CN112073220A - Method and device for constructing network evaluation model - Google Patents

Method and device for constructing network evaluation model Download PDF

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CN112073220A
CN112073220A CN202010820244.XA CN202010820244A CN112073220A CN 112073220 A CN112073220 A CN 112073220A CN 202010820244 A CN202010820244 A CN 202010820244A CN 112073220 A CN112073220 A CN 112073220A
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value
nodes
network
importance
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CN112073220B (en
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李叶
窦猛汉
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Origin Quantum Computing Technology Co Ltd
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Abstract

The invention discloses a method and a device for constructing a network evaluation model, wherein the method comprises the following steps: obtaining the weight W of edges connected among the network nodes, and calculating the value of a preset index for evaluating the importance of the network nodes, wherein the preset index comprises the following steps: and constructing an elastic potential energy model H corresponding to the network according to the strength and the local irreplaceability of the nodes and the value of a preset index. By utilizing the embodiment of the invention, a network evaluation model which can reflect the difference of the network node importance can be constructed, the problem of poor classification result of the network node importance ranking is solved, and the defects in the prior art are overcome.

Description

Method and device for constructing network evaluation model
Technical Field
The invention belongs to the technical field of node sequencing in a complex network, and particularly relates to a method and a device for constructing a network evaluation model.
Background
In real life, many things exist in the form of systems, such as ecosystems, power systems, transportation systems, public health systems, etc., and these systems can be generally abstracted into networks for processing, for example: the food chain in the ecosystem can be abstracted to a network of predation relations among organisms, and the traffic system can be abstracted to a network of traffic communication relations among city nodes, and the like. In recent years, complex networks are continuously concerned by learners, and particularly, many complex networks in real life present different characteristics from previous network theories, such as non-scale characteristics, hierarchical characteristics, small world effects and the like. By studying the network, the characteristics and functions of the corresponding system can be understood deeply.
For the problem of network node importance evaluation, in the existing evaluation model, the static length (rest length) of the elastic potential energy between nodes is set to be 1, but for some network graphs, the obtained effect is poor, because the importance difference of the connected network nodes depends on the index value difference of the importance of the evaluation nodes, if the static length is a fixed parameter, the difference cannot be embodied, and the classification result is poor.
Based on this, it is necessary to construct a network evaluation model that can reflect the difference in importance of network nodes to solve the deficiencies in the prior art.
Disclosure of Invention
The invention aims to provide a method and a device for constructing a network evaluation model, which are used for solving the defects in the prior art, can construct a network evaluation model capable of reflecting the importance difference of network nodes, solve the problem of poor classification result of importance ranking of the network nodes and make up the defects in the prior art.
One embodiment of the present application provides a method for constructing a network evaluation model, where the method includes:
acquiring the weight W of edges connected among the network nodes, and calculating the value of a preset index for evaluating the importance of the network nodes; wherein the preset index comprises: strength of nodes and local irreplaceability;
according to the value of the preset index, constructing an elastic potential energy model H corresponding to the network; wherein,
Figure BDA0002634199860000021
wherein, the
Figure BDA0002634199860000022
An out-node set representing node j, said WjiThe weight value of the edge j → i connecting the node j and the node i, SjThe SjTo quantify the importance value of the importance of node i and node j, T is the rest length of the elastic potential energy between node i and node j, and T is determined according to the strength and/or the local irreplaceability.
The method for constructing a network evaluation model as described above, wherein preferably, the constructing an elastic potential energy model H corresponding to the network includes:
constructing a first local elastic potential energy H of the network nodes according to the weight W of the edges connected among the nodes and the static length T of the elastic potential energy among the nodesji(ii) a Wherein the first local elastic potential energy HjiThe calculation formula of (2) is as follows:
Figure BDA0002634199860000023
according to a first local elastic potential energy H of the network nodejiConstructing an elastic potential energy model H corresponding to the network; the calculation formula of the elastic potential energy model H corresponding to the network is as follows:
Figure BDA0002634199860000024
wherein, the
Figure BDA0002634199860000025
An out-node set representing node j, said WjiThe weight value of the edge j → i connecting the node j and the node i, SiThe SjTo quantify the importance value of the importance of node i, node j, the T is determined according to the strength value and/or the local irreplaceability value.
