CN102880799A - Method for comprehensively evaluating importance of complicated network node based on multi-attribute decision-making - Google Patents

Abstract

The invention provides a method for comprehensively evaluating the importance of a complicated network node based on a multi-attribute decision-making. The importance of a node in a network is determined by performing comprehensive calculation by taking a plurality of indexes, such as the degree centrality, the dielectric centrality, the proximity centrality and the structural cave of the single node in the network, as a plurality of attributes for evaluating the importance of the node. By the method for comprehensively evaluating the importance of the node based on the multi-attribute decision-making, an accurate node importance sequence is obtained, and the shortcoming of the conventional method for evaluating the importance of the node in the complicated network by using a single index is overcome. A calculation result of a 'kite network', an 'automatic radar plotting aid (ARPA) network' and a 'scientific research cooperation network' shows that the importance of the complicated network nodes of different types can be comprehensively calculated, and comprehensive evaluation can be realized by selecting a plurality of different node importance evaluation indexes; and the method is extremely high in extendibility.

Description

A kind of complex network node importance degree integrated evaluating method based on multiple attribute decision making (MADM)

Technical field

The present invention relates to the importance evaluation method of Node Contraction in Complex Networks, be specially a kind of complex network node importance degree integrated evaluating method based on multiple attribute decision making (MADM).

Background technology

The key node of seeking in the network is one of important research content of Network Science.

Complex network non-homogeneous topological structure has in essence determined that the significance level of each node is very different in the network.Especially to various concrete network such as scientific research cooperative network, transmission network, air net, electric power networks etc., the importance of these Node Contraction in Complex Networks is assessed, excavate the important node in the network, have important practical value.For example: in the large-scale computer network, can back up targetedly according to the significance level of server node and redundant the construction, in saving resource, can guarantee again the robustness of network; In criminal's relational network, importance sorting is conducive to distinguish ringleader, key member and follows molecule, locates rapidly criminal gang's the head; In infectious disease, viral network, can be by finding the infected and treat targetedly and isolate pathogeny, thus effectively prevent propagation and the diffusion of virus; In the network that rumour is propagated, also can locate fast important propagation node, effectively block the propagation of rumour etc.In a word, how to excavate the importance node in the complex network, analyze more targetedly its character, thereby strategy and preventive measure are one of basic problems of complex network research in order to formulate correctly effectively.

In various complex networks, seek most important node (limit) in the network with the method for quantitative test, perhaps analysis node has been obtained many progress with respect to the significance level of other one or more nodes.Present general significance level from community network and two kinds of angle analysis nodes of system science.The core concept of methods of social network is " importance is equivalent to conspicuousness ", to the excavation of important node in the network take the globality of not destroying network as the basis.Generally can weigh by the centrality index of node, complex network centrality index degree of having centrality commonly used, betweenness centrality, near centrality, eigenvector centrality etc., these indexs have been portrayed the significance level of individual node network from different angles.The core concept of system science analytical approach is " importance is equivalent to the deleted rear destructiveness to network of this node (collection) ", after deleting certain node (collection), its significance level is determined in variation by indexs such as network connectivties, and the general method that adopts has knot removal method, shrinking etc.

No matter be the community network angle be equivalent to importance based on the node conspicuousness, or the destructiveness of system science angle is equivalent to importance, the measure of network node importance all is based on otherness between the node, from the importance problem of a certain angle Probe into Network node.Such as: the importance appraisal procedure based on degree emphasizes that node and adjacent node connect the quantity on limit, can show to a certain extent the significance level of node in network, but the identical node of degree of having, the significance level in network may not be identical; Betweenness has been portrayed node or limit to the control ability of information in the network or stream, but generally calculates according to shortest path, and does not meet real rule; Eigenvector centrality then takes into full account and the destination node importance of node that connects, and determines the status of destination node by the importance of adjacent node; Subgraph centrality has reflected the contribution of node in the network partial structurtes.Every kind of above-mentioned method has the merits and demerits of self, all puts forward for particular problem, has portrayed respectively the importance of node particular network from different aspects.But the complex network of real world is ever-changing, be difficult to from an index significance level of certain node network is described, the importance of a node is not only relevant with its single Measure Indexes in the network, and relevant with the bulk property of network, need to from different angles, utilize a plurality of indexs of node to carry out comprehensive evaluation.

