CN116975374A - Complex network node ordering method based on multi-feature decision - Google Patents

Complex network node ordering method based on multi-feature decision Download PDF

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CN116975374A
CN116975374A CN202310944995.6A CN202310944995A CN116975374A CN 116975374 A CN116975374 A CN 116975374A CN 202310944995 A CN202310944995 A CN 202310944995A CN 116975374 A CN116975374 A CN 116975374A
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艾达
刘鑫龙
康文哲
陈云
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Abstract

A complex network node ordering method based on multi-feature decision comprises the steps of inputting an adjacency matrix, determining self influence of nodes, determining local influence of nodes, determining global influence of nodes, determining overall influence of nodes and determining ordering results of the nodes. The invention solves the technical problem that the node importance ranking is inaccurate due to the fact that the existing single-dimension node centrality measuring method only considers the statistical characteristics of a certain specific aspect of the node. The method has the advantages of multi-dimensional evaluation of the nodes, high differentiation degree of node sequencing results, high running speed of a network model and the like, and can be applied to the technical fields of public opinion analysis, advertisement delivery, infectious disease prevention and control and the like.

Description

Complex network node ordering method based on multi-feature decision
Technical Field
The invention belongs to the technical field of complex networks, and particularly relates to a complex network node ordering method.
Background
With the complexity of human society and the increasing demands on large-scale, complex systems, research on the importance of complex network nodes is also becoming more and more important. In recent years, many classical node centrality measurement methods have been proposed for complex network node ordering studies. The node importance is measured by mainly considering the number or degree of the first-order neighbor nodes based on the centrality method of the local neighborhood of the node, such as centrality and Clusterrank, H-index, which is an intuitive and simple node ordering method, but because only the first-order neighbor nodes are considered, the influence of the nodes at a longer distance and the network topology information are ignored; the node centrality method is based on the centrality method of node paths, such as medium centrality and near centrality, and the node centrality method focuses on a network global structure, only considers shortest path information among nodes, and does not consider information outside the paths, so that the calculation complexity of a model is high, and the method has a certain limit on a large-scale network; the method emphasizes the number and the quality of neighbor nodes in a network where the nodes are located based on the centrality method of the node feature vectors, the feature vector centrality, the petty sorting and the random walk, but the method involves matrix operation, so that the time complexity is high and the convergence speed is low; the method divides the nodes in the network into different levels according to the K-shell values, and the closer the nodes are to the central position of the network, the greater the influence of the nodes is, but the method cannot distinguish the importance of the nodes in the same level.
The main technical problems existing in the prior art are as follows:
the importance degree of the node is based on the single attribute dimension of the node in the complex network, and the complex network node has various statistical characteristics and attributes, so that the ordering result of the complex network node is limited and unilateral only by determining the single dimension of the node. With the intensive research of a complex network and the mining of node characteristics, the centrality of the node is measured from a plurality of characteristics of the node, so that the centrality of the node is reflected, and the method is called a multi-characteristic decision method. The research of a complex network node ordering method based on node multi-feature decision has an important role, and the key node detection problem is still a big problem to be solved at present.
Disclosure of Invention
The technical problem to be solved by the invention is to overcome the defects of the prior art, and provide a complex network node sequencing method based on multi-feature decision, which has high accuracy, high efficiency and high network model running speed.
The technical scheme adopted for solving the technical problems comprises the following steps:
(1) Input adjacency matrix
Determining an adjacency matrix A of the complex network according to the formula (1):
wherein a is ij Representing node v i And node v j Adjacent matrix element values in between.
(2) Determining self-influence of node
Determining the self-influence SIN (v) of each node in the complex network according to (2) i ):
Wherein d (v) i ) Representing node v i Degree, k of max Representing the maximum value of the nodes in the network.
(3) Determining local influence of a node
Determining local average degree k of node according to (3) nn (v i ):
Wherein d (v) i ) Representing node v i Degree of (d) (v j ) Representing node v i First order neighbor node v of (a) j Degree of (d) (v k ) Representing node v i Is a second order neighbor node v of (2) k N represents the degree of node v i The value of n is a finite positive integer, and m represents node v i The value of m is a finite positive integer.
Determining local decision probability p (v) of node according to (4) i ):
