CN103476051A - Method for evaluating importance of nodes in communication network - Google Patents

Abstract

The invention relates to a method for evaluating the importance of nodes in a communication network, and belongs to the technical field of node analysis in the network. The method for evaluating the importance of the nodes in the communication network comprises the following steps: (1) establishing a mathematical model of a weighted network according to the actual communication network, (2) respectively calculating basic indexes, including a node degree k, a node betweenness b, a feature vector index Ce and a compactness index Cc, of the weighted network, conducting normalization, (3) conducting linear combined weighting on an F1, an F2, an F3 and an F4 to obtain a final score F of a comprehensive evaluation, (4) ranking the n nodes according to the value of the final score F of the comprehensive evaluation, using the nodes in the higher rank as the important nodes in the actual communication network, and therefore determining the importance of the nodes in the actual communication network. According to the method for evaluating the importance of the nodes in the communication network, firstly, the bandwidth is utilized for weighting the actual communication network, and then ranking of the importance of the nodes is achieved through the comprehensive evaluation.

Description

A kind of communication net node importance evaluation method

Technical field

The present invention relates to a kind of communication net node importance evaluation method, the invention belongs to the nodes analysis technical field.

Background technology

Along with the fast development of communication and information technology, the coverage rate of communication network progressively enlarges, and the business of carrying increases gradually, and the effect in modern large-scale network system is more and more important.Meanwhile, the nodes of communication network will constantly increase, and its complexity constantly increases, so to the node importance of communication network research or necessary.The appraisal procedure of complex network node importance mainly contains in recent years:

(1) based on being connected between this node and other nodes: be the criterion using the degree of node as node importance the most simply, think that this node is more important more at most on the limit be connected with node, obvious this appraisal procedure has one-sidedness, some important core node might not have larger connection degree, such as only having two bridge nodes that limit is connected.

(2) method of deleting based on node (collection): core concept is " importance is equivalent to the deleted rear destructiveness to network of this node (collection) ".To the excavation of important node in network, be that the variation of network connectivty before and after deleting by node (collection), performance reflects.A lot of documents have all been used the delet method of node, suppose node failure, by the variation of comparing deletion of node front and back network performance, assess the node importance degree.The problem that the knot removal method exists is that the importance degree of these nodes will be consistent so if the deletion of a plurality of nodes all makes network not be communicated with, thereby makes the assessment result inaccuracy.

(3) node contraction method: by shrinking the limit be connected with this node, think after shrinking that higher this node of network cohesion degree obtained is more important.Network cohesion level index is mainly considered the connection degree of node and the shortest path of process node, assesses the contribution of node to network.Shrinking is to weigh and assess a kind of effective method of node importance in network.Its advantage is mainly: do not need node is removed, basis is more widely arranged in application.Meanwhile, also there is certain shortcoming in shrinking, mainly contains: have no idea symmetrical node is estimated, and for general node, also wayward its contraction scope.

The basic network topological parameter of complex network comprises the degree of node, betweenness, characteristic vector, tightness etc.The number of degrees of node refer to the limit number that connects this node, reflection be the direct influence of a node for other node in network.

Betweenness has been portrayed the possibility of information flow through given node, and the betweenness of arbitrary node all can increase along with the increase of the information flow through this node, utilizes betweenness can determine the network node that information loads is heavy.Brandes betweenness centrality algorithm is to be proposed to solve the algorithm of betweenness by Ulrik Brandes, core concept is to appoint that to get a node be source node, search the shortest path of other node to this node by breadth-first search, then calculate the corresponding betweenness value of these shortest paths.Cumulative take scheme in the arbitrary node betweenness value that is source node, just obtain the final betweenness value of all nodes and limit in figure.

Characteristic vector can be used for analyzing that indirect influence obtained by the adjacent node with height value, can not only directly reflect the Central Position of network, also is applicable to the Long-term Effect power of description node.Consider the meaning of parameters, parameters is carried out to linear combination, can overcome the defect that single index is described Centroid, more can react the center of node in network.