In the method for constructing a network evaluation model as described above, the static length T is preferably calculated in a manner that:
Figure BDA0002634199860000026
wherein λ is1Representing the influence degree of the partial irreplaceability of the connected nodes i and j on the importance of the nodes,
Figure BDA0002634199860000031
a first local irreplaceability value, λ, representing a node i, j connected to it2Indicating the influence degree of the strength of the connected nodes i and j on the importance of the nodes,
Figure BDA0002634199860000032
represents the first intensity value of the connected node i and node j, and satisfies that lambda is more than or equal to 01≤1，0≤λ2≤1，λ1+λ2＝1；
Or,
Figure BDA0002634199860000033
wherein,
Figure BDA0002634199860000034
a second local irreplaceability value representing a node i, j connected to it,
Figure BDA0002634199860000035
and a second intensity value representing the nodes i and j connected with each other.
In the method for constructing a network evaluation model as described above, it is preferable that the calculation of the first intensity includes: determining a second strength of the network node, specifically:
Figure BDA0002634199860000036
wherein, the
Figure BDA0002634199860000037
Is a first strength of node i after being affected by connected node j, said
Figure BDA0002634199860000038
Is the in-degree and out-degree of the node i, DiD the abovejIs the third intensity of node i, node j, said
Figure BDA0002634199860000039
The above-mentioned
Figure BDA00026341998600000310
Is a set of ingress nodes of node i, said
Figure BDA00026341998600000311
And the alpha represents the importance degree of the node on the connected nodes, and the alpha is more than or equal to 0 and less than or equal to 1.
In the method for constructing a network evaluation model as described above, preferably, the second intensity is calculated by:
Figure BDA00026341998600000312
wherein, the
Figure BDA00026341998600000313
Representing a second strength of node i, said p representing the number of classification classes of the network node, said
Figure BDA00026341998600000314
The first intensity is the maximum value and the minimum value of each first intensity.
The method for constructing a network evaluation model as described above, wherein the first local irreplaceability value is preferably calculated in a manner that:
Figure BDA0002634199860000041
wherein, the Wij、WjiThe weight of the side i → j, the side j → i, the Dj、DiIs the third intensity of node j, node i, the Uj、UiIs a third local irreplaceability value of the node j and the node i, the alpha represents the degree of importance of the node on the connected nodes, and alpha is more than or equal to 0 and less than or equal to 1, the
Figure BDA0002634199860000042
The above-mentioned
Figure BDA0002634199860000043
Is a set of ingress nodes of node i, said
Figure BDA0002634199860000044
Is an outbound node set of node i, said
Figure BDA0002634199860000045
Is the first locally non-substitutable value after node i is affected by the connected nodes.
The method for constructing a network evaluation model as described above, wherein the second local irreplaceability value is preferably calculated in a manner that:
Figure BDA0002634199860000046
wherein, the
Figure BDA0002634199860000047
A second local irreplaceability value representing a node i, said
Figure BDA0002634199860000048
Is the maximum value and the minimum value in the first local irreplaceability.
Another embodiment of the present application provides a network evaluation model building apparatus, including:
the computing module is used for obtaining the weight W of edges connected among the network nodes and computing the value of a preset index for evaluating the importance of the network nodes; wherein the preset index comprises: strength of nodes and local irreplaceability;
the building module is used for building an elastic potential energy model H corresponding to the network according to the value of the preset index; wherein,
Figure BDA0002634199860000049
wherein, the
Figure BDA00026341998600000410
An out-node set representing node j, said WjiThe weight value of the edge j → i connecting the node j and the node i, SiThe SjTo quantify the importance value of the importance of node i and node j, T is the rest length of the elastic potential energy between node i and node j, and T is determined according to the strength and/or the local irreplaceability.
