CN103326899A - Weighting network node importance assessment method based on network heterogeneity - Google Patents

Abstract

The invention discloses a weighting network node importance assessment method based on network heterogeneity. The method is based on the contribution entropy of nodes, and takes the network heterogeneity and the range of change of the network heterogeneity as an index for weighing the importance of the network nodes. The heterogeneity reflects the uniformity of a network. The more the heterogeneity of the network changes after some node is removed, the more important the node is on the network. Due to the fact that the network heterogeneity index which can reflect the overall macrostate is adopted, the limitations of focusing on details of the nodes with the existing public method in general use are overcome. The method not only can assess the importance of all the nodes accurately, but also solves the problem that misjudgment may be caused because cut points exist.

Description

A kind of weighted network node importance degree appraisal procedure of heterogeneity Network Based

Technical field

The present invention relates to the appraisal procedure of complex network node importance degree, be specially a kind of node importance degree appraisal procedure of weighted network of heterogeneity Network Based.

Technical background

In complex network, weighted network is a kind of very important type.A large amount of studies show that both at home and abroad, most community network (such as scientific research cooperative network, citation network, epidemic transmission network etc.) and technical network (such as WWW, Internet, electric power networks etc.) all have the characteristic of weighted network.The assessment of the importance degree of weighted network node for the fault-tolerance and reliability, the epiphytotics communication channel of isolation that improve network, hit and disintegrate criminal group etc. extremely important meaning is arranged.

The appraisal procedure of network node importance degree is broadly divided into two classes: methods of social network and the systematic scientific method.Wherein, the basic assumption of methods of social network is " conspicuousness is equivalent to importance ", emphasize effect and function that node is brought into play in network, namely weigh the significance level of this node in network by the number of connection of measuring other nodes in certain node and the network, weighed with various indexs such as node degree (Degree), betweenness (Betweenness), the degrees of approach (Closeness); The basic assumption of the systematic scientific method is " destructiveness is equivalent to importance ", and its principle is can weigh its significance level to the destructiveness that network brings after calculating certain node failure.

In existing disclosed network node importance degree appraisal procedure, the limitation of the following aspects is arranged more or less: 1. excessively emphasize the part, ignore the impact on the overall situation.Many take node degree in the appraisal procedure on basis, only as standards of measurement, less consideration node is on the impact of the overall situation the connection degree of node (the limit number of node connection); Some take betweenness as the basis method in, although considered the impact of each node on the overall situation, calculation of complex, the assessment cost very high; 3. some appraisal procedure, particularly take the appraisal procedure of node degree as the basis, (Cut Vertex) lacks consideration to " cutpoint ", causes those to be in critical positions but the significance level of the node of degree less is underestimated.So-called " cutpoint " refers to those in case can make the node of network division after losing efficacy, and this node is called as " cutpoint " of network.4. most disclosed node importance degree appraisal procedures all concentrate on and have no right network facet, almost do not relate to the appraisal procedure of weighted network.

Summary of the invention

To the objective of the invention is the problems referred to above of existing in the existing network node importance degree appraisal procedure in order solving, to have proposed a kind of network node importance degree appraisal procedure of heterogeneity Network Based.

Having no right network has only reflected connected mode between the node or the topological property of network configuration, degree of strength that can not the description node interphase interaction.The power of correlation between the different nodes, and the size of each node processing ability must rely on the limit to weigh or some power is described, such as the information flow-rate in the Internet, the volume of the flow of passengers in the transportation network, the airport ability in the air net etc.

The present invention is mutual percentage contribution between the ability of node own and neighbor node, in conjunction with methods of social network and the systematic scientific method, defined the heterogeneous index that can reflect the weighted network macrostate-" some power contribution entropy ", and according to the foundation of the rate of change that removes network heterogeneity behind the different nodes as the decision node importance degree.The present invention not only can assess the importance degree of weighted network node, and preferably resolves the assessment Problem of Failure of bringing owing to " cutpoint ".

