CN116032828A - Medium number centrality approximate calculation method and device - Google Patents

Medium number centrality approximate calculation method and device Download PDF

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CN116032828A
CN116032828A CN202310167081.3A CN202310167081A CN116032828A CN 116032828 A CN116032828 A CN 116032828A CN 202310167081 A CN202310167081 A CN 202310167081A CN 116032828 A CN116032828 A CN 116032828A
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centrality
network
nodes
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CN116032828B (en
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王怀习
束妮娜
马涛
王晨
冯也来
黄郡
沈培佳
杨成武
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National University of Defense Technology
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Abstract

The invention discloses a method and a device for approximate calculation of medium centrality. The method comprises the following steps: computing networkGIs characterized by the feature vector centrality of (1); calculating a network by using the feature vector centralityGThe number of the intermediate nodes is counted again to construct a multiple networkG 2 The method comprises the steps of carrying out a first treatment on the surface of the From the multiple networksG 2 Sample nodes are selected to obtain a non-heavy sample node setSThe method comprises the steps of carrying out a first treatment on the surface of the Computing the set of non-heavy sample nodesSCenter of bettery, get networkGThe median centrality approximation. Therefore, the invention selects the sample nodes of the medium number centrality calculation based on the characteristic vector centrality as the basis based on the advantage of low complexity of the characteristic vector centrality calculation, and the shortest paths among the sample nodes can better represent all the shortest paths among the network nodes by calculating the sample nodesThe shortest path between the points obtains the approximate median centrality value of the network, thereby realizing the rapid calculation of the median centrality of the large-scale network.

Description

Medium number centrality approximate calculation method and device
Technical Field
The invention relates to the technical field of networks, in particular to a method and a device for approximate calculation of betweenness centrality.
Background
Since the 21 st century, human society information has been rapidly developed, mobile internet popularization and application and internet of things deployment have rapidly landed, the number of network devices has been significantly increased, and the complexity of the number of physical network devices and the connection relationship has increased. The real networks in the different fields of power network, telecommunication network, traffic network, social network, communication network, internet of things and the like form the network world with all the inclusive sense.
The real network is a plentiful research object for network science, the abstract network is usually embodied with the same network attribute by abstracting different real networks, and the system research of abstract network property and rule forms complex network science with abundant connotation. The main research topics of network science cover network centrality measure and global network characteristics, network model structure and function analysis, network link prediction and recommendation algorithm, network dynamics, network control and optimization and the like, and the network centrality measure research plays a fundamental role in complex network science. In order to characterize the importance of nodes and edges in a network, researchers have proposed various network centrality measures that evaluate the centrality of nodes and edges in a network from various angles. The network centrality measure mainly characterizes the importance of nodes and edges in a network, and provides theoretical support for researching the identification of key nodes and key edges in a real network.
The betweenness centrality is an index for describing the importance of a certain node or a certain side in a network from the perspective of network connectivity, and is also an important research point of a complex network, and the research of a rapid calculation method has profound practical significance. For example, according to the core node in the social network, an influence ranking list is given, users are attracted, and targeted network marketing is carried out on the influence ranking list; by protecting the key server in the network, the key server can be prevented from being attacked by viruses or hackers, so that the whole network can normally operate; by isolating the infectious source, the transmission and spread of infectious viruses and the like can be effectively prevented, and in the practical application, the importance degree of each node in the network needs to be known so as to find out the key nodes in the network. However, as the number of nodes in a network increases and the connection relationship between the nodes is dense, the topology structure of the network is also more complex, and the conventional medium number centrality calculation method is difficult to completely meet the requirement of large-scale medium number centrality calculation in the network. It is highly desirable to design a fast calculation method that achieves the centrality of the bets.
Disclosure of Invention
In view of the above-mentioned problems, the present invention aims to provide a method and a device for approximate calculation of medium centrality, which are based on the advantage of low complexity of calculation of characteristic vector centrality, and based on the characteristic vector centrality, sample nodes for medium centrality calculation are selected, the shortest paths between the sample nodes can better represent all the shortest paths between network nodes, and then approximate medium centrality values are obtained by calculating the shortest paths between the sample nodes, so that the method and the device are favorable for realizing rapid calculation of medium centrality in a large-scale network.
To achieve the above object, in a first aspect of the present invention, an application task scheduling method is disclosed, where the method includes:
computing networkGThe characteristic vector centrality is obtained; the feature vector centrality
Figure SMS_1
The method comprises the steps of carrying out a first treatment on the surface of the The saidnRepresentation vector->
Figure SMS_2
Component numbers of (2); the saidnEqual netCollateralsGTotal number of medium nodes. />
Calculating a network by using the feature vector centralityGThe number of the nodes again, construct the multiple networkG 2 。
From the multiple networksG 2 Sample nodes are selected to obtain a non-heavy sample node setS。
Computing the set of non-heavy sample nodesSCenter of bettery, get networkGThe median centrality approximation.
As an optional implementation manner, in the first aspect of the embodiment of the present invention, the calculating network uses the feature vector centralityGNode weight sequence of (a) to construct a multiple networkG 2 Comprising:
calculating the mean value of each component of the centrality of the feature vector to obtain a component mean value
Figure SMS_3
。
The said
Figure SMS_4
The method comprises the steps of carrying out a first treatment on the surface of the Said->
Figure SMS_5
。
Judging the component mean value
Figure SMS_6
Whether or not it is smaller than a preset average weight numbercAnd obtaining a judging result.
The average weight numbercThe range of the values is as follows
Figure SMS_7
The method comprises the steps of carrying out a first treatment on the surface of the The range of the average weight value sufficiently ensures the universality and the variability of the sampled samples based on the centrality of the feature vector, wherein ∈ >
Figure SMS_8
For networksGIs the average degree of the node.
According to the judging result, utilizing a preset directionCalculating a model of the vector coefficients to obtain the vector coefficients
Figure SMS_9
。
Centering the feature vector with the vector coefficients
Figure SMS_10
Multiplying to obtain a second feature vector; said feature vector centrality->
Figure SMS_11
The method comprises the steps of carrying out a first treatment on the surface of the Said second eigenvector->
Figure SMS_12
。
And rounding up each component in the second feature vector to obtain a node weight vector.
The node weight vector
Figure SMS_13
The method comprises the steps of carrying out a first treatment on the surface of the Said->
Figure SMS_14
The method comprises the steps of carrying out a first treatment on the surface of the Said->
Figure SMS_15
Is a non-negative integer; the i-th component in the node weight vector +.>
Figure SMS_16
Characterizing a networkGI node->
Figure SMS_17
Corresponding weight number.
Using node weight vectors for the networkGProcessing to obtain multiple networksG 2 。
The said
Figure SMS_18
。
In an optional implementation manner, in a first aspect of the embodiment of the present invention, according to the determination result, a vector coefficient is obtained by using a preset vector coefficient calculation model, where the method includes:
when the judgment result is yes, calculating the minimum integer for enabling the preset first vector coefficient calculation model to be established
Figure SMS_19
The minimum integer +.>
Figure SMS_20
As vector coefficient->
Figure SMS_21
Is a value of (2).