Tightness is the inverse apart from sum of all other nodes of this node arrival, arrive the complexity of other node in network by network for the node of portraying network, what reflect is the ability that node is exerted one's influence to other nodes by network, more can reflect the global structure of network.Internodal distance can be obtained by the Floyd algorithm, and its main thought is: from representing any 2 vertex v _ito v _jthe cum rights adjacency matrix of distance start, insert a vertex v at every turn _k, then by v _ito v _jbetween known shortest path with insert vertex v _kissuable v during as intermediate vertex (other summits in a paths except initial point and terminal) _ito v _jpath distance relatively, is got smaller value to obtain new distance matrix.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, on the basis of network characterization parametric synthesis, by the bandwidth in communication network, be weighted, take full advantage of the intrinsic property of communication network, solve the importance ranking problem of node in communication network, a kind of communication net node importance evaluation method is provided.

A kind of communication net node importance evaluation method, the method comprises the following steps:

Step 1: according to actual communication network, set up the network Model of having the right;

In actual communication network, the node number is n, and the number on limit is m, the figure G for network Model that has the right of this actual communication network _gand connection matrix H=[h _ij] be described below:

G _G=(N,L) (1)

In formula: the set that N is node in communication network, N={n ₁, n ₂, n ₃... n _n;

The set that L is one group of limit of having the right, L={l ₁, l ₂, l ₃... l _m;

Element h in connection matrix H _ijbe defined as follows:

Limit power adjacency matrix W _gas follows:

Wherein, limit power adjacency matrix W _gmatrix element W _gijfor:

In formula, Bi _jweights for circuit between node i and node j;

The connection matrix H after weighting _qcan be expressed as:

H _Q=H*W _G (5)

In formula, in the * representing matrix, corresponding element multiplies each other;

Step 2: the node number of degrees k that calculates respectively weighted network _i, node betweenness b _i, characteristic vector index C _eand tightness index C (i) _c(i) basic index, the professional etiquette of going forward side by side is formatted, and obtains degree of normalization index F ₁, normalization betweenness index F ₂, normalization characteristic vector index F ₃, normalization tightness index F ₄:

1) normalization degree index F ₁

The number of degrees k of i node _ithe number that connects the limit of this node,

$k_i=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_Q[i,j]---\left(6\right)$

To k _istandardized, can degree of normalization index F ₁as follows:

F ₁=k _i/(n-1) (7)

2) normalization betweenness index F ₂

The betweenness b of i node _iportrayed the influence power of the node in the network for information flow; If network has n node, the betweenness b of node i _ibe defined as:

$b_i=\underset{s\≠t\≠i}{\mathrm{\Σ}}{\mathrm{\δ}}_{\mathrm{st}}\left(i\right)---\left(8\right)$

${\mathrm{\δ}}_{\mathrm{st}}\left(i\right)=g_{\mathrm{st}}\left(i\right)/g_{\mathrm{st}}---\left(9\right)$

In formula, δ _st(i) mean to account for by the shortest path number of this node (limit) ratio of all shortest paths, g _stmean the shortest path number between node s and node t; g _st(i) mean the shortest path number of process node i between node s and node t, betweenness b _ican utilize Brandes betweenness centrality algorithm to obtain;

To b _istandardized, betweenness index F obtains standardizing ₂as follows:

F ₂=2b _i/(n-1)(n-2) (10)

3) normalization characteristic vector index F ₃

If λ is matrix H _qdominant eigenvalue, e=(e ₁, e ₂..., e _n) be λ characteristic of correspondence vector, the characteristic vector index C of i node _e(i) be defined as:

$C_e\left(i\right)=\frac{1}{\mathrm{\λ}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{h}_{\mathrm{ij}}{e}_j,i=\mathrm{1,2},...,n---\left(11\right)$

Wherein λ and e meet:

H _Q·e=λ·e (12)

To C _e(i) standardized, the characteristic vector of can standardizing index F ₃as follows:

F ₃=C _e(i)/max(C _e) (13)

4) normalization tightness index F ₄

The tightness index C of i node _c(i) be defined as the inverse apart from sum that this node arrives all other nodes, that is:

$C_c\left(i\right)=1/\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}---\left(14\right)$

Wherein, d _ijfor connecting the shortest path length of any two node i and j, can be obtained by the Floyd algorithm;

To C _c(i) standardized, the tightness of can standardizing index F ₄as follows:

F ₄=C _c(i)i(n-1) (15)

Step 3: to the normalization degree index F of n node of weighted network ₁, normalization betweenness index F ₂, normalization characteristic vector index F ₃with normalization tightness index F ₄, carrying out Result for Combinations, to obtain the final score F of each node overall merit as follows:

$F=\underset{k=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_k{F}_k---\left(16\right)$

Wherein, α _kweight coefficient, $\underset{k=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_k=1;k=\mathrm{1,2,3,4};$

Step 4: according to the size of the final score F value of n node overall merit, n node sorted, get the forward node of sequence, as the important node in actual communication network, thereby determine the importance of node in power telecom network.

Beneficial effect of the present invention: at first the present invention utilizes bandwidth to be weighted actual communication network, then the basic parameters such as degree, betweenness, characteristic vector and tightness of network topology are carried out comprehensively, realizes the sequence of node importance.This invention is all considered the network various aspects, is particularly suitable for communication network, and the conceptual design of relevant issues is had to certain reference, simultaneously also significant for the maintenance of network.

The accompanying drawing explanation

Fig. 1 is the FB(flow block) of the inventive method;

Fig. 2 is the network topology structure schematic diagram of example of the present invention;

Fig. 3 is the network topology structure schematic diagram after weighting of the present invention.

Embodiment

Below in conjunction with accompanying drawing, embodiments of the present invention are described further:

As shown in Figure 1, the FB(flow block) of the inventive method, a kind of communication net node importance evaluation method, is characterized in that, the method comprises the following steps:

Step 1: according to actual communication network, set up the network Model of having the right;

In the network of having the right of actual communication network, the node number is n, and the number on limit is m, figure G for the Mathematical Modeling of the network of having the right of this actual communication network _gand connection matrix H=[h _ij] be described below:

G _G=(N,L) (1)

In formula, the set that N is node in communication network, N={n ₁, n ₂, n ₃... n _n;

The set that L is one group of limit of having the right, L={l ₁, l ₂, l ₃... l _m;

Element h in connection matrix H _ijbe defined as follows:

See Fig. 2, the connection matrix with network topological diagram of connection shows as follows:

$H=\left(\begin{array}{cccccccccccccc}0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 1& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 1& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 1& 0& 1& 1& 1& 0& 0& 0& 0& 0\\ 0& 0& 1& 1& 0& 1& 1& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 1& 0& 0& 1& 1& 0& 0& 0\\ 0& 0& 0& 1& 1& 1& 0& 1& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 1& 0& 1& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 1& 0& 1& 1& 1& 0& 0\\ 0& 0& 0& 0& 1& 1& 0& 0& 1& 0& 1& 1& 0& 0\\ 0& 0& 0& 0& 0& 1& 1& 1& 1& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0\end{array}\right)$

Limit power adjacency matrix W _gas follows:

Wherein, limit power adjacency matrix W _gmatrix element W _gijfor:

In formula, B _ijweights for circuit between node i and node j.