Optionally, the building module includes:
a first constructing unit, configured to construct a first local elastic potential energy H of the network node according to the weight W of the edge connected between the nodes and the static length T of the elastic potential energy between the nodesji(ii) a Wherein the first local elastic potential energy HjiThe calculation formula of (2) is as follows:
Figure BDA0002634199860000051
a second construction unit for constructing a network node from a first local elastic potential energy H of the network nodejiConstructing an elastic potential energy model H corresponding to the network; the calculation formula of the elastic potential energy model H corresponding to the network is as follows:
Figure BDA0002634199860000052
wherein, the
Figure BDA0002634199860000053
An out-node set representing node j, said WjiThe weight value of the edge j → i connecting the node j and the node i, SiThe SjTo quantify importance values for node i, node j importance, the T is based on the strengthA value of the local irreplaceability and/or the local irreplaceability value.
Optionally, the static length T is calculated in the following manner:
Figure BDA0002634199860000054
wherein λ is1Representing the influence degree of the partial irreplaceability of the connected nodes i and j on the importance of the nodes,
Figure BDA0002634199860000055
a first local irreplaceability value, λ, representing a node i, j connected to it2Indicating the influence degree of the strength of the connected nodes i and j on the importance of the nodes,
Figure BDA0002634199860000056
represents the first intensity value of the connected node i and node j, and satisfies that lambda is more than or equal to 01≤1，0≤λ2≤1，λ1+λ2＝1；
Or,
Figure BDA0002634199860000057
wherein,
Figure BDA0002634199860000058
a second local irreplaceability value representing a node i, j connected to it,
Figure BDA0002634199860000059
and a second intensity value representing the nodes i and j connected with each other.
Optionally, the calculation manner of the first intensity includes: determining a second strength of the network node, specifically:
Figure BDA0002634199860000061
wherein, the
Figure BDA0002634199860000062
Is a first strength of node i after being affected by connected node j, said
Figure BDA0002634199860000063
Is the in-degree and out-degree of the node i, DiD the abovejIs the third intensity of node i, node j, said
Figure BDA0002634199860000064
The above-mentioned
Figure BDA0002634199860000065
Is a set of ingress nodes of node i, said
Figure BDA0002634199860000066
And the alpha represents the importance degree of the node on the connected nodes, and the alpha is more than or equal to 0 and less than or equal to 1.
Optionally, the second intensity is calculated in the following manner:
Figure BDA0002634199860000067
wherein, the
Figure BDA0002634199860000068
Representing a second strength of node i, said p representing the number of classification classes of the network node, said
Figure BDA0002634199860000069
The first intensity is the maximum value and the minimum value of each first intensity.
Optionally, the first local irreplaceability value is calculated by:
Figure BDA00026341998600000610
wherein, the Wij、WjiThe weight of the side i → j, the side j → i, the Dj、DiIs the third intensity of node j, node i, the Uj、UiIs a third local irreplaceability value of the node j and the node i, the alpha represents the degree of importance of the node on the connected nodes, and alpha is more than or equal to 0 and less than or equal to 1, the
Figure BDA00026341998600000611
The above-mentioned
Figure BDA00026341998600000612
Is a set of ingress nodes of node i, said
Figure BDA00026341998600000613
Is an outbound node set of node i, said
Figure BDA00026341998600000614
Is the first locally non-substitutable value after node i is affected by the connected nodes.
Optionally, the second local irreplaceability value is calculated in the following manner:
Figure BDA0002634199860000071
wherein, the
Figure BDA0002634199860000072
A second local irreplaceability value representing a node i, said
Figure BDA0002634199860000073
Is the maximum value and the minimum value in the first local irreplaceability.
A further embodiment of the application provides a storage medium having a computer program stored thereon, wherein the computer program is arranged to perform the method of any of the above when executed.
Yet another embodiment of the present application provides an electronic device comprising a memory having a computer program stored therein and a processor configured to execute the computer program to perform the method of any of the above.