The first vector coefficient calculation model is
Figure SMS_22
。
Wherein, the said
Figure SMS_23
；/>
Figure SMS_24
Representing an upward rounding; the saidn=Network systemGThe total number of the middle nodes; the said
Figure SMS_25
Is an integer greater than 0; said->
Figure SMS_26
Representing a preset average weight +.>
Figure SMS_27
。
When the judgment result is NO, calculating the maximum integer for enabling the preset second vector coefficient calculation model to be established
Figure SMS_28
The maximum integer +.>
Figure SMS_29
Is the reciprocal of the vector coefficient->
Figure SMS_30
Is a value of (2).
The second vector coefficient calculation model is
Figure SMS_31
。/>
Wherein, the said
Figure SMS_32
；/>
Figure SMS_33
Representing an upward rounding; the saidn=Network systemGThe total number of the middle nodes; said->
Figure SMS_34
Is an integer greater than 0; said->
Figure SMS_35
Representing a preset average weight +.>
Figure SMS_36
。
As an optional implementation manner, in the first aspect of the embodiment of the present invention, the multiple network is selected from the multiple networksG 2 Sample nodes are selected to obtain a non-heavy sample node setSComprising:
from the multiple networksG 2 In the method, the method is selected according to uniform random probability distribution
Figure SMS_37
Obtaining a first sample node set by the nodes; said->
Figure SMS_38
The method comprises the steps of carrying out a first treatment on the surface of the Said->
Figure SMS_39
Representing an upward rounding; the saidn=Network systemGThe total number of the middle nodes; said->
Figure SMS_40
Characterizing a predetermined sampling rate, +.>
Figure SMS_41
The value range is +.>
Figure SMS_42
The sampling proportion is selected by comprehensively considering the representativeness of the sampling sample and the efficiency of an approximate calculation method.
And judging whether the number of the repeated nodes exists in the first sample node set or not to obtain a second judging result.
If the second judgment result is yes, deleting repeated nodes in the first sample node set, selecting new nodes from a method of uniform random probability distribution in a multiple network, adding the new nodes into the first sample node set, and enabling the total number of the nodes in the first sample node set to reach
Figure SMS_43
And triggering and executing the judgment whether the first sample node set has the repeated nodes or not to obtain a second judgment result.
If the second judgment result is negative, the first sample node set is confirmed to be a non-heavy sample node setS。
As an optional implementation manner, in the first aspect of the embodiment of the present invention, the computing networkGFeature vector centrality, resulting in feature vector centrality, comprising:
constructing a networkGAdjacent matrix a of (a);
the said
Figure SMS_44
If the network isGMiddle node->
Figure SMS_45
And node->
Figure SMS_46
With edges in between, then->
Figure SMS_47
The method comprises the steps of carrying out a first treatment on the surface of the Otherwise
Figure SMS_48
。
And constructing a first characteristic equation based on the adjacency matrix A.
The first characteristic equation is
Figure SMS_49
。
Where A is the adjacency matrix of the network,
Figure SMS_50
is characteristic value (I)>
Figure SMS_51
Is a feature vector.
And carrying out calculation processing on the first characteristic equation, calculating to obtain a characteristic vector corresponding to the maximum characteristic value, and taking the characteristic vector corresponding to the maximum characteristic value as characteristic vector centrality.
As an optional implementation manner, in the first aspect of the embodiment of the present invention, the computing the set of non-heavy sample nodesSCenter of bettery, get networkGA median centrality approximation comprising:
using a median centrality calculation model for the non-heavy sample node set SAnd processing to obtain the medium centrality of the sample node set S.
The medium centrality calculation model is as follows:
Figure SMS_52
/>
Figure SMS_53
in the method, in the process of the invention,
Figure SMS_57
representing node->
Figure SMS_59
Center of betting, ->
Figure SMS_65
Representing edge->
Figure SMS_55
Center of betting, ->
Figure SMS_61
For node->
Figure SMS_62
To node->
Figure SMS_67
Is>
Figure SMS_54
For node->
Figure SMS_60
To node->
Figure SMS_63
Through node->
Figure SMS_66
The number of shortest paths of (a); />
Figure SMS_56
For node->
Figure SMS_58
To node->
Figure SMS_64
Pass by edge->
Figure SMS_68
The number of shortest paths of (a);Srepresenting a set of non-heavy sample nodesS。
Determining the medium centrality of the sample node set S as a networkGIs approximated to the median centrality of (a) to obtain a networkGIs a median centrality approximation of (c).
In a second aspect of an embodiment of the present invention, there is disclosed a medium centrality approximation calculation apparatus, the apparatus including:
a first computing module for computing a networkGThe characteristic vector centrality is obtained; the feature vector centrality
Figure SMS_69
The method comprises the steps of carrying out a first treatment on the surface of the The saidnRepresentation vector->
Figure SMS_70
Component numbers of (2); the saidnEqual to the networkGThe total number of the middle nodes;
a first network construction module for calculating a network using the feature vector centralityGThe number of the nodes again, construct the multiple networkG 2 ；
A second network construction module for constructing a network from the multiple networksG 2 Sample nodes are selected to obtain a non-heavy sample node set S；
A second calculation module for calculating the non-heavy sample node setSCenter of bettery, get networkGThe median centrality approximation.
In a second aspect of the embodiment of the present invention, the first computing module computes a networkGThe characteristic vector centrality is obtained by the specific way that:
constructing a networkGIs a contiguous matrix a of (a).
The said
Figure SMS_71
If the network isGMiddle node->
Figure SMS_72
And node->
Figure SMS_73
With edges in between, then->
Figure SMS_74
The method comprises the steps of carrying out a first treatment on the surface of the Otherwise
Figure SMS_75
。
And constructing a first characteristic equation based on the adjacency matrix A.
The first characteristic equation is
Figure SMS_76
。
Where A is the adjacency matrix of the network,
Figure SMS_77
is characteristic value (I)>
Figure SMS_78
Is a feature vector.
And carrying out calculation processing on the first characteristic equation, calculating to obtain a characteristic vector corresponding to the maximum characteristic value, and taking the characteristic vector corresponding to the maximum characteristic value as characteristic vector centrality.
In a second aspect of the embodiment of the present invention, the first network construction module calculates a network using the feature vector centralityGThe number of the nodes again, construct the multiple networkG 2 The method specifically comprises the following steps:
calculating the mean value of each component of the centrality of the feature vector to obtain a component mean value
Figure SMS_79
。/>
The said
Figure SMS_80
The method comprises the steps of carrying out a first treatment on the surface of the Said->
Figure SMS_81
。
Judging the component mean value
Figure SMS_82
Whether or not it is smaller than a preset average weight numbercAnd obtaining a judging result.
The average weight numbercThe range of the values is as follows
Figure SMS_83
The method comprises the steps of carrying out a first treatment on the surface of the The range of the average weight value sufficiently ensures the universality and the variability of the sampled samples based on the centrality of the feature vector, wherein ∈>
Figure SMS_84
For networksGIs the average degree of the node.
