. complex network node importance appraisal procedure according to claim 1, is characterized in that, the computational methods of described node K core iteration factor comprise:
Wherein,
for arbitrary node n in complex network
ik core iteration factor; K is K nuclear decomposition process interior joint n
ithe Ks value be endowed; M is that in K nuclear decomposition process, angle value is the total degree of the iterative operation of k; In this m time iterative operation, node n
ibe removed when n-th iteration, 1≤n≤m.
3. complex network node importance appraisal procedure according to claim 1, it is characterized in that, the computational methods of described node importance comprise:
Wherein,
for arbitrary node n in complex network
iimportance;
for node n
ik core iteration factor;
for node n
iangle value; N
ifor node n
ineighbor node set; n
jfor node n
ineighbor node, n
j∈ N
i;
for node n
jk core iteration factor;
for node n
jangle value.
4. a complex network node importance evaluating system, is characterized in that, described complex network node importance evaluating system comprises:
K nuclear decomposition module, carries out K nuclear decomposition to given complex network, and the Ks value of the iterative information preserved in decomposable process and each node;
Node K core iteration factor computing module, is connected with described K nuclear decomposition module, and the described iterative information produced according to K nuclear decomposition process and the Ks value of each node, calculate the K core iteration factor of each node;
Node importance computing module, is connected with described node K core iteration factor computing module, according to described K core iteration factor, calculates the importance of each node.
5. complex network node importance evaluating system according to claim 4, is characterized in that, the computing function of described node K core iteration factor computing module is:
Wherein,
for arbitrary node n in complex network
ik core iteration factor; K is K nuclear decomposition process interior joint n
ithe Ks value be endowed; M is that in K nuclear decomposition process, angle value is the total degree of the iterative operation of k; In this m time iterative operation, node n
ibe removed when n-th iteration, 1≤n≤m.
6. complex network node importance evaluating system according to claim 4, is characterized in that, the computing function of described node importance computing module is:
Wherein,
for arbitrary node n in complex network
iimportance;
for node n
ik core iteration factor;
for node n
iangle value; N
ifor node n
ineighbor node set; n
jfor node n
ineighbor node, n
j∈ N
i;
for node n
jk core iteration factor;
for node n
jangle value.
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