Summary of the invention

The technical matters that solves

In order to overcome the deficiency of existing node importance evaluation method, the present invention proposes a kind of complex network node importance degree integrated evaluating method based on multiple attribute decision making (MADM), utilize individual node in the network degree centrality, betweenness centrality, carry out COMPREHENSIVE CALCULATING near a plurality of indexs such as centrality, structural holes as a plurality of attributes of this node importance evaluation, thereby determine the significance level of node in network.

Technical scheme

The present invention at first regards each node in the complex network as a scheme, with degree centrality, near the Criterion Attribute of a plurality of Assessment of Important indexs such as centrality, betweenness centrality, structural hole as this scheme evaluation, thereby the evaluation of complex network node importance is converted into Multiple Attribute Decision Problems, and the criterion of decision-making is to estimate the significance level of each scheme in complex network.

Technical scheme of the present invention is:

Described a kind of complex network node importance degree integrated evaluating method based on multiple attribute decision making (MADM) is characterized in that: may further comprise the steps:

Step 1: determine the decision scheme of each node in the complex network N node, the set of formation decision scheme is: A={A ₁..., A _i..., A _N, A wherein _iRepresent i the decision scheme that node is corresponding; Determine that the Criterion Attribute set of estimating each node importance degree is S={S ₁..., S _m; Make up decision matrix X:

A wherein _i(S _j) be j index attribute value of i node, i=1 ..., N, j=1 ..., m;

Step 2: decision matrix X is carried out standardization according to following formula:

A wherein _i(S _j) ^Max=max{A _i(S _i) | 1≤i≤N}, A _i(S _j) ^Min=min{A _i(S _j) | 1≤i≤N}, described benefit type index is that the desired value attribute is higher, the index that importance degree is larger, cost type index is that the desired value attribute is higher, the index that importance degree is less; The decision matrix that obtains after the standardization is R=(r _Ij) _{N * m}

Step 3: adopt analytical hierarchy process to determine the weight of each index, wherein the weight of j index is w _j, j=1 ..., m, ∑ w _j=1;

Step 4: the decision matrix R=(r that is obtained by step 2 _Ij) _{N * m}With each index weights that step 3 obtains, make up weighting standardization matrix Y:

Determine positive desirable decision scheme A according to matrix Y ⁺With negative ideal decision-marking option A ^-:

$A^{+}=\{\underset{i\∈L}{\max }{y}_{i1},...,\underset{i\∈L}{\max }{y}_{\mathrm{im}}\}=\{y_1^{\max },...,y_m^{\max }\}$

$A^{-}=\{\underset{i\∈L}{\min }{y}_{i1},...,\underset{i\∈L}{\min }{y}_{\mathrm{im}}\}=\{y_1^{\min },...,y_m^{\min }\}$

L={1 wherein ..., N}; Calculate each decision scheme A _iTo positive desirable option A ⁺With negative ideal scheme A ^-Distance:

$D_i^{+}={\left[\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{(y_{\mathrm{ij}}-y_j^{\max })}^2\right]}^{1/2},$ (i＝1，...，N；j＝1，...，m)

$D_i^{-}={\left[\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{(y_{\mathrm{ij}}-y_j^{\min })}^2\right]}^{1/2},$ (i＝1，...，N；j＝1，...，m)

Calculate each decision scheme A _iApproach degree Z to ideal scheme _i:

$Z_i=D_i^{-}/(D_i^{-}+D_i^{+}),$ 0≤Z _i≤1，i＝1，...，N

With the approach degree Z of each decision scheme to ideal scheme _iBy sorting from big to small, approach degree is larger, and then the significance level of corresponding node in network is higher.

Described a kind of complex network node importance degree integrated evaluating method based on multiple attribute decision making (MADM) is characterized in that: the Criterion Attribute of estimating each node importance degree is for degree centrality, betweenness centrality, near centrality and structural hole; Its moderate centrality, be benefit type index near centrality, betweenness centrality, structural hole is cost type index.