According to the judgment result, a preset vector coefficient calculation model is utilized to obtain a vector coefficient
Figure SMS_85
。
Centering the feature vector with the vector coefficients
Figure SMS_86
Multiplying to obtain a second feature vector; said feature vector centrality->
Figure SMS_87
The method comprises the steps of carrying out a first treatment on the surface of the Said second eigenvector->
Figure SMS_88
。
And rounding up each component in the second feature vector to obtain a node weight vector.
The node weight vector
Figure SMS_89
The method comprises the steps of carrying out a first treatment on the surface of the Said->
Figure SMS_90
The method comprises the steps of carrying out a first treatment on the surface of the The said
Figure SMS_91
Is a non-negative integer; the i-th component in the node weight vector +.>
Figure SMS_92
Characterizing a networkGI node->
Figure SMS_93
Corresponding weight number.
Using node weight vectors for the networkGProcessing to obtain multiple networksG 2 。
The said
Figure SMS_94
。
In a second aspect of the embodiment of the present invention, the first network construction module calculates a model by using a preset vector coefficient according to the determination result to obtain a vector coefficient, and specifically includes:
When the judgment result is yes, calculating the minimum integer for enabling the preset first vector coefficient calculation model to be established
Figure SMS_95
The minimum integer +.>
Figure SMS_96
As vector coefficient->
Figure SMS_97
Is a value of (2).
The first vector coefficient calculation model is
Figure SMS_98
。
Wherein, the said
Figure SMS_99
；/>
Figure SMS_100
Representing an upward rounding; saidn=Network systemGThe total number of the middle nodes; said->
Figure SMS_101
Is an integer greater than 0; said->
Figure SMS_102
Representing a preset average weight +.>
Figure SMS_103
。
When the judgment result is NO, calculating the maximum integer for enabling the preset second vector coefficient calculation model to be established
Figure SMS_104
The maximum integer +.>
Figure SMS_105
Is the reciprocal of the vector coefficient->
Figure SMS_106
Is a value of (2).
The second vector coefficient calculation model is
Figure SMS_107
。
Wherein, the said
Figure SMS_108
；/>
Figure SMS_109
Representing an upward rounding; the saidn=Network systemGThe total number of the middle nodes; said->
Figure SMS_110
Is an integer greater than 0; said->
Figure SMS_111
Representing a preset average weight +.>
Figure SMS_112
。/>
As an optional implementation manner, in the second aspect of the embodiment of the present invention, the second network building module is configured from the multiple networksG 2 Sample nodes are selected to obtain a non-heavy sample node setSThe method specifically comprises the following steps:
from the multiple networksG 2 In the method, the method is selected according to uniform random probability distribution
Figure SMS_113
Obtaining a first sample node set by the nodes; said->
Figure SMS_114
The method comprises the steps of carrying out a first treatment on the surface of the Said->
Figure SMS_115
Representing an upward rounding; the said n=Network systemGThe total number of the middle nodes; said->
Figure SMS_116
Characterizing a predetermined sampling rate, +.>
Figure SMS_117
The value range is +.>
Figure SMS_118
The sampling proportion is selected by comprehensively considering the representativeness of the sampling sample and the efficiency of an approximate calculation method.
And judging whether the number of the repeated nodes exists in the first sample node set or not to obtain a second judging result.
When the second judgment result is yes, deleting repeated nodes in the first sample node set, selecting new nodes from a method of uniform random probability distribution in a multiple network, and adding the new nodes into the first sample node set to enable the total number of the nodes in the first sample node set to reachsAnd triggering and executing the judgment whether the first sample node set has the repeated nodes or not to obtain a second judgment result.
When the second judgment result is no, the first sample node set is confirmed to be a no-heavy sample node setS。
As an optional implementation manner, in the second aspect of the embodiment of the present invention, the second calculation module calculates the set of non-heavy sample nodesSCenter of bettery, get networkGThe median centrality approximation value specifically comprises:
using a median centrality calculation model for the non-heavy sample node set SAnd processing to obtain the medium centrality of the sample node set S.
The medium centrality calculation model is as follows:
Figure SMS_119
Figure SMS_120
in the method, in the process of the invention,
Figure SMS_124
representing node->
Figure SMS_129
Center of betting, ->
Figure SMS_133
Representing edge->
Figure SMS_123
Center of betting, ->
Figure SMS_128
For node->
Figure SMS_132
To node->
Figure SMS_135
Is>
Figure SMS_121
For node->
Figure SMS_125
To node->
Figure SMS_126
Through node->
Figure SMS_131
The number of shortest paths of (a); />
Figure SMS_122
For node->
Figure SMS_127
To node->
Figure SMS_130
Pass by edge->
Figure SMS_134
The number of shortest paths of (a);Srepresenting a set of non-heavy sample nodesS。
Determining the medium centrality of the sample node set S as a networkGIs approximated to the median centrality of (a) to obtain a networkGThe median centrality approximation.
Another aspect of the invention discloses another medium number centrality approximation calculation device, the device comprising:
a memory storing executable program code;
a processor coupled to the memory;
the processor invokes the executable program code stored in the memory to perform some or all of the steps in the method for median centering approximation calculation disclosed in the first aspect of the embodiment of the present invention.
A fourth aspect of the present invention discloses a computer storage medium storing computer instructions for performing part or all of the steps in the method for central approximation of a betweenness disclosed in the first aspect of the present invention when called.
The invention has the beneficial effects that:
the invention relates to a method for approximate calculation of betweenness centrality, which uses a calculation networkGThe characteristic vector centrality is obtained; calculating a network by using the feature vector centralityGThe number of the intermediate nodes is counted again to construct a multiple networkG 2 The method comprises the steps of carrying out a first treatment on the surface of the From the multiple networksG 2 Sample nodes are selected to obtain a non-heavy sample node setSThe method comprises the steps of carrying out a first treatment on the surface of the Computing the set of non-heavy sample nodesSCenter of bettery, get networkGThe median centrality approximation. It can be seen that the inventionBased on the advantage of low complexity of feature vector centrality calculation, sample nodes of the medium centrality calculation are selected based on feature vector centrality, shortest paths among the sample nodes can better represent all shortest paths among network nodes, and network approximate medium centrality values are obtained by calculating the shortest paths among the sample nodes, so that the medium centrality of a large-scale network is rapidly calculated.
Drawings
FIG. 1 is a flow chart of a method for calculating a median centrality approximation in accordance with an embodiment of the present invention;
FIG. 2 is a schematic diagram of an exemplary three-layer routing network according to one embodiment of the present invention;
FIG. 3 is a schematic diagram of a medium-center approximation calculation device according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of another medium-center approximation calculation apparatus according to an embodiment of the present invention.