Compared with the prior art, the invention provides a method for constructing a network evaluation model, which comprises the steps of firstly obtaining the weight W of edges connected among network nodes, and calculating the value of a preset index for evaluating the importance of the network nodes; wherein the preset index comprises: and constructing an elastic potential energy model corresponding to the network according to the preset index value and the intensity and the local irreplaceability of the node, wherein the elastic potential energy model comprises the index value difference of the intensity and the local irreplaceability of the node and the like, so that the parameter of the static length is not fixed, thereby constructing a network evaluation model capable of reflecting the network node importance difference, solving the problem of poor sorting and classifying result of the network node importance and making up the defects in the prior art.
Drawings
Fig. 1 is a block diagram of a hardware structure of a computer terminal of a method for constructing a network evaluation model according to an embodiment of the present invention;
fig. 2 is a schematic flow chart of a method for constructing a network evaluation model according to an embodiment of the present invention;
fig. 3 is a schematic diagram of a node network according to an embodiment of the present invention;
fig. 4 is a schematic diagram of another node network according to an embodiment of the present invention;
fig. 5 is a schematic structural diagram of a device for constructing a network evaluation model according to an embodiment of the present invention.
Detailed Description
The embodiments described below with reference to the drawings are illustrative only and should not be construed as limiting the invention.
It is noted that the terms first, second and the like in the description and in the claims of the present invention are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order.
In real life, most complex systems (such as social systems, biological systems, information systems, economic and financial network systems, electric power and traffic systems, infectious disease transmission systems, etc.) can be abstracted into the structure of the network, and the problems existing on the systems can be quantitatively described and solved by using the theory of the network. Sometimes we are concerned with important objects in the research system. For example, in the spread of infectious diseases, users want to find out which widely-contacted individuals want to isolate the individuals, and the widely-contacted individuals can be regarded as important network nodes.
The method has the advantages that the importance comprehensive evaluation is carried out on the complex network nodes, the problem of network influence maximization is explored, the theoretical significance is achieved, and the method has great application value in many fields, such as epidemic situation control, advertisement putting, communication network guarantee, prediction of popular research results, protein interaction and the like.
Based on this, the invention firstly introduces a method for constructing a network evaluation model, which can be applied to electronic equipment, such as computer terminals, specifically ordinary computers, quantum computers and the like.
This will be described in detail below by way of example as it would run on a computer terminal. Fig. 1 is a block diagram of a hardware structure of a computer terminal of a method for constructing a network evaluation model according to an embodiment of the present invention. As shown in fig. 1, the computer terminal may include one or more (only one shown in fig. 1) processors 102 (the processor 102 may include, but is not limited to, a processing device such as a microprocessor MCU or a programmable logic device FPGA) and a memory 104 for storing data, and optionally, a transmission device 106 for communication functions and an input-output device 108. It will be understood by those skilled in the art that the structure shown in fig. 1 is only an illustration and is not intended to limit the structure of the computer terminal. For example, the computer terminal may also include more or fewer components than shown in FIG. 1, or have a different configuration than shown in FIG. 1.
The memory 104 may be configured to store software programs and modules of application software, such as program instructions/modules corresponding to the method for constructing the network evaluation model in the embodiment of the present application, and the processor 102 executes various functional applications and data processing by running the software programs and modules stored in the memory 104, so as to implement the above-mentioned method. The memory 104 may include high speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some examples, the memory 104 may further include memory located remotely from the processor 102, which may be connected to a computer terminal over a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
The transmission device 106 is used for receiving or transmitting data via a network. Specific examples of the network described above may include a wireless network provided by a communication provider of the computer terminal. In one example, the transmission device 106 includes a Network adapter (NIC) that can be connected to other Network devices through a base station to communicate with the internet. In one example, the transmission device 106 can be a Radio Frequency (RF) module, which is used to communicate with the internet in a wireless manner.
In the prior art, in order to simplify the model, the rest length (rest length) of the elastic potential energy between the nodes is set to be 1, but for some complex networks, the effect obtained by the method is poor, because the importance difference of the connected nodes depends on the index value difference of the nodes, if the rest length is a fixed parameter, the difference cannot be embodied, the classification result is poor, and therefore, the size of the rest length is set to be more reasonable according to the index value difference of the nodes. When the index difference of the connected nodes is larger, the static length between the connected nodes is set to be larger, and vice versa.