Determining local information entropy E (v) of node according to (5) i ):
Wherein j represents node v i The value j is a finite positive integer.
Determining local self-influencing LIN (v) of the node according to (6) i ):
Wherein N represents the total number of nodes in the complex network, and the value of N is a finite positive integer.
(4) Determining global influence of a node
Determining global influence GIN (v) of node according to (7) i ):
Wherein Ks (v j ) Representation and node v i There is the shortestNode v of the path j K-Shell value, d (v) ij ) Representation and node v i Node v where shortest path exists j Degree of (d) ij Representing node v i And node v j The shortest path between them, i.noteq.j.
(5) Determining the overall impact of a node
Determining the overall impact SLGC (v) of the node according to (8) i ):
SLGC(v i )=αSIN(v i )×βLIN(v i )×γGIN(v i ) (8)
Wherein SIN (v) i ) Representing node v i Is due to its own influence, LIN (v) i ) Representing node v i Is of local influence, GIN (v) i ) Representing node v i Global influence of (a); alpha, beta and gamma are weight parameters, alpha is a limited positive integer, beta is a limited positive integer, and gamma is a limited positive integer.
(6) Determining ordering results of nodes
The overall influence SLGC (v) of the node obtained according to equation (8) is determined by a natural descending method i ) And according to the overall influence value of the nodes, natural descending order sorting is carried out from large to small, and the sorting result of the nodes in the complex network is determined.
The step (5) of the invention determines that the overall influence of the node is:
determining the overall impact SLGC (v) of the node according to (8) i ):
SLGC(v i )=αSIN(v i )×βLIN(v i )×γGIN(v i ) (8)
Wherein SIN (v) i ) Representing node v i Is due to its own influence, LIN (v) i ) Representing node v i Is of local influence, GIN (v) i ) Representing node v i Global influence of (a); alpha, beta and gamma are weight parameters, alpha epsilon [0.5,1.5 ]],β∈[0.5,1.5],γ∈[0.5,1.5]。
The step (5) of the invention determines that the overall influence of the node is:
determining the overall impact SLGC (v) of the node according to (8) i ):
SLGC(v i )=αSIN(v i )×βLIN(v i )×γGIN(v i ) (8)
Wherein SIN (v) i ) Representing node v i Is due to its own influence, LIN (v) i ) Representing node v i Is of local influence, GIN (v) i ) Representing node v i Global influence of (a); alpha, beta and gamma are weight parameters, the optimal value of alpha is 1, the optimal value of beta is 1, and the optimal value of gamma is 1.
The method and the system solve the technical problem that the importance of the node cannot be comprehensively estimated by single characteristic dimension of the traditional node from the aspects of self influence, local influence and global influence of the node and the importance degree of the node in the multi-dimensional comprehensive decision complex network.
The method measures the centrality of the node by adopting the multi-feature decision method of the self influence, the local influence and the global influence of the slave node, reflects the importance of the node, considers a plurality of feature indexes of the node, and can evaluate the importance of the node in the network more comprehensively. The invention adopts e index function to determine the self influence of the node, limits the transition caused by the difference between the node degrees and evaluates the importance of the node; and determining the local influence of the nodes by using the information entropy of the nodes, and quantifying the distribution situation of the nodes. According to the method, the node centrality is determined from the node multi-feature decision angle, the node importance evaluation accuracy is improved, and the accuracy and the efficiency of the method are greatly improved. The method has the advantages of multi-dimensional evaluation of the nodes, high differentiation degree of node sequencing results, high running speed of a network model and the like, and can be applied to the fields of public opinion analysis, advertisement delivery, infectious disease prevention and control and the like.
Drawings
Fig. 1 is a flow chart of embodiment 1 of the present invention.
Detailed Description
The technical aspects of the present invention will be clearly and specifically described below with reference to the drawings and examples, but the present invention is not limited to the following embodiments.
Example 1
In fig. 1, the complex network node ordering method based on multi-feature decision of the present embodiment is composed of the following steps:
(1) Input adjacency matrix
Determining an adjacency matrix A of the complex network according to the formula (1):
wherein a is ij Representing node v i And node v j Adjacent matrix element values in between.
(2) Determining self-influence of node
Determining the self-influence SIN (v) of each node in the complex network according to (2) i ):
Wherein d (v) i ) Representing node v i Degree, k of max Representing the maximum value of the nodes in the network.
(3) Determining local influence of a node
Determining local average degree k of node according to (3) nn (v i ):
Wherein d (v) i ) Representing node v i Degree of (d) (v j ) Representing node v i First order neighbor node v of (a) j Degree of (d) (v k ) Representing node v i Is a second order neighbor node v of (2) k N represents the degree of node v i The value of n is a finite positive integer, and m represents node v i The value of m is a finite positive integer.
Determining local decision probability p (v) of node according to (4) i ):
Determining local information entropy E (v) of node according to (5) i )。
Wherein j represents node v i The value j is a finite positive integer.