In communication network as shown in Figure 3 between node 7 and node 11 bandwidth on limit be 2.5GHz, other sideband is wide is 1GHz, to the limit between node 7 and node 11, gives 2.5 weights, the weights on other limit are 1, power connection matrix in limit is as follows:

$W_G=\left(\begin{array}{cccccccccccccc}0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 1& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 1& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 1& 0& 1& 1& 1& 0& 0& 0& 0& 0\\ 0& 0& 1& 1& 0& 1& 1& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 1& 0& 0& 1& 1& 0& 0& 0\\ 0& 0& 0& 1& 1& 1& 0& 1& 0& 0& 2.5& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 1& 0& 1& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 1& 0& 1& 1& 1& 0& 0\\ 0& 0& 0& 0& 1& 1& 0& 0& 1& 0& 1& 1& 0& 0\\ 0& 0& 0& 0& 0& 1& 2.5& 1& 1& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0\end{array}\right)$

The connection matrix H after weighting _qcan be expressed as:

H _Q=H*W _G (5)

In formula, in the * representing matrix, corresponding element multiplies each other, limit power adjacency matrix H _qembodied the variation of the connection matrix after the weighting.

The connection matrix after weighting is:

$H_Q=H*W_G=\left(\begin{array}{cccccccccccccc}0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 1& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 1& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 1& 0& 1& 1& 1& 0& 0& 0& 0& 0\\ 0& 0& 1& 1& 0& 1& 1& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 1& 0& 0& 1& 1& 0& 0& 0\\ 0& 0& 0& 1& 1& 1& 0& 1& 0& 0& 2.5& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 1& 0& 1& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 1& 0& 1& 1& 1& 0& 0\\ 0& 0& 0& 0& 1& 1& 0& 0& 1& 0& 1& 1& 0& 0\\ 0& 0& 0& 0& 0& 1& 2.5& 1& 1& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0\end{array}\right)$

Step 2: node number of degrees k, the node betweenness b, the characteristic vector index C that calculate respectively weighted network _ewith tightness index C _cdeng basic index, the professional etiquette of going forward side by side is formatted:

1) normalization degree index F ₁

The number of degrees k of i node _ithe number that connects the limit of this node,

$k_i=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_Q[i,j]---\left(6\right)$

To k _istandardized, can degree of normalization index F ₁as follows:

F ₁=k _i/(n-1) (7)

2) normalization betweenness index F ₂

The betweenness b of i node _iportrayed the influence power of the node in the network for information flow.If network has n node, the betweenness b of node i _ibe defined as:

$b_i=\underset{s\≠t\≠i}{\mathrm{\Σ}}{\mathrm{\δ}}_{\mathrm{st}}\left(i\right)---\left(8\right)$

${\mathrm{\δ}}_{\mathrm{st}}\left(i\right)=g_{\mathrm{st}}\left(i\right)/g_{\mathrm{st}}---\left(9\right)$

In formula, δ _st(i) mean to account for by the shortest path number of this node (limit) ratio of all shortest paths, g _stmean the shortest path number between node s and node t; g _st(i) mean the shortest path number of process node i between node s and node t.Betweenness b _ican utilize Brandes betweenness centrality algorithm to obtain, concrete steps are:

The betweenness value of the arbitrary node i of definition based on source node s:

${\mathrm{\δ}}_{s\·}\left(i\right)=\underset{t\∈N}{\mathrm{\Σ}}{g}_{\mathrm{st}}\left(i\right)---\left(10\right)$

Wherein N is the node set of figure G:

$b_i=\underset{s\≠t\≠i}{\mathrm{\Σ}}{\mathrm{\δ}}_{\mathrm{st}}\left(t\right)=\underset{s\∈N}{\mathrm{\Σ}}\underset{t\∈N}{\mathrm{\Σ}}{\mathrm{\δ}}_{\mathrm{st}}\left(i\right)=\underset{s\∈N}{\mathrm{\Σ}}{\mathrm{\δ}}_{s\·}\left(i\right)---\left(11\right)$

And δ _s(i) can, by take s as root node, the breadth first traversal of figure G be tried to achieve.