Beneficial effect

The invention has the beneficial effects as follows: owing to the node importance integrated evaluating method that has adopted based on multiple attribute decision making (MADM), obtained accurately node importance ordering, overcome the deficiency of utilizing single index to estimate Node Contraction in Complex Networks importance in the existing invention.Utilize the present invention that the result of calculation of " kite network ", " ARIA network ", " scientific research cooperative network " is shown, the present invention not only can carry out for dissimilar complex network node the COMPREHENSIVE CALCULATING of its importance, and can select a plurality of different node importance evaluation indexes to carry out comprehensive evaluation, have good extendability.

Therefore, the present invention proposes a kind of integrated evaluating method of the node importance based on multiple attribute decision making (MADM), the method is regarded each node in the complex network as a scheme, its a plurality of Assessment of Important indexs are as the attribute of this scheme, by calculating each scheme to the degree of closeness of ideal scheme, finally obtain the importance comprehensive evaluation result of this node.Utilize the present invention that the result of calculation of " kite network ", " ARIA network ", " scientific research cooperative network " is shown, the present invention can estimate the importance of individual node in the dissimilar complex network effectively.In addition, the present invention is not limited to the evaluation index of several node importance degrees cited in the invention book, can also expand easily.

For clear elaboration advantage of the present invention, method of the present invention and existing document have been done contrast for the result of calculation of ARPA net, document [1]: utilize importance degree to estimate matrix and determine the complex network key node, Acta Physica Sinica, 2012, vol.61 (5): 050201, considered the importance degree contribution of efficient, node degree value and the adjacent node of nodes in this document, characterize it to the importance degree contribution of adjacent node with degree of node value and efficiency value, then provided definite algorithm of key node, the comparatively desirable effect that obtains; But because the document has only been considered degree of node value and efficiency value, do not consider the calculating of betweenness, to being in the key node of " bridge " position in some networks, can not well find its importance.Document [2]: the evaluation method of node importance in communication networks. the communication journal, 2004,25 (8): 129-134, after the document was based on and removes node, the variation of network diameter and the number of variations of spanning tree were determined the significance level of node; But what the document adopted is the analytical approach of system science, that the globality of destroying network is come the significance level of evaluation node in network, there is not to consider to remove the node importance when causing network topology change behind the node, and the method that this each node is analyzed separately need to solve because node removes network topology structure variation even the divided problem that causes.Document [3]: utilize the importance contribute matrix to determine most important node in the communication network, BJ University of Aeronautics ﹠ Astronautics's journal, 2009, vol.35 (9): 1076-1079, the method has defined the node importance contribute matrix, emphasis has considered that different internodal connecting relations are on the impact of node importance in the communication network, the initial importance of node is made as the betweenness of this node, each node is relevant with this degree of node to the contribution of its adjacent node significance level, thereby the important node in the evaluating network has obtained preferably effect; But the document has only been considered betweenness and the degree value of node, does not consider other indexs such as efficient of nodes, so do not obtain good effect in the isolated community that forms after the important node deletion.The present invention has adopted a plurality of indexs based on social network analysis, test for dissimilar complex network, node importance evaluation result at three above-mentioned documents of the experiment neutralization of ARPA net contrasts, after experimental result shows front 5 network-critical knot removals that the inventive method finds, the ARPA net can be divided into 7 isolated communities, and can be divided into 3 isolated communities after front 5 important node of document [1] deletion, can be divided into 5 isolated communities after front 5 important node of document [3] deletion, can be divided into 7 isolated communities after front 5 important node of document [2] deletion, and coming to the same thing of obtaining of the present invention.But what document [2] adopted is exactly the method for knot removal, to judge important node in the network by the connectivity of destroying network, and the used index of the present invention all is the centrality evaluation indexes in the community network, be the globality of not destroying network be the significance level that the comprehensive evaluation node is come on the basis, so the result of two kinds of methods has different.