For a network, the node importance evaluation index value has no fixed range, in order to make the difference between the index values adapt to the classification category number p of the network, the index values are converted from the original distribution to the [1, p ] distribution, the difference of the index values of the connected nodes is used as the static length, when the importance of the nodes is poor and meets the index value difference, the elastic potential energy between the nodes is minimum, namely the local system is most stable.
When the basis of the network node importance classification is a plurality of preset indexes, the preset indexes are considered to be independent, namely the preset indexes are not influenced mutually, and an elastic model for evaluating the network node importance is constructed by utilizing the preset indexes, so that the elastic potential energy between the nodes can be obtained. The total elastic potential energy of the system is the sum of the local elastic potential energy, when the total potential energy is the lowest, the system is the most stable, and the corresponding node importance value is the optimal solution.
Referring to fig. 2, fig. 2 is a schematic flowchart of a method for constructing a network evaluation model according to an embodiment of the present invention, where the method may include:
s201: acquiring the weight W of edges connected among the network nodes, and calculating the value of a preset index for evaluating the importance of the network nodes; wherein the preset index comprises: the strength of the node and local irreplaceability.
Specifically, the preset index value of the importance of the network node refers to a value of an index that affects the importance of the network node, which is preset by a user as needed, for example: the strength of the node and local irreplaceability, etc.
The weight W of the edge connected between the nodes is a value describing the actual influence of each node in the network, and in different network systems, the weight of the edge connected between the nodes can be set according to the actual situation, for example, taking a traffic network as an example, the size of the round-trip traffic between the a-ground and the B-ground can be described by the weight between the a-node and the B-node. In the present application, for convenience of explanation, the weights W of the connected edges may be all set to 1.
The rationality of the index of the strength of the node and the calculation manner are described below.
1. The node degree in the weighted directed network is also called the strength of the node, and is defined as the sum of the weights of the edges connected with the node, and the strength of the directed network is divided into the out degree and the in degree according to the direction of the edges, namely:
the degree of income is as follows:
Figure BDA0002634199860000101
the output is as follows:
Figure BDA0002634199860000102
the total strength was:
Figure BDA0002634199860000103
wherein, Wij、WjiThe weights of side i → j and side j → i,
Figure BDA0002634199860000104
is an ingress node set and an egress node set of the node i,
Figure BDA0002634199860000105
Dithe in-degree, out-degree, and total strength (third strength) of the node i.
2. For a weighted directed network graph G, in a local network centered on node i, there is
Figure BDA0002634199860000106
If the path j → i → k is the shortest path for the node j to reach the node k (i.e. the node j is not directly connected to the node k), the path is considered to be locally irreplaceable, and the total number of locally irreplaceable paths passing through the node i can be defined as the locally irreplaceable traffic Ri：
Figure BDA0002634199860000107
Wherein,
Figure BDA0002634199860000108
wherein,
Figure BDA0002634199860000109
is the set of outbound nodes for node j,
Figure BDA00026341998600001010
set of ingress nodes being node k, fjkF is an intermediate parameter, when the node j is not directly connected with the node k, if the intersection of the exit node set of the node j and the entry node set of the node k comprises the node ijk1 indicates that there is a locally non-replaceable path through node i, otherwise it indicates no.
Taking the network diagram of fig. 3 as an example, the edges between the nodes O, A, B, C, D, E, F, G, H are not specifically directed, and can be understood as bi-directional connections between the nodes. For node B and node E, available RB6, are respectively: ABC, CBA, ABE, EBA, ABD, DBA; rEBEH, HEB, CEG, GEC, DEF, FED, respectively, 6. If only by RiTo judge the importance of node i, then because RB＝REThey were found to be equally important. However, as can be seen from the analysis of fig. 3, if the B point is deleted, the a point is disconnected from the rest of the nodes, and on the contrary, the deletion of the E point does not affect the connectivity between the other nodes in the graph, mainly because R is the node RiThe method is only a local index, and the information expressed by the local index is limited, so that the importance of the node cannot be effectively represented by the index alone.