Detailed Description
In order that those skilled in the art will better understand the present invention, a technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
For the sake of easy understanding of the embodiments of the present application, the following will briefly introduce related concepts:
the median centrality. The betweenness centrality is generally divided into node betweenness centrality and edge betweenness centrality, and betweenness centrality index is an important centrality index in key node and key link identification. Given network
Figure SMS_136
Represents node set and edge set, respectively,/-of the network>
Figure SMS_137
Representing the number of nodes in the network, < >>
Figure SMS_138
Representing the number of edges in the network.
Node bets are defined as the ratio of the number of all shortest paths through the node to the total number of shortest paths in the network. Node in network
Figure SMS_139
The betweenness of (a) is defined as:
Figure SMS_140
wherein the method comprises the steps of
Figure SMS_141
For node->
Figure SMS_142
To node->
Figure SMS_143
Is>
Figure SMS_144
For node->
Figure SMS_145
To node->
Figure SMS_146
Through node->
Figure SMS_147
Is used for the number of shortest paths of the network.
Edge betweenness is defined as the ratio of the number of all shortest paths through the edge to the total number of shortest paths in the network. Edge(s)eThe betweenness of (a) is defined as:
Figure SMS_148
wherein the method comprises the steps of
Figure SMS_149
For node->
Figure SMS_150
To node->
Figure SMS_151
Pass by edge->
Figure SMS_152
Is used for the number of shortest paths of the network.
For ease of research, node and edge betweenness centrality in a network is often normalized, and normalized betweenness centrality in an undirected network is defined as:
Figure SMS_153
the closer the normalized value is to 1, the higher the frequency of the node on the shortest path between the network nodes is, and the more important is; when the normalized value is 0, the node is not present on the shortest path between other nodes, and the importance is very low.
Theorem: in a connected network, the sum of node normalization medians is equal to the average shortest distance of the network
Figure SMS_154
Subtracting 1; the sum of the edge normalized medians is equal to the average shortest distance +.>
Figure SMS_155
I.e.
Figure SMS_156
The relationship between the mid-distance centrality and the edge mid-distance centrality in the network and the average shortest distance of the network is given by the mid-distance centrality identity, which reveals the inter-implication relationship between the mid-distance centrality and the average shortest path of the network, and establishes the relationship between the mid-distance centrality and the small world network. The medium center identity is established not only on the connected network but also on the general network.
The betweenness centrality calculation usually adopts a Brandes algorithm, and the algorithm uses a depth-first search algorithm when calculating the betweenness centrality of an unauthorized network, wherein the calculation complexity is that
Figure SMS_157
The method comprises the steps of carrying out a first treatment on the surface of the In calculating the betweenness centrality of the weighted network, the Dijkstra algorithm is used, and the calculation complexity is +.>
Figure SMS_158
. When the network isGIn case of dense network, the->
Figure SMS_159
The median centrality computational complexity is +.>
Figure SMS_160
The computational complexity is high and cannot be applied to a large-scale network.
Feature vector centrality. Feature vector centrality is an important measure of node centrality in a network, the feature vector centrality is related to the number of adjacent nodes and the importance of each adjacent node in the nodes, and node information of the centrality is more abundant than the number of the centrality.
Order the
Figure SMS_161
Representing a networkGIs described as (1) if the node is->
Figure SMS_162
And node->
Figure SMS_163
With edges in between
Figure SMS_164
The method comprises the steps of carrying out a first treatment on the surface of the Otherwise->
Figure SMS_165
. Node->
Figure SMS_166
The feature vector centrality of (1) may be defined as: />
Figure SMS_167
Wherein,,
Figure SMS_168
is node->
Figure SMS_169
A set of all neighboring nodes,>
Figure SMS_170
is a constant.
Feature vector centrality definitions may be expressed as matrix-vector tokens,
Figure SMS_172
constant->
Figure SMS_174
Is an adjacency matrixAIs>
Figure SMS_177
Is characteristic value +.>
Figure SMS_173
Corresponding feature vectors. Typically, an adjacency matrix AThere are a number of different characteristic values +.>
Figure SMS_176
There is also a corresponding feature vector. However, the fact that all elements of the matrix are positive means that only the largest eigenvalues will produce the required centrality measure. The eigenvectors of the adjacency matrix are +.>
Figure SMS_178
The individual components give the nodes +.>
Figure SMS_179
Is used for the feature vector centrality value of (1). Since the eigenvector point multiplied by an arbitrary constant is still eigenvalue +.>
Figure SMS_171
The patent introduces an average weight parameter to determine feature vector values when constructing multiple networks based on feature vector centrality. The feature vector centrality temporal complexity is +.>
Figure SMS_175
The computational complexity is low.
Example 1
Referring to fig. 1, fig. 1 is a schematic flow chart of a method for calculating a median centrality approximation according to an embodiment of the present invention. The method described in fig. 1 is applicable to an information network, a social network, an internet of things and a traffic network, and the embodiment of the invention is not limited. As shown in fig. 1, the method for calculating the median centrality approximation of the feature vector centrality may include the following operations:
101. computing networkGAnd obtaining the characteristic vector centrality.
In the embodiment of the invention, the characteristic vector centrality
Figure SMS_180
The method comprises the steps of carrying out a first treatment on the surface of the The saidnRepresentation vector->
Figure SMS_181
Component numbers of (2); the saidnRepresenting a networkGTotal number of medium nodes.
102. Computing networks using feature vector centralityGThe number of the nodes again, construct the multiple networkG 2 。
103. From multiple networksG 2 Sample nodes are selected to obtain a non-heavy sample node setS。
104. Computing a set of non-duplicate sample nodesSCenter of bettery, get networkGThe median centrality approximation.
Therefore, by implementing the method for approximate calculation of the betweenness centrality described by the embodiment of the invention, the centrality of the feature vector is obtained by calculating the centrality of the feature vector of the original network, the non-heavy sample node set is selected based on the centrality of the feature vector, and the value of the betweenness centrality of the non-heavy sample node set is calculated to obtain the value of the approximate betweenness centrality of the original network, so that the calculation is simplified, the complexity is reduced, and the rapid calculation of the betweenness centrality of the large-scale network is realized.
In an alternative embodiment, the computing network is calculated in step 101 aboveGFeature vector centrality, resulting in feature vector centrality, comprising:
constructing a networkGIs a contiguous matrix a of (a).
The said
Figure SMS_182
If the network isGMiddle node->
Figure SMS_183
And node->
Figure SMS_184
With edges in between, then->
Figure SMS_185
The method comprises the steps of carrying out a first treatment on the surface of the Otherwise
Figure SMS_186
。
And constructing a first characteristic equation based on the adjacency matrix A.
The first characteristic equation is
Figure SMS_187
。
In the method, in the process of the invention,
Figure SMS_188
for the adjacency matrix of the network,>
Figure SMS_189
is characteristic value (I)>
Figure SMS_190
Is a feature vector; />
Figure SMS_191
。
According to the Perron-Frobenius theorem,
Figure SMS_192
. Based on this characteristic, feature vector centrality calculation is often developed by a matrix exponentiation method, i.e., an initial vector +.>
Figure SMS_193
Then iterate to calculate +.>
Figure SMS_194
When the number of iterationstWhen a certain threshold is reached, the person is allowed to go (I)>
Figure SMS_195
The value is close to the maximum characteristic value
Figure SMS_196
The corresponding feature vector, i.e. feature vector centrality.