Description of drawings

The process flow diagram of Fig. 1 the inventive method

Fig. 2 kite network

The sort result figure that Fig. 3 kite network uses the present invention to calculate

Fig. 4 ARIA network

Delete after front 5 important node after Fig. 5 ARIA network calculates and the as a result comparison diagram of other documents

Wherein (a) this paper algorithm is deleted the figure behind front 5 nodes, (b) figure behind front 5 nodes of document [1] deletion, (c) figure behind front 5 nodes of document [2] deletion, (d) figure behind front 5 nodes of document [3] deletion

The Top5% important node schematic diagram that Fig. 6 adopts the present invention to calculate to C-DLBP " scientific research cooperative net "

The Top10% important node schematic diagram that Fig. 7 adopts the present invention to calculate to C-DLBP " scientific research cooperative net "

Embodiment

Below in conjunction with specific embodiment the present invention is described:

Embodiment 1:

The present embodiment is take " the kite network " of Krackhardt design as example, with reference to accompanying drawing 2, this network has 10 nodes, Criterion Attribute degree of having centrality DC, the betweenness centrality BC of each node importance degree, near centrality CC, structural hole C, wherein, degree centrality, be benefit type index near centrality, betweenness centrality, namely index attribute value is larger, and then the significance level of node is higher; And structural hole is cost type index, and index attribute value is less, and the significance level of node is higher.

Above-mentioned each Criterion Attribute is defined as open source literature is general:

Definition 1: degree centrality (Degree centrality)

The ratio of the maximum limit number that the limit number that node i is associated and node i may exist.Spending central expression formula is:

DC _i＝k _i/(N-1),

K wherein _iThe limit number related with node i in the expression network.Degree centrality definition list understands the ability of a node and other node direct communication, and numerical value is larger, and is more important in network.

Definition 2: near centrality (Closeness centrality)

Suppose d _IjExpression is take node i as starting point, the quantity on contained limit in the shortest path take j as terminal point, and then node i can be expressed as the inverse of its other all nodal distance sums in the network near centrality.Near central expression formula be:

${\mathrm{CC}}_i=N/\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{d}_{\mathrm{ij}},$

Node is larger near central value, shows that node occupy the degree of network center position larger, and is correspondingly also just more important.

Definition 3: betweenness centrality (Betweenness centrality)

The central expression formula of betweenness is:

${\mathrm{BC}}_i=\underset{j\≠i\≠k\∈V}{\mathrm{\Σ}}\frac{g_{\mathrm{jk}}\left(i\right)}{g_{\mathrm{jk}}},$

G in the formula _Jk(i) number of the shortest path by node i between expression node j and the k.g _JkBe the sum from node j to all shortest paths the node k.Betweenness centrality definition think if node be in the network other node between the only way which must be passed of communication, then it must have critical role in network.The central value of node betweenness is higher, and then the influence power of this node is larger, and is correspondingly also just more important.

Definition 4: structural hole (Structure Hole)

If do not have direct connection between two individualities or two colonies in network, and do not have indirect redundancy relationship between them, then between the two obstruction is exactly structural hole.Burt has proposed the network constraint coefficient in computation structure hole to be estimated network closure and structural hole.The calculation expression of the network constraint coefficient of node i is:

$C_i=\underset{j}{\mathrm{\Σ}}{(P_{\mathrm{ij}}+\underset{q\≠i\≠j}{\mathrm{\Σ}}{P}_{\mathrm{iq}}{P}_{\mathrm{qj}})}^2,$

Wherein, q is the indirect node of connected node i and node j, P _IjFor node i spends in the ratio that time (energy) on the node j accounts for its T.T. (energy).Network constraint coefficient C _iLess, the structural hole degree is larger, and the position of node is more important.

According to the These parameters definition, we obtain the result of calculation of each index of node in " kite network ", namely obtain decision matrix X, again X are carried out standardization:

A wherein _i(S _j) ^Max=max{A _i(S _j) | 1≤i≤N}, A _i(S _j) ^Min=min{A _i(S _j) | 1≤i≤N}, the decision matrix that obtains after the standardization is R=(r _Ij) _{N * m}, as shown in the table:

ID

DC

C

CC

BC

1	0.1111	1.25	0.3448	0.00
					2	0.2222	0.5556	0.4762	16.00
3	0.3333	0.4944	0.6667	28.00
					4	0.5556	0.4701	0.7143	16.67
5	0.5556	0.4701	0.7143	16.67
					6	0.3333	0.7059	0.5556	0.00
7	0.6667	0.4746	0.6667	7.33
					8	0.3333	0.7059	0.5556	0.00
9	0.4444	0.5783	0.5882	1.67
					10	0.4444	0.5783	0.5882	1.67

Can find out from decision matrix R: the node of this network moderate central value maximum is node 7, although node 3 degree central values only have 3, but occupied information the driver's seat best in the network, maximum betweenness central value is arranged, node 4 and 5 has the maximum structural hole value near central value and minimum, and the position in network structure is identical.