Technical scheme:

Definition 1: in weighted network G=(V, E), V={v ₁, v ₂..., v _nThe set of node, E={e ₁, e ₂..., e _mThe set on limit, if node v _iWith node v _jBetween the weights on limit be w _Ij, then claim

Wij is node v _iNode strength, claim

That neighbor node is to v _iContribution degree, wherein: τ (i) is node v _iNeighbor node set.

Definition 2: in the weighted network of as mentioned above definition, claim

Be the some power contribution entropy of network G, wherein: $I_i=(s_i+s_i^{\′})/\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(s_i+s_i^{\′}).$

Easily proof point power contribution entropy is obtained maximum in fully even (namely have no right full-mesh) network:

$H_{\mathrm{Max}}=-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{I}_i\ln \left(I_i\right)=\ln \left(n\right)$

Wherein, $I_i=(s_i+s_i^{\′})/\underset{i=1}{\overset{n}{\mathrm{\Σ}}}(s_i+s_i^{\′})=\frac{1}{n}$

If with node v _iReach all coupled limits and remove from network G, then the network G point of this moment power contribution entropy is H _i, and claim

For removing node v _iThe time network G heterogeneous rate of change, H wherein ₀Be network initial point power contribution entropy.If v _iBe cutpoint, and remove v _iAfter cause network G to be split into several separate subnets, be assumed to be: G ₁, G ₂..., G _l(l 〉=1), the some power contribution entropy of each subnet is H _Ik(k=1,2 ..., l), then $H_i=\underset{k=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\γ}}_k{H}_{\mathrm{ik}},$ Wherein ${\mathrm{\γ}}_k=\frac{n_k}{n-1}$ Be factor of influence, n _kBe k the number of nodes that subnet has.

The heterogeneous rate of change that changes of the network that causes behind above-mentioned each node failure is sorted, and its node sequence is exactly the order of each node importance degree in the network.According to technical scheme, concrete steps of the present invention are as follows:

Step 1: initialization comprises: calculate respectively node strength and the contribution degree of each node according to network adjacent matrix, form the V of node queue and calculate initial point power contribution entropy H ₀

Step 2: take out node v from the V of node queue in order _i, and from network G, remove node v _iAnd all coupled limits, make network split into the individual independently sub-network G of l (l 〉=1) ₁, G ₂..., G _l

Step 3: the some power contribution entropy and the factor of influence that calculate respectively each sub-network.

Step 4: calculate and remove v _iAnd the some power of network is contributed entropy H behind the corresponding limit _iWith heterogeneous rate of change C _i

Step 5: recovery nodes v in matrix G _iAnd all and v _iThe limit and the weights that connect.

Step 6: if set V non-NULL, then repeating step 2 is to step 5.

Step 7: order from big to small sorts to heterogeneous rate of change, and the node importance degree that heterogeneous rate of change is larger is higher.

Wherein, specifically comprise in the step 1:

Make up the weighting adjacency matrix of network G:

$G=\left(\begin{array}{cccc}0& w_{12}& ...& w_{n1}\\ w_{21}& 0& ...& w_{n2}\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ w_{n1}& w_{n2}& ...& 0\end{array}\right),i,j=1,...,n,$ w _IjBe node v _iWith node v _jBetween the limit weights, and w _Ij=w _Ji, w _Ii=0.

The node strength of each node in the computing network:

$s_i=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{w}_{\mathrm{ij}},i=\mathrm{1,2},...,n$

The contribution degree that each node obtains in the computing network:

$s_i^{\′}=\underset{j\∈\mathrm{\τ}\left(i\right)}{\mathrm{\Σ}}{w}_{\mathrm{ij}}/s_j,i-\mathrm{1,2},...,n$

Calculate initial point power contribution entropy:

${\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="2013102390426100003DEST\_PATH\_IMAGE001.png,2013102390426100003DEST\_PATH\_IMAGE003.png"\; state="\{\{state\}\}">H</figure-callout>}}_0=-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{I}_i\ln \left(I_i\right),$ Wherein: $I_i=(s_i+s_i^{\&prime;})/\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}(s_j+s_j^{\&prime;})$

Make up set of network nodes:

V={v ₁，v ₂，...，v _n}

Wherein, specifically comprise in the step 2:

From node set V, take out in order a node v _i

From network, remove node v _iAnd all connected limits, make G split into the individual complete separate subnet of l (l 〉=1), be designated as G ₁, G ₂..., G _l

Wherein, calculate the some power contribution entropy H of each subnet in the step 3 _IkConcrete grammar be:

(the individual subnet of 1≤k≤l) is established it and is had n for k _kIndividual node, its some power is contributed being calculated as follows of entropy:

Calculate the contribution degree that each node obtains in the subnet:

$s_v^{\&prime;}=\underset{u\&Element;\mathrm{\&tau;}\left(v\right)}{\mathrm{\&Sigma;}}{w}_{\mathrm{vu}}/s_v,v=1,2,...,n_k,$ S wherein _vNode capacity, the node strength in step 1 namely.

The point power contribution entropy of subnet is:

$H_{\mathrm{ik}}=\underset{v=1}{\overset{n_k}{\mathrm{\&Sigma;}}}{I}_v\ln \left(I_v\right),$ Wherein, $I_v=(s_v+s_v^{\&prime;})/\underset{u=1}{\overset{n_k}{\mathrm{\&Sigma;}}}(s_u+s_u^{\&prime;})$

Wherein, calculate the factor of influence γ of each subnet in the step 3 _kConcrete grammar be:

${\mathrm{\&gamma;}}_k=\frac{n_k}{n-1}$

Wherein, remove node v in the step 4 _iAnd the point of network G is weighed the computational methods of contributing entropy and heterogeneous rate of change after the corresponding edge:

$H_i=\underset{k=1}{\overset{l}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_k{H}_{\mathrm{ik}}$

$C_i=\frac{|H_0-H_i|}{H_0}$

Beneficial effect

Point power contribution entropy is the macro-indicators of weighing the network uniformity coefficient, the present invention based on this, and take the significance level of heterogeneous rate of change as each node of index evaluation, changed the undue limitation of paying close attention to the local nodes details in the existing method, reflect accurately each node and contribute to its neighbor node and even to the difference of network integral body, solved the not normal problem of the assessment that causes owing to cutpoint.Simultaneously, have no right network to be 1 weighted network as each limit power, so the present invention also can assess easily and haves no right the node significance level of network.

Description of drawings

Fig. 1 is the flow chart of the inventive method.

Fig. 2 is Chinese education and scientific research computer network (CERNET).

Chinese education and the scientific research computer network node significance level distribution map of Fig. 3 for using the inventive method to calculate.

Fig. 4 is AIDS patient's sexual intercourse network.

The AIDS patient sexual intercourse network node significance level distribution map of Fig. 5 for using the inventive method to calculate.

Embodiment

Below in conjunction with instantiation explanation the present invention.

Example 1: Chinese education and scientific research computer network

Chinese education and scientific research computer network (being called for short CERNET) are one of largest the Internets of China, cover more than 200 city of 31 provinces, cities and autonomous regions in the whole nation, the university that networks, educational institution, R﹠D institution surpass 2000, and the user reaches more than 2,000 ten thousand people.

On September 4th, 2012, CERNET its official website announce by the end of in December, 2011 time CERNET backbone network topological structure schematic diagram (http://www.edu.cn/cngiabc_7955/20120904/t20120904_838713.shtml), wherein the bandwidth of each link is respectively by 10G, 2.5G and 155M etc.

