CN103476051B - A kind of communication net node importance evaluation method - Google Patents

Abstract

The present invention relates to a kind of communication net node importance evaluation method, the invention belongs to nodes analysis technical field.A kind of communication net node importance evaluation method, the method comprises the following steps: step 1: the communication network according to reality sets up network Model of having the right; Step 2: the node number of degrees k, node betweenness b, the characteristic vector index C that calculate weighted network respectively _ewith tightness index C _c, professional etiquette of going forward side by side is formatted; Step 3: to F ₁, F ₂, F ₃and F ₄, carry out the final score F that Result for Combinations obtains overall merit; Step 4: sort to n node according to the final score F value of overall merit is descending, gets the node that sequence is forward, as the important node in the communication network of reality, thus determines the importance of actual communication network interior joint.First the present invention utilizes the communication network of bandwidth to reality to be weighted, and is then realized the sequence of node importance by overall merit.

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 nodes analysis technical field.

Background technology

Along with communication and the fast development of information technology, the coverage rate of communication network progressively expands, 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 the connection between this node and other nodes: be using the criterion of 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 Connected degree, such as only has the bridge node that two limits are connected.

(2) based on the method that node (collection) is deleted: 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 reflected by the change of network connectivty, performance before and after node (collection) deletion.The delet method of node all used by a lot of document, namely supposes node failure, assesses pitch point importance by comparing the change of network performance before and after deletion of node.Knot removal method Problems existing is if the deletion of multiple node all makes network not be communicated with, and so the importance degree of these nodes will be consistent, thus makes assessment result inaccuracy.

(3) node contraction method: by shrinking the limit be connected with this node, thinks that higher then this node of network cohesion degree obtained after shrinking is more important.Network cohesion level index then mainly considers the Connected degree of node and the shortest path through node, assesses the contribution of node to network.Shrinking is the effective method of one weighing and assess node importance in network.Its advantage is mainly: do not need to remove node, and application has basis more widely.Meanwhile, also there is certain shortcoming in shrinking, mainly contains: have no idea to evaluate symmetrical nodes, and for general node, also wayward its shrinks 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 connecting this node, reflection be the direct influence of a node for other node in network.

Betweenness features the possibility of information flow through given node, and the betweenness of any node all can increase along with the increase of the information flow through this node, utilizes betweenness can the network node of comformed information heavy load.Brandes betweenness centrality algorithm is the algorithm being proposed to solve betweenness by UlrikBrandes, core concept appoints 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 betweenness value corresponding to these shortest paths.The cumulative betweenness value that is source node with arbitrary node in scheming, just obtains the final betweenness value on all nodes and limit in figure.

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

Tightness is the inverse that this node arrives the distance sum of other nodes all, for portraying the complexity of the node in network by other node in network arrival 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 Floyd algorithm, and its main thought is: from representing any 2 vertex v _ito v _jthe weighted 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 _kas issuable v time intermediate vertex (other summits in a paths except initial point and terminal) _ito v _jpath distance compares, and gets 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, the basis of network characterization parametric synthesis is weighted by the bandwidth in communication network, make full use of the intrinsic property of communication network, solve the importance ranking problem of communication network interior joint, provide a kind of communication net node importance evaluation method.

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

Step 1: the communication network according to reality sets up network Model of having the right;

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

G _G＝(N,L)(1)

In formula: N is the set of communication network interior joint, N={n ₁, n ₂, n ₃... n _n;

L is the set on 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 _ijfor the weights of circuit between node i and node j;

Connection matrix H then after weighting _qcan be expressed as:

H _q=H*W _g(5), in formula, in * representing matrix, corresponding element is multiplied;

Step 2: the node number of degrees k calculating weighted network respectively _i, node betweenness b _i, characteristic vector index C _e(i) and tightness index C _ci (), professional etiquette of going forward side by side is formatted, and obtains normalization degree 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-th node _ithe number on the limit connecting this node, namely

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

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

F ₁＝k _i/(n-1)(7)

2) standardize betweenness index F ₂

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

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

δ _st(i)＝g _st(i)/g _st

(9)

In formula, δ _sti () represents the ratio being accounted for all shortest paths by the shortest path number of this node, g _strepresent the shortest path number between node s and node t; g _sti () represents the shortest path number through node i between node s and node t, betweenness b _ibrandes betweenness centrality algorithm can be utilized to obtain;

To b _istandardize, obtain normalization betweenness index F ₂as follows:

F ₂＝2b _i/(n-1)(n-2)(10)

3) standardize 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-th node _ei () is defined as:

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

Wherein λ and e meets _:

H _Q·e＝λ·e(12)

To C _ei () is standardized, characteristic vector of can standardizing index F ₃as follows:

F ₃＝C _e(i)/max(C _e)(13)

4) standardize tightness index F ₄

The tightness index C of i-th node _ci () is defined as the inverse that this node arrives the distance sum of other nodes all, that is:

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

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

To C _ci () is standardized, tightness of can standardizing index F ₄as follows:

F ₄＝C _c(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:

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

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

Step 4: sort to n node according to the final score F value of n node overall merit is descending, gets the node that sequence is forward, as the important node in the communication network of reality, thus determines the importance of power telecom network interior joint.

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

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, it is characterized in that, the method comprises the following steps:

Step 1: the communication network according to reality sets up network Model of having the right;

Actual communication network have the right in network, node number is n, and the number on limit is m, then the Mathematical Modeling of the network of having the right of the communication network of this reality schemes G _gand connection matrix H=[h _ij] be described below:

G _G＝(N,L)(1)

In formula, N is the set of communication network interior joint, N={n ₁, n ₂, n ₃... n _n;

L is the set on 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 the 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 _ijfor the weights of circuit between node i and node j.