Adopt analytical hierarchy process (AHP-Analytic Hierarchy Process) to determine the weight of each index, wherein the weight of j index is w _j, j=1 ..., m, ∑ w _j=1, analytical hierarchy process is set up a comparator matrix B after at first adopting (0,1,2) three scaling laws to carry out in twos relatively to each index, secondly by conversion comparator matrix is converted into judgment matrix, and carries out consistency check, obtains at last index weights.

Element is defined as among the comparator matrix B:

To spending centrality DC, betweenness centrality BC, near centrality CC and four indexs of structural hole C according to the comparator matrix B that three scaling laws make up being:

B	DC	C	CC	BC
					DC
	1	0	0	0
					C	2	1	1	0
CC	2	1	1	0
					BC	2	2	2	1

The structure of comparator matrix B is considered based on following factor: because the network structure factor that relates to of degree centrality is minimum, so to compare importance relatively poor with other indexs; And the structural hole index with compare near the centrality index, be difficult in theory the quality of two indexs of contrast, in matrix B, provided the identical evaluation of importance; Three indexs of betweenness centrality and other are compared, accurate " bridge " node in the discovering network, and other three indexs are then without this function, so this paper has given the value higher than other index importance in the structure of matrix B betweenness centrality.

To comparing matrix B, according to the range method Judgement Matricies, after consistency check, the value that obtains each index of correlation weight is respectively: w _DC=0.0861, w _C=0.2073, w _CC=0.2073, w _BC=0.4993.

According to the decision matrix R=(r that obtains _Ij) _{N * m}With the weight of four indexs, according to formula:

The weighting standardization matrix Y that sets up is:

$\left(\begin{array}{cccc}0.0143& 0.0780& 0.1001& 0\\ 0.0287& 0.1754& 0.1382& 0.2853\\ 0.0430& 0.1971& 0.1935& 0.4993\\ 0.0718& 0.2073& 0.2073& 0.2972\\ 0.0718& 0.2073& 0.2073& 0.2972\\ 0.0430& 0.1381& 0.1612& 0\\ 0.0861& 0.2053& 0.1935& 0.1308\\ 0.0430& 0.1381& 0.1612& 0\\ 0.0574& 0.1685& 0.1707& 0.0297\\ 0.0574& 0.1685& 0.1707& 0.0297\end{array}\right)$

Determine positive desirable decision scheme A according to matrix Y ⁺With negative ideal decision-marking option A ^-:

$A^{+}=\{\underset{i\&Element;L}{\max }{y}_{i1},...,\underset{i\&Element;L}{\max }{y}_{\mathrm{im}}\}=\{{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00002180243600021.png,HDA00002180243600022.png"\; state="\{\{state\}\}">y</figure-callout>}}_1^{\max },...,y_m^{\max }\}$

$A^{-}=\{\underset{i\&Element;L}{\min }{y}_{i1},...,\underset{i\&Element;L}{\min }{y}_{\mathrm{im}}\}=\{{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00002180243600021.png,HDA00002180243600022.png"\; state="\{\{state\}\}">y</figure-callout>}}_1^{\min },...,y_m^{\min }\}$

Positive desirable decision scheme A wherein ⁺For: { 0.0861 0.2073 0.2073 0.4993}; Negative ideal decision-marking option A ^-For: { 0.0143 0.0780 0.1001 0}.