It can be seen that the value of the centrality of the feature vector characterizes the networkGThe importance of a node in the set determines the probability that the node is selected as a sample node.
In another alternative embodiment, the feature vector centrality is used in step 102 to calculate a networkGNode weight sequence of (a) to construct a multiple networkG 2 Comprising:
calculating the mean value of each component of the centrality of the feature vector to obtain a component mean value
Figure SMS_197
。
The said
Figure SMS_198
The method comprises the steps of carrying out a first treatment on the surface of the Said->
Figure SMS_199
。
Judging the component mean value
Figure SMS_200
Whether or not it is smaller than a preset average weight numbercAnd obtaining a judging result.
The average weight numbercThe range of the values is as follows
Figure SMS_201
The method comprises the steps of carrying out a first treatment on the surface of the Wherein->
Figure SMS_202
For networksGIs the average degree of the node.
According to the judgment result, a preset vector coefficient calculation model is utilized to obtain a vector coefficient
Figure SMS_203
。
Centering the characteristic vector and vector coefficient
Figure SMS_204
Multiplying to obtain a second feature vector; the characteristic vector centrality->
Figure SMS_205
The method comprises the steps of carrying out a first treatment on the surface of the The second feature vector->
Figure SMS_206
。
And rounding up each component in the second characteristic vector to obtain a node weight vector.
The node weight vector
Figure SMS_207
The method comprises the steps of carrying out a first treatment on the surface of the Above->
Figure SMS_208
The method comprises the steps of carrying out a first treatment on the surface of the Above-mentioned
Figure SMS_209
Is a non-negative integer; the i-th component in the node weight vector +.>
Figure SMS_210
Characterizing a networkGI node->
Figure SMS_211
Corresponding weight number.
Using node weight vector to networkGProcessing to obtain multiple networksG 2 。
The said
Figure SMS_212
。
Therefore, the universality and the diversity of the sampled samples based on the characteristic vector centrality are fully ensured by reasonably taking the average weight, the weight of the network node is determined according to the average value of each component of the characteristic vector centrality and the average weight, the weight of the node in the multiple network is in direct proportion to the characteristic vector centrality of the node, and the more important node becomes the sample node with higher probability due to the construction of the multiple network.
In yet another optional embodiment, the calculating a model according to the determination result by using a preset vector coefficient to obtain a vector coefficient includes:
when the judgment result is yes, calculating the minimum integer for enabling the preset first vector coefficient calculation model to be established
Figure SMS_213
The minimum integer is +.>
Figure SMS_214
As vector coefficient->
Figure SMS_215
Is a value of (2).
The first vector coefficient calculation model is as follows
Figure SMS_216
。
Wherein, the above
Figure SMS_217
；/>
Figure SMS_218
Representing an upward rounding; above-mentionednRepresenting the number of components in the centrality of the feature vector; above->
Figure SMS_219
Is an integer greater than 0; above->
Figure SMS_220
Representing a preset average weight +.>
Figure SMS_221
。
When the judgment result is NO, calculating the maximum integer for enabling the preset second vector coefficient calculation model to be established
Figure SMS_222
The maximum integer +.>
Figure SMS_223
Is the reciprocal of the vector coefficient->
Figure SMS_224
Is a value of (2).
The second vector coefficient calculation model is as follows
Figure SMS_225
。
Wherein, the above
Figure SMS_226
；/>
Figure SMS_227
Representing an upward rounding; above-mentionednRepresenting the number of components in the centrality of the feature vector; said->
Figure SMS_228
Is an integer greater than 0; said->
Figure SMS_229
Representing a preset average weight +.>
Figure SMS_230
。
It can be seen that the value of the centrality of the feature vector represents the importance degree of different nodes, and the average weight is used to control the value of the vector coefficient to construct multiple networksG 2 Thereby ensuring that important nodes appear in the multiple network with higher numbers of weights and that secondary nodes appear in the multiple network with lower numbers of weights while the total number of weights of the multiple network is controlled within a reasonable range.
In yet another alternative embodiment, the step 103 is performed from multiple networks G 2 Sample nodes are selected to obtain a non-heavy sample node setSComprising:
from multiple networksG 2 In the method, the method is selected according to uniform random probability distribution
Figure SMS_231
Obtaining a first sample node set by the nodes; above->
Figure SMS_232
The method comprises the steps of carrying out a first treatment on the surface of the Above->
Figure SMS_233
Representing an upward rounding; above-mentionednRepresenting the number of components in the centrality of the feature vector; above->
Figure SMS_234
Characterizing a predetermined sampling rate, +.>
Figure SMS_235
The value range is +.>
Figure SMS_236
The sampling proportion is selected by comprehensively considering the representativeness of the sampling sample and the efficiency of an approximate calculation method.
Judging whether the first sample node set has the number of repeated nodes or not to obtain a second judging result;
if the second judgment result is yes, deleting repeated nodes in the first sample node set, selecting new nodes from a method of uniform random probability distribution in the multiple networks, adding the new nodes into the first sample node set, and enabling the total number of the nodes in the first sample node set to reach
Figure SMS_237
And triggering and executing the judgment whether the first sample node set has the repeated node or not, and obtaining a second judgment result.
If the second judgment result is no, the first sample node set is confirmed to be a non-heavy sample node setS。
It can be seen that the sampling proportion is preset by comprehensively considering the representativeness of the sampling samples and the efficiency of the approximate calculation method, so that the node set without the heavy samples SScale of (a) is compared with the initial networkGScale between 0.1 and 0.2.
In yet another alternative embodiment, a set of no-heavy sample nodes is calculated in step 104 aboveSCenter of bettery, get networkGA median centrality approximation comprising:
for the node set without heavy sample by using the medium number centrality calculation modelSAnd processing to obtain the medium centrality of the sample node set S.
The above-mentioned medium centrality calculation model is:
Figure SMS_238
Figure SMS_239
in the method, in the process of the invention,
Figure SMS_243
representing node->
Figure SMS_248
Center of betting, ->
Figure SMS_254
Representing edge->
Figure SMS_242
Center of betting, ->
Figure SMS_246
For node->
Figure SMS_250
To node->
Figure SMS_253
Is>
Figure SMS_240
For node->
Figure SMS_245
To node->
Figure SMS_247
Through node->
Figure SMS_251
The number of shortest paths of (a); />
Figure SMS_241
For node->
Figure SMS_244
To node->
Figure SMS_249
Pass by edge->
Figure SMS_252
The number of shortest paths of (a)SRepresenting a set of non-heavy sample nodesS。
Determining the medium centrality of the sample node set S as a networkGThe medium number centrality approximation of the network G node is obtained.