Determining local self-influencing LIN (v) of the node according to (6) i ):
Wherein N represents the total number of nodes in the complex network, and the value of N is a finite positive integer.
(4) Determining global influence of a node
Determining global influence GIN (v) of node according to (7) i ):
Wherein Ks (v j ) Representation and node v i Node v where shortest path exists j K-Shell value, d (v) ij ) Representation and node v i Node v where shortest path exists j Degree of (d) ij Representing node v i And node v j The shortest path between them, i.noteq.j.
(5) Determining the overall impact of a node
Determining the overall impact SLGC (v) of the node according to (8) i ):
SLGC(v i )=αSIN(v i )×βLIN(v i )×γGIN(v i ) (8)
Wherein SIN (v) i ) Representing node v i Is due to its own influence, LIN (v) i ) Representing node v i Is of local influence, GIN (v) i ) Representing node v i Global influence of (a); alpha, beta and gamma are weight parameters, alpha epsilon [0.5,1.5 ]],β∈[0.5,1.5],γ∈[0.5,1.5]In this embodiment, α is 1, β is 1, and γ is 1.
(6) Determining ordering results of nodes
The overall influence SLGC (v) of the node obtained according to equation (8) is determined by a natural descending method i ) And according to the overall influence value of the nodes, natural descending order sorting is carried out from large to small, and the sorting result of the nodes in the complex network is determined.
And (3) completing the complex network node ordering method based on multi-feature decision.
Example 2
The complex network node ordering method based on multi-feature decision in the embodiment comprises the following steps:
(1) Input adjacency matrix
This step is the same as in example 1.
(2) Determining self-influence of node
This step is the same as in example 1.
(3) Determining local influence of a node
This step is the same as in example 1.
(4) Determining global influence of a node
This step is the same as in example 1.
(5) Determining the overall impact of a node
Determining the overall impact SLGC (v) of the node according to (8) i ):
SLGC(v i )=αSIN(v i )×βLIN(v i )×γGIN(v i ) (8)
Wherein SIN (v) i ) Representing node v i Is due to its own influence, LIN (v) i ) Representing node v i Is of local influence, GIN (v) i ) Representing node v i Global influence of (a); alpha, beta and gamma are weight parameters, alpha epsilon [0.5,1.5 ]],β∈[0.5,1.5],γ∈[0.5,1.5]The α value of this example was 0.5, the β value was 0.5, and the γ value was 0.5.
The other steps were the same as in example 1.
And (3) completing the complex network node ordering method based on multi-feature decision.
Example 3
The complex network node ordering method based on multi-feature decision in the embodiment comprises the following steps:
(1) Input adjacency matrix
This step is the same as in example 1.
(2) Determining self-influence of node
This step is the same as in example 1.
(3) Determining local influence of a node
This step is the same as in example 1.
(4) Determining global influence of a node
This step is the same as in example 1.
(5) Determining the overall impact of a node
Determining the overall impact SLGC (v) of the node according to (8) i ):
SLGC(v i )=αSIN(v i )×βLIN(v i )×γGIN(v i ) (8)
Wherein SIN (v) i ) Representing node v i Is due to its own influence, LIN (v) i ) Representing node v i Is of local influence, GIN (v) i ) Representing node v i Global influence of (a); alpha, beta and gamma are weight parameters, alpha epsilon [0.5,1.5 ]],β∈[0.5,1.5],γ∈[0.5,1.5]The α value of this example was 1.5, the β value was 1.5, and the γ value was 1.5.
The other steps were the same as in example 1.
And (3) completing the complex network node ordering method based on multi-feature decision.
To verify the effectiveness of the present invention, the inventors performed comparative simulation experiments using the complex network node ordering method based on multi-feature decisions (hereinafter abbreviated SLGC) of example 1 of the present invention with existing degree centrality (hereinafter abbreviated DC), medium centrality (hereinafter abbreviated BC), near centrality (hereinafter abbreviated CC), feature vector centrality (hereinafter abbreviated EC), cookie ordering (hereinafter abbreviated PR), clustered Local-degree centrality (hereinafter abbreviated CLD), global Structure Model (hereinafter abbreviated GSM), local-and-Global Centrality (hereinafter abbreviated LGC). In the experiment, six different complex networks, namely Jazz, european communication network (EEC), email network (Email), social network between online users (Hamster), social network (Facebook) and online contact network (PGP), are listed as the first left column of the table 1, the node ordering result is obtained by using 8 methods, the experiment is carried out under a monotonicity function model, and the validity analysis is carried out on the node ordering result. And inputting node ordering results obtained by different methods into the monotonicity function. The experimental results are shown in Table 1.
Table 1 comparative simulation experiment results of example 1 and comparative method
As shown in Table 1, the monotonicity function value in the table has a value range of 0,1, and the monotonicity function value approaches to 1, which means that the node ordering result obtained by the method distributes nodes to different ranks, and the method has high degree of distinguishing node ordering. The node ordering obtained by the method of the embodiment 1 has higher monotonicity function values than that obtained by the contrast method, and compared with the contrast experimental method, the node ordering effect obtained by the method of the embodiment 1 is most obvious, and the discrimination capability degree of the nodes is good.