Between communication network interior joint 7 as shown in Figure 3 and node 11, the bandwidth on limit is 2.5GHz, and other edge-band width is 1GHz, the limit between node 7 and node 11 is given to the weights of 2.5, and the weights on other limit are 1, and limit power connection matrix is as follows:

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

Connection matrix H then after weighting _qcan be expressed as:

H _Q＝H*W _G(5)

In formula, in * representing matrix, corresponding element is multiplied, limit power adjacency matrix H _qembody the change of the connection matrix after weighting.

Connection matrix then after weighting is:

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

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

1) normalization degree index F ₁

The number of degrees k of i-th node _ithe number on the limit connecting this node,

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

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

F ₁＝k _i/(n-1)(7)

2) standardize betweenness index F ₂

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

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

δ _st(i)＝g _st(i)/g _st

(9)

In formula, δ _sti () represents the ratio being accounted for all shortest paths by the shortest path number of this node, g _strepresent the shortest path number between node s and node t; g _sti () represents the shortest path number through node i between node s and node t.Betweenness b _ibrandes betweenness centrality algorithm can be utilized to obtain, and concrete steps are:

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

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

Wherein N is figure G _gnode set, then:

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

And δ _si () then can pass through with s is root node, to figure G _ga breadth first traversal try to achieve.

To b _istandardize, obtain normalization betweenness index F ₂as follows:

F ₂＝2b _i/(n-1)(n-2)(12)

3) standardize 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-th node _ei () is defined as:

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

Wherein λ and e meets:

H _Q·e＝λ·e(14)

The solution procedure of λ and e is as follows:

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

B () obtains (H to each eigenvalue λ _q-λ E) the basic course laboratory e of X=0 ₁, e ₂..., e _n;

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

To C _ei () is standardized, characteristic vector of can standardizing index F ₃as follows:

F ₃＝C _e(i)/max(C _e)(15)

4) standardize tightness index F ₄

The tightness index C of i-th node _ci () is defined as the inverse that this node arrives the distance sum of other nodes all, that is:

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

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

Floyd algorithm adjacency matrix D used is:

Define the information that a matrix P is used for recording institute insertion point, P [i, j] represents from V _ito V _jneed the point of process, initialization P [i, j]=j.

Each summit is inserted in figure respectively, then compares the size of the distance after inserting summit k and former distance respectively:

D[i,j]＝min(D[i,j],D[i,k]+D[k,j])(18)

If the value of D [i, j] diminishes, then P [i, j]=k.Then the final information including shortest path length between 2 in D, then contains the information in shortest path footpath in P.

To C _ci () is standardized, tightness of can standardizing index F ₄as follows:

F ₄＝C _c(i)·(n-1)(19)

Calculate the normalization degree of each node after non-weighted sum weighting, betweenness, characteristic vector and tightness index respectively, as table 1, shown in table 2.

The normalization degree of each node of the non-weighted network of table 1, betweenness, characteristic vector, tightness index

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

To n node normalization degree index F 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:

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

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

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

Step 4: sort to n node according to the final score F value of n node overall merit is descending, gets the node that sequence is forward, as the important node in the communication network of reality, thus determines the importance of actual communication network interior joint.

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

Table 3 node importance result of calculation contrasts

In network topological diagram as shown in Figure 2, before non-weighting, utilize synthesis and shrinkage method 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 significantly improves, and for shrinkage method be still node 4,5,9,10 important, sufficient proof this method can have certain advantage for the selection of core node in weighted network like this.Especially for power telecom network, 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 bandwidth weighting, calculated by synthesis, very effectively can find Centroid.

Claims (1)

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

Step 1: the communication network according to reality sets up network Model of having the right;

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

G _G＝(N,L)(1)

In formula: N is the set of communication network interior joint, N={n ₁, n ₂, n ₃... n _n;

L is the set on 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 _ijfor the weights of circuit between node i and node j;

Connection matrix H then after weighting _qcan be expressed as:

H _Q＝H*W _G(5)

In formula, in * representing matrix, corresponding element is multiplied;

Step 2: the node number of degrees k calculating weighted network respectively _i, node betweenness b _i, characteristic vector index C _e(i) and tightness index C _ci (), professional etiquette of going forward side by side is formatted, and obtains normalization degree 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-th node _ithe number on the limit connecting this node, namely

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

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

F ₁＝k _i/(n-1)(7)

2) standardize betweenness index F ₂

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

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

δ _st(i)＝g _st(i)/g _st

(9)

In formula, δ _sti () represents the ratio being accounted for all shortest paths by the shortest path number of this node, g _strepresent the shortest path number between node s and node t; g _sti () represents the shortest path number through node i between node s and node t, betweenness b _ibrandes betweenness centrality algorithm can be utilized to obtain;

To b _istandardize, obtain normalization betweenness index F ₂as follows:

F ₂＝2b _i/(n-1)(n-2)(10)

3) standardize 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-th node _ei () is defined as:

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

Wherein λ and e meets:

H _Q·e＝λ·e(12)

To C _ei () is standardized, characteristic vector of can standardizing index F ₃as follows:

F ₃＝C _e(i)/max(C _e)(13)

4) standardize tightness index F ₄

The tightness index C of i-th node _ci () is defined as the inverse that this node arrives the distance sum of other nodes all, that is:

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

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

To C _ci () is standardized, tightness of can standardizing index F ₄as follows:

F ₄＝C _c(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:

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

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

Step 4: sort to n node according to the final score F value of n node overall merit is descending, gets the node that sequence is forward, as the important node in the communication network of reality, thus determines the importance of power telecom network interior joint.