It can be seen that the pass is required in defining the median centrality accuratelyReplacing the shortest path set between any node of the calendar with only traversing the no-duplicate sample node setSThe shortest path set among the inner nodes greatly reduces the scale of path search, and meanwhile, the approximate value of the centrality of the betweenness keeps the magnitude sequence relation of the centrality values of the betweenness of different nodes and edges as much as possible. Node set due to no heavy sample SIs only between 0.1 and 0.2 of the initial node set size, so as to have no heavy sample node setSThe calculation complexity of the approximation of the computation of the betweenness centrality is equivalent to 0.01 to 0.04 of the complexity of the accurate calculation method, so that the betweenness calculation complexity of the large-scale network is rapidly reduced.
To specifically illustrate the method of the present embodiment, a typical three-layer routing network is used
Figure SMS_255
An explanation is given.
The above-mentioned typical three-layer routing network structure is shown in fig. 2, and numerals 1 to 31 in fig. 2 respectively denote routing networks
CollateralsG31 router nodes in (1), 31 router nodes constitute a router node setV，Connection of routers
Forming edges, all edges forming an edge setE。
Specifically, the network
Figure SMS_256
Middle router node set +.>
Figure SMS_257
Sum of edges->
Figure SMS_258
The following are provided:
Figure SMS_259
Figure SMS_260
Figure SMS_261
。
in order to calculate the betweenness centrality of nodes in the network, an approximate calculation method based on the feature vector centrality is performed as follows:
step 1: computing networkGThe feature vector values of the nodes, and the feature vector centrality of the nodes are shown in table 1:
table 1 feature vector centrality for each node
Figure SMS_262
Step 2: and calculating the weight of the network G node by utilizing the centrality of the feature vector, and constructing a multiple network G2.
Setting average weight number, due to average degree of node
Figure SMS_263
Selecting average weight- >
Figure SMS_264
；
The node weight distribution is determined from the distribution of feature vector centrality as shown in table 2 below:
table 2 node weight distribution
Figure SMS_265
Constructing multiple networks based on node reconstruction numbersG 2 As shown in table 2,G 2 including 14 nodes 1,9 nodes 2, … …,3 nodes 31.
Step 3: from multiple networksG 2 Sample nodes are selected to obtain a non-heavy sample node set S;
according to the node weight distribution and the method of uniform random probability distribution, the node sampling probability distribution can be calculated as shown in table 3:
TABLE 3 node sampling probability distribution
Figure SMS_266
Setting sampling proportion
Figure SMS_267
=0.2。/>
According to sampling probability
Figure SMS_268
Sample node set can be knownSScale of +.>
Figure SMS_269
Calculated no-heavy sample node set +.>
Figure SMS_270
。
Step 4: calculating the centrality of S bets of node sets without heavy samples to obtain a networkGThe median centrality approximation is shown in table 4:
table 4 networkGIntermediate center approximation
Figure SMS_271
Since the approximation and the exact value of the median centrality adopt the same normalization coefficient, but the node sets involved between the approximation and the exact value are respectivelySAndVtherefore, there is no practical significance in comparing the actual numerical values between the two. The selection of key nodes and key edges mainly depends on the order of magnitude of the median centrality values. From the approximate distribution of the betweenness centrality, the importance of the nodes is as follows: 1,4,6,3,5,2,7,9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31.
To analyze the effect of the median center approximation calculation method, table 5 gives the exact value distribution of the median center, and it is known that the node importance degree is: 1,2,3,4,5,6,7,9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31.
Table 5 networkGCenter of median precision value
Figure SMS_272
By comparing the approximate value and the accurate value sequencing result of the centrality of the medians, the accuracy rate reaches more than 90 percent except that the importance degree of the nodes 2,3 and 5 is changed and the sequences of other nodes are maintained.
When the node of the node set without the heavy sample is selected, the network needs to be traversed for accurate calculation of the medium number centralityGThe shortest paths between any pair of nodes are counted, the frequency of each shortest path passing through the nodes and the edges is counted, and the medium centrality of the nodes and the edges is calculated. Because the upper limit of the number of node pairs in the network is
Figure SMS_273
，nIs the number of nodes in the network. Time complexity of accurate calculation of the median centrality +.>
Figure SMS_274
The computational complexity is high and cannot be applied to a large-scale network. In->
Figure SMS_275
Representing the number of nodes in the network, < >>
Figure SMS_276
Representing the number of edges in the network. In order to solve the problem of central rapid calculation of medium numbers in a large-scale network, the network is replaced by a node set without heavy samples in the method SThe number of node pairs is from->
Figure SMS_277
Reduced to->
Figure SMS_278
The workload of shortest path traversal can be reduced to +.>
Figure SMS_279
. Meanwhile, sample nodes generated based on feature vector centrality sampling represent important nodes in a network, shortest paths among the sample nodes represent typical shortest paths in the network, the relative sequence of the betweenness centrality accurate values of the nodes and the edges can be well reserved based on the approximate value of the betweenness centrality calculated by the shortest paths among the sample nodes, the betweenness centrality relative sequence of the nodes and the edges is a problem which is focused on in a real network application scene, and the order keeping performance of the betweenness centrality approximate value can effectively solve the real network application problem.
Example two
Referring to fig. 3, fig. 3 is a schematic diagram of a median center approximation calculation apparatus according to an embodiment of the invention. The device described in fig. 3 is applicable to an information network, a social network, an internet of things and a traffic network, and the embodiment of the invention is not limited. As shown in fig. 3, the apparatus may include:
a first computing module for computing a networkGThe characteristic vector centrality is obtained; center of the feature vector
Figure SMS_280
The method comprises the steps of carrying out a first treatment on the surface of the Above-mentionednRepresentation vector->
Figure SMS_281
Component numbers of (2); above-mentionednEqual to the networkGThe total number of the middle nodes;
a first network construction module for calculating a network using feature vector centralityGThe number of the nodes again, construct the multiple networkG 2 ；
A second network construction module for constructing multiple networksG 2 Sample nodes are selected to obtain a non-heavy sample node setS；
A second calculation module for calculating a set of non-heavy sample nodesSCenter of bettery, get networkGThe median centrality approximation.
Therefore, by implementing the intermediate number centrality approximation calculation device described in fig. 3, the intermediate number centrality of the non-heavy sample node set can be used as the intermediate number centrality approximation value of the original network by reasonably selecting the non-heavy sample node set, so that the scale of path search can be greatly reduced, and meanwhile, the intermediate number centrality approximation value also maintains the magnitude sequence relation of intermediate number centrality values of different nodes and edges as much as possible.
In another alternative embodiment, as shown in FIG. 3, the first computing module computes a networkGThe characteristic vector centrality is obtained by the specific way that:
constructing a networkGIs a contiguous matrix a of (a).
Above-mentioned
Figure SMS_282
If the network isGMiddle node->
Figure SMS_283
And node- >
Figure SMS_284
With edges in between, then->
Figure SMS_285
The method comprises the steps of carrying out a first treatment on the surface of the Otherwise->
Figure SMS_286
。
Based on the adjacency matrix A, a first characteristic equation is constructed.