Each decision scheme A _iTo positive desirable option A ⁺With negative ideal scheme A ^-Distance:

$D_i^{+}={\left[\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{(y_{\mathrm{ij}}-y_j^{\max })}^2\right]}^{1/2},$ (i＝1，...，N；j＝1，...，m)

$D_i^{-}={\left[\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{(y_{\mathrm{ij}}-y_j^{\min })}^2\right]}^{1/2},$ (i＝1，...，N；j＝1，...，m)

And each decision scheme A _iApproach degree Z to ideal scheme _i:

$Z_i=D_i^{-}/(D_i^{-}+D_i^{+}),$ 0≤Z _i≤1，i＝1，...，N

Wherein

And Z _iThe result be:

ID	D +	D -	Z i
				1	0.5317	0.0000	0.0000
2	0.2343	0.3042	0.5650
				3	0.0463	0.5225	0.9185
4	0.2026	0.3462	0.6308
				5	0.2026	0.3462	0.6308
6	0.5080	0.0904	0.1511
				7	0.3688	0.2173	0.3707
8	0.5080	0.0904	0.1511
				9	0.4735	0.1262	0.2104
10	0.4735	0.1262	0.2104

With the approach degree Z of each decision scheme to ideal scheme _iBy sorting from big to small, approach degree is larger, and then the significance level of corresponding node in network is higher.

From upper table, can draw: Z ₃＞(Z ₄=Z ₅)＞Z ₂＞Z ₇＞(Z ₉=Z ₁₀)＞(Z ₆=Z ₈)＞Z ₁

Reasonably be interpreted as: for the kite network, node 3 is in the position of global information control ability maximum, and the deletion of node 3 can cause no longer UNICOM of network, so its importance degree is maximum; Therefore and node 4 is identical with node 5 locations of structures in network, has identical Z value, and the deletion of node 4 or node 5 can cause the communication distance increase between nodes, so importance degree takes second place; Node 2 is the larger nodes of betweenness value, and deletion of node 2 can cause node 1 and network to disconnect, and only disconnects 1 node, though illustrate that node 2 is important, not large than deletion of node 4 and 5 impacts that network is caused; Although node 7 number of degrees are maximum, the deletion of node 7 only so that the communication redundancy degree of kite network reduces, does not affect the communication capacity of whole network; For node 9 and node 10, node 6 and node 8, the locations of structures in network is identical respectively, but the deletion of these nodes do not impact the communication of network, after therefore ordering is more leaned on.

From finding out " kite network " experiment, use the present invention can obtain good result to the evaluation of simple network node importance degree, can distinguish well the significance level between each node, effectively avoid the deficiency of the single attribute evaluation significance level of individual node.

Embodiment 2:

The present embodiment adopts U.S. ARPA (the Advanced Research Project Agency) network topology that provides in the accompanying drawing 3, and it is comprised of 21 nodes and 23 links.The main line network topology of generally using when the ARPA topology is present analysis network node importance, its network average degree central value is between 2-3, and most of degree of node central value is 2.

Following table has provided the ranking results of estimating according to the ARIA network node importance of determining with document [1], document [2] and the described method of document [3] of mentioning in method of the present invention and " background technology ".

The node importance ordering that four kinds of algorithms draw is all slightly variant, mainly is because judgement emphasis separately is different.Document [1] and document [3] have used the analytical approach of community network, utilize the node importance degree to estimate matrix and determine key node in the complex network; Document [2] has used the method for system science, be based on remove node after, the variation of network diameter and the number of variations of spanning tree are determined the significance level of node.The most important node that the inventive method adopts the algorithm of comprehensive evaluation to draw is 3, and the conclusion that same document [2] [3] draws is consistent.

Fig. 5 has provided the situation after front 5 important node are deleted in the ARPA net node significance level ordering of adopting above-mentioned four kinds of methods to obtain afterwards.Fig. 5 (a) deletes figure after front 5 important node for this paper algorithm, can find out front 5 important node deletion after, ARIA network is divided into 7 communities independently, illustrate that the inventive method has calculated the key node that ARPA nets well; Fig. 5 (b) and Fig. 5 (d) have provided the figure after front 5 important node of deletion after the result of calculation ordering that document [1] and document [3] obtain, wherein only network is divided into 3 communities among Fig. 5 (b), then network is divided into 5 communities among Fig. 5 (d), comparing result illustrates that evaluation method of the present invention is better than the method in document [1] and the document [3].Fig. 5 (c) also obtains 7 isolated communities, on single quantity of cutting apart from community, identical with the result of put forward the methods of the present invention, but what document [2] adopted is exactly the method for knot removal, to judge important node in the network by the connectedness of destroying network, and the used index of the present invention all is the centrality evaluation indexes in the community network, be the globality of not destroying network be the significance level that the comprehensive evaluation node is come on the basis, so the result of two kinds of methods has different.