According to the above topology schematic diagram, the weighted network that obtains as shown in Figure 2.Wherein, the bandwidth of each link of Bian Quanwei.According to the method that the present invention proposes, as follows for the node significance level evaluation process of CERNET:

Initialization

According to the present situation of each node of CERNET and link thereof, have 36 nodes, two internodal multilinks are merged into a link, and the bandwidth addition, the link of 47 different bandwidths is then arranged.If link bandwidth is regarded as the weights on each limit, then can obtain weighting adjacency matrix G.

This is a typical sparse matrix, and wherein front 8 is backbone node, is responsible for respectively connecting separately other interior nodes of zone.These 8 backbone nodes are: 1 Beijing, 2 Shanghai, 3 Guangzhou, 4 Wuhan, 5 Xi'an, 6 Nanjing, 7 Shenyang and 8 Chengdu.

Initial point power contribution entropy according to step 1 computing network:

H ₀=-Σ I _iLn (I _i), wherein: $I_i=(s_i+s_i^{\&prime;})/\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}(s_i+s_j^{\&prime;})$

Obtain H ₀=-Σ I _iLn (I _i)=-262.970493343233

Evaluation process

From network, remove each node with this, and calculate the rate of change of the some power contribution entropy remove network behind this node and the network heterogeneity that causes therefrom.Ranking results is as shown in table 1.

The significance level of each node of table 1:CERNET backbone network

From upper table, can see, and its significance level of the node that node degree is large, node strength is high even the node attention rate is high is not necessarily just high.Such as node 2(Shanghai), node 4(Wuhan) and node 6(Nanjing), although these three nodes have larger node degree, node strength and node attention rate, but their significance level is on the contrary in node 5(Xi'an), node 7(Shenyang) and node 8(Chengdu) under, this is because if in node 5, node 7 and the node 8 any one go wrong (removing), network will divide, and the network heterogeneity will have greatly changed.Therefore the present invention can well estimate cutpoint.

On the other hand, except estimating the cutpoint, the present invention also assesses the significance level of node from the variation of network integrality.Such as node 3(Guangzhou) and node 5(Xi'an), be removed such as node 5 and cause the larger decline of node 8 importance, so the heterogeneity of network integral body changes larger; Node 3 remove the decline that does not cause main node importance, so the heterogeneity of network integral body changes less.

According to upper table, draw and obtain CERNET network node significance level distribution map (Fig. 3).

Example 2: AIDS patient's sexual intercourse network

1985, the AIDS patient's sexual intercourse network model that is proposed by Alden S.Klovdahl, and obtain admitting comparatively widely in the community network research field, Fig. 4 is this topology of networks.Klovdahl proposes is one and haves no right network model, has 41 limits of 40 nodes, in order to calculate, it to be looked limit power be 1 weighted network model, and by this tectonic network adjacency matrix G.

Fig. 5 is the AIDS patient's sexual intercourse network node significance level distribution map that utilizes the inventive method to calculate.

Because AIDS patient's sexual intercourse network model that Klovdahl proposes in the industry cycle has considerable influence power, also there are many scholars to adopt diverse ways that the node significance level of this network is assessed, comprise PageRank method that influence power is very large and betweenness method etc., table 2 is that the inventive method and additive method are for front 10 the node sequencing contrast of significance level in the above-mentioned network.

Table 2: front 10 important node ordering of AIDS patient's sexual intercourse network contrast

Sequence number	Node degree	Betweenness	PageRank	Heterogeneous rate of change
					1	16	16	16	16
2	26	26	5	26
					3	5	22	26	11
4	22	11	22	31
					5	38	31	8	5
6	31	5	38	8
					7	28	20	20	22
8	20	8	11	32
					9	11	32	34	38
10	8	28	28	28

Although every kind of appraisal procedure has the emphasis of oneself, which is better and which is worse hardly.Because PageRank method tremendous influence power, just be analyzed for the method for PageRank and the present invention's proposition here:

Think that about node 26:PageRank node 5 is more important than node 26.Yet, from Fig. 5, can see easily egress 26 in the network site, the aspect such as betweenness or degree of approach all has prior position than node 5, as long as and control node 26 well and can greatly reduce the diffusibility of AIDS in network;

About node 11: and node 26 is similar, node 11 also has more importance than node 5.In PageRank, the significance level of node 11 comes the 8th, yet node 11 thinks that with node 16, node 5 these two PageRank most important node has the limit of company respectively as can see from Figure 5, and its significance level is discharged to the 8th on the contrary, and some is unimaginably queer really.