The first characteristic equation is
Figure SMS_287
。
In the method, in the process of the invention,
Figure SMS_288
for the adjacency matrix of the network,>
Figure SMS_289
is characteristic value (I)>
Figure SMS_290
Is a feature vector.
And carrying out calculation processing on the first characteristic equation, calculating to obtain a characteristic vector corresponding to the maximum characteristic value, and taking the characteristic vector corresponding to the maximum characteristic value as characteristic vector centrality.
It can be seen that the value of the centrality of the feature vector characterizes the networkGThe importance of a node in the set determines the probability that the node is selected as a sample node.
In yet another alternative embodiment, as shown in FIG. 3, the first network construction module calculates the network using feature vector centralityGThe number of the nodes again, construct the multiple networkG 2 The method specifically comprises the following steps:
calculating the mean value of each component of the centrality of the feature vector to obtain a component mean value
Figure SMS_291
。
Above-mentioned
Figure SMS_292
The method comprises the steps of carrying out a first treatment on the surface of the Above->
Figure SMS_293
。
Judging the component mean value
Figure SMS_294
Whether or not it is smaller than a preset average weight numbercAnd obtaining a judging result.
The average weight numbercThe range of the values is as follows
Figure SMS_295
The method comprises the steps of carrying out a first treatment on the surface of the The range of the average weight value sufficiently ensures the universality and the variability of the sampled samples based on the centrality of the feature vector, wherein ∈>
Figure SMS_296
For networks GIs the average degree of the node.
According to the judgment result, a preset vector coefficient calculation model is utilized to obtain a vector coefficient
Figure SMS_297
；
Centering the feature vector with the vector coefficients
Figure SMS_298
Multiplying to obtain a second feature vector; the characteristic vector centrality->
Figure SMS_299
The method comprises the steps of carrying out a first treatment on the surface of the The second feature vector->
Figure SMS_300
；
And rounding up each component in the second characteristic vector to obtain a node weight vector.
The node weight vector
Figure SMS_301
The method comprises the steps of carrying out a first treatment on the surface of the Above->
Figure SMS_302
The method comprises the steps of carrying out a first treatment on the surface of the Above-mentioned
Figure SMS_303
Is a non-negative integer; the i-th component in the node weight vector +.>
Figure SMS_304
Characterizing a networkGI node->
Figure SMS_305
Corresponding weight number.
Using node weight vector to networkGProcessing to obtain multiple networksG 2 。
Above-mentioned
Figure SMS_306
。
Therefore, the universality and the diversity of the sampled samples based on the characteristic vector centrality are fully ensured by reasonably taking the average weight, the weight of the network node is determined according to the average value of each component of the characteristic vector centrality and the average weight, the weight of the node in the multiple network is in direct proportion to the characteristic vector centrality of the node, and the more important node becomes the sample node with higher probability due to the construction of the multiple network.
In yet another optional embodiment, the first network construction module obtains the vector coefficient by using a preset vector coefficient calculation model according to the determination result, and specifically includes:
When the judgment result is yes, calculating the minimum integer for enabling the preset first vector coefficient calculation model to be established
Figure SMS_307
The minimum integer is +.>
Figure SMS_308
As vector coefficient->
Figure SMS_309
Is a value of (2).
The first vector coefficient calculation model is as follows
Figure SMS_310
。
Wherein, the above
Figure SMS_311
；/>
Figure SMS_312
Representing an upward rounding; above-mentionednThe number of components in the centrality of the feature vector; said->
Figure SMS_313
Is an integer greater than 0; said->
Figure SMS_314
Representing a preset average weight +.>
Figure SMS_315
。
When the judgment result is NO, calculating the maximum integer for enabling the preset second vector coefficient calculation model to be established
Figure SMS_316
The maximum integer +.>
Figure SMS_317
Is the reciprocal of the vector coefficient->
Figure SMS_318
Is a value of (2).
The second vector coefficient calculation model is as follows
Figure SMS_319
。
Wherein, the above
Figure SMS_320
；/>
Figure SMS_321
Representing an upward rounding; above-mentionednRepresenting the number of components in the centrality of the feature vector; above->
Figure SMS_322
Is an integer greater than 0; said->
Figure SMS_323
Representing a preset average weight +.>
Figure SMS_324
。
In yet another alternative embodiment, as shown in FIG. 3, the second network building block is derived from multiple networksG 2 Sample nodes are selected to obtain a non-heavy sample node setSThe method specifically comprises the following steps:
from multiple networksG 2 In the method, the method is selected according to uniform random probability distribution
Figure SMS_325
Obtaining a first sample node set by the nodes; above->
Figure SMS_326
The method comprises the steps of carrying out a first treatment on the surface of the Above->
Figure SMS_327
Representing an upward rounding; above-mentionednRepresenting the number of components in the centrality of the feature vector; above-mentioned
Figure SMS_328
Characterizing a predetermined sampling rate, +.>
Figure SMS_329
The value range is +.>
Figure SMS_330
The sampling proportion is selected by comprehensively considering the representativeness of the sampling sample and the efficiency of an approximate calculation method.
Judging whether the first sample node set has the number of repeated nodes or not to obtain a second judging result;
if the second judgment result is yes, deleting repeated nodes in the first sample node set, selecting new nodes from a method of uniform random probability distribution in the multiple networks, adding the new nodes into the first sample node set, and enabling the total number of the nodes in the first sample node set to reach
Figure SMS_331
And triggering and executing the judgment whether the first sample node set has the repeated node or not, and obtaining a second judgment result.
If the second judgment result is no, the first sample node set is confirmed to be a non-heavy sample node setS。
In yet another alternative embodiment, as shown in FIG. 3, the second calculation module calculates a set of no-heavy sample nodesSCenter of bettery, get networkGThe median centrality approximation value specifically comprises:
using the medium number centrality calculation model to collect the non-heavy sample nodesSAnd processing to obtain the medium centrality of the sample node set S.
The above-mentioned medium centrality calculation model is:
Figure SMS_332
/>
Figure SMS_333
in the method, in the process of the invention,
Figure SMS_337
representing node->
Figure SMS_342
Center of betting, ->
Figure SMS_346
Representing edge->
Figure SMS_336
Center of betting, ->
Figure SMS_339
For node->
Figure SMS_344
To node->
Figure SMS_348
Is>
Figure SMS_334
For node->
Figure SMS_338
To node->
Figure SMS_341
Through node->
Figure SMS_343
The number of shortest paths of (a); />
Figure SMS_335
For node->
Figure SMS_340
To the node/>
Figure SMS_345
Pass by edge->
Figure SMS_347
The number of shortest paths of (a);Srepresenting a set of non-heavy sample nodesS。
Aggregating the sample nodesSIs determined as a networkGIs approximated to the median centrality of (a) to obtain a networkGNode betweenness centrality approximation.
Example III
Referring to fig. 4, fig. 4 is a schematic structural diagram of another intermediate center-to-center approximation calculation apparatus according to an embodiment of the present invention. The device described in fig. 4 is applicable to an information network, a social network, an internet of things and a traffic network, and the embodiment of the invention is not limited. As shown in fig. 4, the apparatus may include:
a memory 401 storing executable program codes;
a processor 402 coupled with the memory 401;
the processor 402 invokes executable program code stored in the memory 401 for performing the steps in the medium centrality approximation calculation method of feature vector centrality described in embodiment one.