Embodiment 3:

The present embodiment adopts the subset of the maximum of C-DBLP " scientific research cooperative net ", wherein comprises 462 nodes, 975 limits.After the method that proposes according to the present invention is carried out the assessment of node importance degree to this network, Fig. 6 has provided the diagram of choosing the Top5% important node in the result of calculation ordering of adopting algorithm of the present invention, wherein maximum circular node represents the center of network, and other larger circular node is important node.Fig. 7 is the figure of having chosen the Top10% important node.Can find out, the node of Top5% and Top10% can well cover the important node in " scientific research cooperative net ", and these nodes generally all are the responsible officials of seminar, they with the project cooperation of other seminars in played very important anastomosis.

Claims (2)

1. complex network node importance degree integrated evaluating method based on multiple attribute decision making (MADM) is characterized in that: may further comprise the steps:

Step 1: determine the decision scheme of each node in the complex network N node, the set of formation decision scheme is:

A={A ₁..., A _i..., A _N, A wherein _iRepresent i the decision scheme that node is corresponding; Determine that the Criterion Attribute set of estimating each node importance degree is S={S ₁..., S _m; Make up decision matrix X:

A wherein _i(S _j) be j index attribute value of i node, i=1 ..., N, j=1 ..., m;

Step 2: decision matrix X is carried out standardization according to following formula:

A wherein _i(S _j) ^Max=max{A _i(S _j) | 1≤i≤N}, A _i(S _j) ^Min=min{A _i(S _j) | 1≤i≤N}, described benefit type index is that the desired value attribute is higher, the index that importance degree is larger, cost type index is that the desired value attribute is higher, the index that importance degree is less; The decision matrix that obtains after the standardization is R=(r _Ij) _{N * m}

Step 3: adopt analytical hierarchy process to determine the weight of each index, wherein the weight of j index is w _j, j=1 ..., m, ∑ w _j=1;

Step 4: the decision matrix R=(r that is obtained by step 2 _Ij) _{N * m}With each index weights that step 3 obtains, make up weighting standardization matrix Y:

Determine positive desirable decision scheme A according to matrix Y ⁺With negative ideal decision-marking option A ^-:

$A^{+}=\{\underset{i\&Element;L}{\max }{y}_{i1},...,\underset{i\&Element;L}{\max }{y}_{\mathrm{im}}\}=\{y_1^{\max },...,y_m^{\max }\}$

$A^{-}=\{\underset{i\&Element;L}{\min }{y}_{i1},...,\underset{i\&Element;L}{\min }{y}_{\mathrm{im}}\}=\{y_1^{\min },...,y_m^{\min }\}$

L={1 wherein ..., N}; Calculate each decision scheme A _iTo positive desirable option A ⁺With negative ideal scheme A ^-Distance:

$D_i^{+}={\left[\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{(y_{\mathrm{ij}}-y_j^{\max })}^2\right]}^{1/2},$ (i＝1，...，N；j＝1，...，m)

$D_i^{-}={\left[\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{(y_{\mathrm{ij}}-y_j^{\min })}^2\right]}^{1/2},$ (i＝1，...，N；j＝1，...，m)

Calculate each decision scheme A _iApproach degree Z to ideal scheme _i:

$Z_i=D_i^{-}/(D_i^{-}+D_i^{+}),$ 0≤Z _i≤1，i＝1，...，N

With the approach degree Z of each decision scheme to ideal scheme _iBy sorting from big to small, approach degree is larger, and then the significance level of corresponding node in network is higher.

2. described a kind of complex network node importance degree integrated evaluating method based on multiple attribute decision making (MADM) according to claim 1 is characterized in that: the Criterion Attribute of estimating each node importance degree is for degree centrality, betweenness centrality, near centrality and structural hole; Its moderate centrality, be benefit type index near centrality, betweenness centrality, structural hole is cost type index.

Images