To b _istandardized, betweenness index F obtains standardizing ₂as follows:

F ₂=2b _i/(n-1)(n-2) (12)

3) normalization characteristic vector index F ₃

If λ is matrix H _qdominant eigenvalue, e=(e ₁, e ₂..., e _n) be λ characteristic of correspondence vector, the characteristic vector index C of i node _e(i) be defined as:

$C_e\left(i\right)=\frac{1}{\mathrm{\λ}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{h}_{\mathrm{ij}}{e}_j,i=\mathrm{1,2},...,n---\left(13\right)$

Wherein λ and e meet:

H _Q·e=λ·e (14)

The solution procedure of λ and e is as follows:

(a) first obtain the characteristic value of matrix: | H _q-λ E|=0;

(b) each eigenvalue λ is obtained to (H _q-λ E) Basic Solutions of X=0 is e ₁, e ₂..., e _n;

(c) H _qthe characteristic vector that belongs to eigenvalue λ be exactly e ₁, e ₂..., e _nnon-zero linear combination.

To C _e(i) standardized, the characteristic vector of can standardizing index F ₃as follows:

F ₃=C _e(i)/max(C _e) (15)

4) normalization tightness index F ₄

The tightness index C of i node _c(i) be defined as the inverse apart from sum that this node arrives all other nodes, that is:

$C_c\left(i\right)=1/\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}---\left(16\right)$

Wherein, d _ijfor the shortest path length of node i and j, can be obtained by the Floyd algorithm.Concrete computational process is as follows:

Floyd algorithm adjacency matrix D used is:

Define a matrix P and be used for recording the information of institute insertion point, P[i, j] mean from V _ito V _jthe point that needs process, initialization P[i, j]=j.

Each summit is inserted in figure respectively, more relatively inserts respectively the size of distance after the k of summit and former distance:

D[i,j]=min(D[i,j],D[i,k]+D[k,j]) (18)

If D[i, j] value diminish, P[i, j]=k.Finally in D, include the information of shortest path length between 2, comprised the information in shortest path footpath in P.

To C _c(i) standardized, the tightness of can standardizing index F ₄as follows:

F ₄=C _c(i)i(n-1) (19)

Calculate respectively normalization degree, betweenness, characteristic vector and the tightness index of each node after not weighted sum weighting, as table 1, shown in table 2.

Table 1 is normalization degree, betweenness, characteristic vector, the tightness index of each node of weighted network not

The normalization degree of each node of table 2 weighted network, betweenness, characteristic vector, tightness index

N the node normalization degree index F to weighted network ₁, normalization betweenness index F ₂, normalization characteristic vector index F ₃with normalization tightness index F ₄, carrying out Result for Combinations, to obtain the final score F of each node overall merit as follows:

$F=\underset{k=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_k{F}_k---\left(20\right)$

Wherein, α _kweight coefficient, $\underset{k=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_k=1.k=\mathrm{1,2,3,4};$

The weight coefficient of normalization degree, betweenness, characteristic vector and the tightness of node gets respectively 0.2,0.25,0.35,0.2;

Step 4: according to the size of the final score F value of n node overall merit, n node sorted, get the forward node of sequence, as the important node in actual communication network, thereby determine the importance of node in actual communication network.

The node importance sequence obtained, as shown in table 3.

The contrast of table 3 node importance result of calculation

In network topological diagram as shown in Figure 2, for before weighting not, utilize synthesis and shrinkage method at first to calculate node importance, as shown in Table 3, node 4, node 5, node 9, node 10 are most important side by side; For the network after weighting, as Fig. 3, weighting node 7-11, the importance that can be obtained node 7 and node 11 by synthesis obviously improves, and it is important to be still node 4,5,9,10 for shrinkage method, like this can sufficient proof this method for the selection of core node in weighted network, there is certain advantage.Especially for power telecom network, the power telecom network Centroid is important, but the degree of its Centroid is often not high, be difficult to find Centroid according to the method for not weighting, and due to the intrinsic property of Centroid, add the bandwidth weighting, calculated by synthesis, can very effectively find Centroid.