Example IV
The embodiment of the invention discloses a computer-readable storage medium storing a computer program for electronic data exchange, wherein the computer program causes a computer to execute the steps in the medium centrality approximation calculation method characterized by the feature vector centrality described in the embodiment.
Example five
The embodiment of the invention discloses a computer program product, which comprises a non-transitory computer readable storage medium storing a computer program, and the computer program is operable to cause a computer to execute the steps in the method for calculating the centrality approximation of the betweenness of the centrality vectors described in the embodiment.
Finally, it should be noted that: the embodiment of the invention discloses a median centrality approximate calculation method, which is disclosed by the embodiment of the invention only for illustrating the technical scheme of the invention, but not limiting the technical scheme; although the invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art will understand that; the technical scheme recorded in the various embodiments can be modified or part of technical features in the technical scheme can be replaced equivalently; such modifications and substitutions do not depart from the spirit and scope of the corresponding technical solutions.

Claims (9)

1. A method for central approximation calculation of a betweenness, comprising:
computing networkGThe characteristic vector centrality is obtained; the number of components in the centrality of the characteristic vector is equal to the networkGThe total number of the middle nodes;
calculating a network by using the feature vector centralityGThe number of the intermediate nodes is counted again to construct a multiple networkG 2 ；
From the multiple networksG 2 Sample nodes are selected to obtain a non-heavy sample node setS；
Computing the set of non-heavy sample nodesSCenter of bettery, get networkGThe median centrality approximation.
2. The method of claim 1, wherein the computing network uses the feature vector centralityGNode weight sequence of (a) to construct a multiple networkG 2 Comprising:
calculating the mean value of each component of the centrality of the feature vector to obtain a component mean value;
judging whether the component mean value is smaller than a preset average weight numbercObtaining a judgment result;
according to the judgment result, a preset vector coefficient calculation model is utilized to obtain a vector coefficient
Figure QLYQS_1
；
Centering the feature vector with the vector coefficients
Figure QLYQS_2
Multiplying to obtain a second feature vector;
rounding up each component in the second feature vector to obtain a node weight vector;
Using node weight vectors for the networkGProcessing to obtain multiple networksG 2 。
3. The method for central approximation calculation of betweenness according to claim 2, wherein the calculating the model using the predetermined vector coefficients according to the determination result to obtain the vector coefficients comprises:
when the judgment result is yes, calculating a minimum integer for enabling a preset first vector coefficient calculation model to be established
Figure QLYQS_3
The minimum integer +.>
Figure QLYQS_4
As vector coefficient->
Figure QLYQS_5
Is a value of (2);
the first vector coefficient calculation model is
Figure QLYQS_6
Wherein, the said
Figure QLYQS_7
Any component of the feature vector centrality; />
Figure QLYQS_8
Representing an upward rounding; the saidThe saidnA component number in the centrality of the feature vector; said->
Figure QLYQS_9
Is an integer greater than 0; said->
Figure QLYQS_10
Representing a preset average weight +.>
Figure QLYQS_11
；
When the judging result is NO, calculating a maximum integer for enabling a preset second vector coefficient calculation model to be established
Figure QLYQS_12
The maximum integer +.>
Figure QLYQS_13
Is the reciprocal of the vector coefficient->
Figure QLYQS_14
Is a value of (2);
the second vector coefficient calculation model is
Figure QLYQS_15
；
Wherein, the said
Figure QLYQS_16
Any component of the feature vector centrality; />
Figure QLYQS_17
Representing an upward rounding; the saidnA component number in the centrality of the feature vector; said- >
Figure QLYQS_18
Is an integer greater than 0; said->
Figure QLYQS_19
Representing a preset average weight +.>
Figure QLYQS_20
。
4. The method of median centrality approximation calculation according to claim 1, wherein the slave multiple networksG 2 Sample nodes are selected to obtain a non-heavy sample node setSComprising:
from the multiple networksG 2 In the method, the method is selected according to uniform random probability distribution
Figure QLYQS_21
Obtaining a first sample node set by the nodes; said->
Figure QLYQS_22
The method comprises the steps of carrying out a first treatment on the surface of the Said->
Figure QLYQS_23
Representing a preset sampling proportion; said->
Figure QLYQS_24
For networksGThe total number of the middle nodes;
judging whether repeated nodes exist in the first sample node set or not to obtain a second judging result;
when the second judging result is yes, deleting repeated nodes in the first sample node set, selecting new nodes from a method of uniform random probability distribution in a multiple network, adding the new nodes into the first sample node set, enabling the total number of the nodes in the first sample node set to be s, triggering and executing the judgment on whether repeated nodes exist in the first sample node set, and obtaining a second judging result;
when the second judgment result is no, the first sample node set is confirmed to be a no-heavy sample node setS。
5. The method of median centrality approximation calculation of claim 1, wherein the calculation network GFeature vector centrality, resulting in feature vector centrality, comprising:
constructing a networkGAdjacent matrix a of (a);
constructing a first characteristic equation based on the adjacency matrix A;
the first characteristic equation is
Figure QLYQS_25
；
Where A is the adjacency matrix of the network,
Figure QLYQS_26
is characteristic value (I)>
Figure QLYQS_27
Is a feature vector;
and carrying out calculation processing on the first characteristic equation, calculating to obtain a characteristic vector corresponding to the maximum characteristic value, and taking the characteristic vector corresponding to the maximum characteristic value as characteristic vector centrality.
6. The method of median centrality approximation calculation of claim 1, wherein the calculating the set of weight-free sample nodesSCenter of bettery, get networkGA median centrality approximation comprising:
using a median centrality calculation model for the non-heavy sample node setSProcessing to obtain the medium centrality of the sample node set S;
aggregating the sample nodesSIs determined as a networkGIs approximated to the median centrality of (a) to obtain a networkGThe median centrality approximation.
7. A medium centrality approximation calculation apparatus, the apparatus comprising:
a first computing module for computing a networkGIn feature vectors Heart, obtaining the centrality of the feature vector; the number of components in the centrality of the characteristic vector is equal to the networkGThe total number of the middle nodes;
a first construction module for calculating a network using the feature vector centralityGThe number of the nodes again, construct the multiple network
Figure QLYQS_28
；
A second building block for building up a network from the multiple networksG 2 Sample nodes are selected to obtain a non-heavy sample node setS；
A second calculation module for calculating the non-heavy sample node setSCenter of bettery, get networkGThe median centrality approximation.
8. A medium centrality approximation calculation apparatus, the apparatus comprising:
a memory storing executable program code;
a processor coupled to the memory;
the processor invokes the executable program code stored in the memory to perform the betweenness centrality approximation calculation method of any of claims 1-6.
9. A computer storage medium storing computer instructions which, when invoked, perform the medium centrality approximation calculation method of any one of claims 1-6.
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