About node 22:PageRank node 22 is come the 4th, have important position.Yet as can be seen from Figure 5, node 22 does not have special feature again except being the cutpoint of node 23, node 24, node 25, and its effect in network can be substituted by node 19 fully.Therefore, 22 of nodes come the 7th position in the method that the present invention proposes.

About node 31: in the PageRank method, the significance level of node 31 is in after the 10th, and the method that the present invention proposes is thought that node 31 has with one of most important node node 26 and is directly connected the limit, and be the cutpoint that reaches 6 nodes, in case node 31 is moved out of, whole network will be split into three independently subnets, and its significance level is far from node 34 and node 38 is comparable.

Therefore, according to above-mentioned analysis, in this example, the node significance level appraisal procedure that the present invention proposes has more reasonability than PageRank method, and is more effective aspect research and control aids transmission at least.

Claims (5)

1. weighted network node importance degree appraisal procedure based on heterogeneous rate of change

Step 1: initialization comprises: determine weighted network adjacency matrix G, weighted network node set V and calculate initial point power contribution entropy H ₀

Step 2: take out node v from V in order _iAnd from matrix G, remove v _iAnd all coupled limits, make G split into the individual independently sub-network G of l (l 〉=1) ₁, G ₂..., G _l

Step 3: the some power contribution entropy and the factor of influence that calculate respectively each sub-network.

Step 4: calculate and remove v _iAnd the some power of network G is contributed entropy H behind the corresponding limit _iWith heterogeneous rate of change C _i

Step 5: recovery nodes v in matrix G _iAnd all and v _iThe limit and the weights that connect.

Step 6: if set V non-NULL, then repeating step 2 is to step 5.

Step 7: to all heterogeneous rate of change C that obtains _iAccording to sorting from big to small, the node importance degree that heterogeneous rate of change is larger is higher.

2. a kind of weighted network node importance degree appraisal procedure based on heterogeneous rate of change as claimed in claim 1 is characterized in that, described step 1 specifically comprises:

Set up the weighted network adjacency matrix

Wherein, w _IjBe node v _iWith node v _jBetween the limit weights, and w _Ij=w _Ji, w _Ii=0.

Calculate the node strength of each node among the G:

Each node strength that calculates will as the ability of node, can not change along with removing of node.

The contribution degree that each node obtains in the computing network:

Calculate initial point power contribution entropy:

Wherein:

Set up the node set of network G:

V={v ₁，v ₂，...，v _n}。

3. a kind of weighted network node importance degree appraisal procedure based on heterogeneous rate of change as claimed in claim 1 is characterized in that, described step 3 specifically comprises:

(the individual subnet of 1≤k≤l) is established it and is had n for k _kIndividual node, its some power is contributed being calculated as follows of entropy:

Calculate the contribution degree that each node obtains in the subnet:

S wherein _vNode capacity, the node strength in claim 2 namely.

The point power contribution entropy of subnet is:

Wherein,

4. a kind of weighted network node importance degree appraisal procedure based on heterogeneous rate of change as claimed in claim 1 is characterized in that, described step 3 specifically comprises:

(the individual subnet of 1≤k≤l) is established it and is had n for k _kIndividual node, the factor of influence of its subnet is:

。

5. a kind of weighted network node importance degree appraisal procedure based on heterogeneous rate of change as claimed in claim 1 is characterized in that, described step 4 specifically comprises:

According to right 3 and right 4 described computational methods, remove node v _iAnd the weighting topological entropy of network G is behind all company limits:

Heterogeneous rate of change is:

。

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