Claims (3)

1. The complex network node ordering method based on multi-feature decision is characterized by comprising the following steps:
(1) Input adjacency matrix
Determining an adjacency matrix A of the complex network according to the formula (1):
wherein a is ij Representing node v i And node v j Adjacent matrix element values in between;
(2) Determining self-influence of node
Determining the self-influence SIN (v) of each node in the complex network according to (2) i ):
Wherein d (v) i ) Representing node v i Degree, k of max Representing a maximum value of a node in the network;
(3) Determining local influence of a node
Determining local average degree k of node according to (3) nn (v i ):
Wherein d (v) i ) Representing node v i Degree of (d) (v j ) Representing node v i First order neighbor node v of (a) j Degree of (d) (v k ) Representing node v i Is a second order neighbor node v of (2) k N represents the degree of node v i The value of n is a finite positive integer, and m represents node v i The value of m is a finite positive integer;
determining local decision probability p (v) of node according to (4) i ):
Determining local information entropy E (v) of node according to (5) i ):
Wherein j represents node v i The value j is a finite positive integer;
determining local self-influencing LIN (v) of the node according to (6) i ):
Wherein N represents the total number of nodes in the complex network, and the value of N is a finite positive integer;
(4) Determining global influence of a node
Determining global influence GIN (v) of node according to (7) i ):
Wherein Ks (v j ) Representation and node v i Node v where shortest path exists j K-Shell value, d (v) ij ) Representation and node v i Node v where shortest path exists j Degree of (d) ij Representing node v i And node v j The shortest path between them, i not equal to j;
(5) Determining the overall impact of a node
Determining the overall impact SLGC (v) of the node according to (8) i ):
SLGC(v i )=αSIN(v i )×βLIN(v i )×γGIN(v i ) (8)
Wherein SIN (v) i ) Representing node v i Is due to its own influence, LIN (v) i ) Representing node v i Is of local influence, GIN (v) i ) Representing node v i Global influence of (a); alpha, beta and gamma are weight parameters, alpha is a limited positive integer, beta is a limited positive integer, and gamma is a limited positive integer;
(6) Determining ordering results of nodes
The overall influence SLGC (v) of the node obtained according to equation (8) is determined by a natural descending method i ) And according to the overall influence value of the nodes, natural descending order sorting is carried out from large to small, and the sorting result of the nodes in the complex network is determined.
2. The complex network node ordering method based on multi-feature decision according to claim 1, wherein the step (5) determines that the overall influence of the node is:
determining the overall impact SLGC (v) of the node according to (8) i ):
SLGC(v i )=αSIN(v i )×βLIN(v i )×γGIN(v i ) (8)
Wherein SIN (v) i ) Representing node v i Is due to its own influence, LIN (v) i ) Representing node v i Is of local influence, GIN (v) i ) Representing node v i Global influence of (a); alpha, beta and gamma are weight parameters, alpha epsilon [0.5,1.5 ]],β∈[0.5,1.5],γ∈[0.5,1.5]。
3. The complex network node ordering method based on multi-feature decision according to claim 1 or 2, characterized in that the step (5) determines the overall influence of the nodes as:
determining the overall impact SLGC (v) of the node according to (8) i ):
SLGC(v i )=αSIN(v i )×βLIN(v i )×γGIN(v i ) (8)
Wherein SIN (v) i ) Representing node v i Is due to its own influence, LIN (v) i ) Representing node v i Is of local influence, GIN (v) i ) Representing node v i Global influence of (a); alpha, beta and gamma are weight parameters, alpha takes 1, beta takes 1, and gamma takes 1.
CN202310944995.6A 2023-07-31 2023-07-31 Complex network node ordering method based on multi-feature decision Pending CN116975374A (en)

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