Claims (1)

1. a communication net node importance evaluation method, is characterized in that, the method comprises the following steps:

Step 1: according to actual communication network, set up the network Model of having the right;

In actual communication network, the node number is n, and the number on limit is m, the figure G for network Model that has the right of this actual communication network _gand connection matrix H=[h _ij] be described below:

G _G=(N,L) (1)

In formula: the set that N is node in communication network, N={n ₁, n ₂, n ₃... n _n;

The set that L is one group of limit of having the right, L={l ₁, l ₂, l ₃... l _m;

Element h in connection matrix H _ijbe defined as follows:

Limit power adjacency matrix W _gas follows:

Wherein, limit power adjacency matrix W _gmatrix element W _gijfor:

In formula, B _ijweights for circuit between node i and node j;

The connection matrix H after weighting _qcan be expressed as:

H _Q=H*W _G (5)

In formula, in the * representing matrix, corresponding element multiplies each other;

Step 2: the node number of degrees k that calculates respectively weighted network _i, node betweenness b _i, characteristic vector index C _eand tightness index C (i) _c(i) basic index, the professional etiquette of going forward side by side is formatted, and obtains degree of normalization index F ₁, normalization betweenness index F ₂, normalization characteristic vector index F ₃, normalization tightness index F ₄:

1) normalization degree index F ₁

The number of degrees k of i node _ithe number that connects the limit of this node,

$k_i=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{H}_Q[i,j]---\left(6\right)$

To k _istandardized, can degree of normalization index F ₁as follows:

F ₁=k _i/(n-1) (7)

2) normalization betweenness index F ₂

The betweenness b of i node _iportrayed the influence power of the node in the network for information flow; If network has n node, the betweenness b of node i _ibe defined as:

$b_i=\underset{s\≠t\≠i}{\mathrm{\Σ}}{\mathrm{\δ}}_{\mathrm{st}}\left(i\right)---\left(8\right)$

${\mathrm{\δ}}_{\mathrm{st}}\left(i\right)=g_{\mathrm{st}}\left(i\right)/g_{\mathrm{st}}---\left(9\right)$

In formula, δ _st(i) mean to account for by the shortest path number of this node (limit) ratio of all shortest paths, g _stmean the shortest path number between node s and node t; g _st(i) mean the shortest path number of process node i between node s and node t, betweenness b _ican utilize Brandes betweenness centrality algorithm to obtain;

To b _istandardized, betweenness index F obtains standardizing ₂as follows:

F ₂=2b _i/(n-1)(n-2) (10)

3) normalization characteristic vector index F ₃

If λ is matrix H _qdominant eigenvalue, e=(e ₁, e ₂..., e _n) be λ characteristic of correspondence vector, the characteristic vector index C of i node _e(i) be defined as:

$C_e\left(i\right)=\frac{1}{\mathrm{\λ}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{h}_{\mathrm{ij}}{e}_j,i=\mathrm{1,2},...,n---\left(11\right)$

Wherein λ and e meet:

H _Q·e=λ·e (12)

To C _e(i) standardized, the characteristic vector of can standardizing index F ₃as follows:

F ₃=C _e(i)/max(C _e) (13)

4) normalization tightness index F ₄

The tightness index C of i node _c(i) be defined as the inverse apart from sum that this node arrives all other nodes, that is:

$C_c\left(i\right)=1/\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}---\left(14\right)$

Wherein, d _ijfor connecting the shortest path length of any two node i and j, can be obtained by the Floyd algorithm;

To C _c(i) standardized, the tightness of can standardizing index F ₄as follows:

F ₄=C _c(i)i(n-1) (15)

Step 3: to the normalization degree index F of n node of weighted network ₁, normalization betweenness index F ₂, normalization characteristic vector index F ₃with normalization tightness index F ₄, carrying out Result for Combinations, to obtain the final score F of each node overall merit as follows:

$F=\underset{k=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_k{F}_k---\left(16\right)$

Wherein, α _kweight coefficient, $\underset{k=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\α}}_k=1;k=\mathrm{1,2},\mathrm{3,4};$

Step 4: according to the size of the final score F value of n node overall merit, n node sorted, get the forward node of sequence, as the important node in actual communication network, thereby determine the importance of node in power telecom network.

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