3. For a weighted directed network graph G, in a local network centered on node i, there is
Figure BDA0002634199860000111
If all the paths from all the ingress nodes j to all the egress nodes k are total
Figure BDA0002634199860000112
Then a local uniqueness UR of node i can be definedi：
Figure BDA0002634199860000113
Continuing with the example of figure 3, with the example,
Figure BDA0002634199860000114
so that the importance ratio of the B point is the E pointHigh, this result is reasonable. However, URAIf only the local uniqueness index of the node is considered, the importance of the point a is greater than that of the point B, which is obviously unreasonable. At this time, RA＝2，RBIf the local irreplaceable traffic of the node is taken as a standard, it is reasonable that the importance of the point B is higher than that of the point a. Thus, from the above analysis, neither of these two indicators can be used alone to evaluate node importance. The two nodes can be partially irreplaceable to different degrees, if only the former node is considered, the local uniqueness of the node cannot be embodied, and if only the latter node is considered, the local irreplaceable traffic of the node cannot be embodied.
4. In order to balance the local irreplaceable traffic RiAnd local uniqueness URiThese two indices may be used in combination. For a weighted directed graph G, a third local irreplaceability value U for node i may be definedi：
Ui＝Ri*URi
Continuing with the example of FIG. 3, the rationality of the index is verified to obtain UA＝2，UB＝3，
Figure BDA0002634199860000115
That is, the importance of node A, B, E is B > A > E in the order of B > E as determined by the third locally irreplaceable value, which is reasonable as shown in FIG. 3.
5. As can be seen from the above, the node importance is determined to some extent by each index (weight W, strength D, local irreplaceable traffic R, local uniqueness UR, local irreplaceable value U). However, the importance among the nodes is interactive, and the interactive effect can be reflected on each index, that is, when the index value of the node j is larger than that of the connected node i, the node j has an enhancing effect on the node i, and the node i has a weakening effect on the node j. Since the network is weighted in a directed manner, the degree of interaction between the nodes is related to these weights. The influence of the out-weight and the in-weight on the node can be the same, the influence coefficient of the node j on the node i is the ratio of the sum of the out-weight and the in-weight to the total weight of the node j,the influence coefficient of the node i by the node j is the ratio of the sum of the outgoing weight and the incoming weight to the total weight of the node i, and then a first local irreplaceable value of the node i after being influenced by the connected node j is defined
Figure BDA0002634199860000121
The first local irreplaceability value is calculated by:
Figure BDA0002634199860000122
wherein, the Wij、WjiThe weight of the side i → j, the side j → i, the Dj、DiIs the third intensity of node j, node i, the Uj、UiIs a third local irreplaceability value of the node j and the node i, the alpha represents the degree of importance of the node on the connected nodes, and alpha is more than or equal to 0 and less than or equal to 1, the
Figure BDA0002634199860000123
The above-mentioned
Figure BDA0002634199860000124
Is a set of ingress nodes of node i, said
Figure BDA0002634199860000125
Is an outbound node set of node i, said
Figure BDA0002634199860000126
Is the first locally non-substitutable value after node i is affected by the connected nodes.
Similarly, a mutual influence formula of the strength is constructed, and the second strength of the node i after being influenced by the connected nodes is calculated
Figure BDA0002634199860000127
The first intensity is calculated by: determining a second strength of the network node, specifically:
Figure BDA0002634199860000128
wherein, the
Figure BDA0002634199860000129
Is a first strength of node i after being affected by connected node j, said
Figure BDA00026341998600001210
Is the in-degree and out-degree of the node i, DiD the abovejIs the third intensity of node i, node j, said
Figure BDA00026341998600001211
The above-mentioned
Figure BDA00026341998600001212
Is a set of ingress nodes of node i, said
Figure BDA00026341998600001213
And the alpha represents the importance degree of the node on the connected nodes, and the alpha is more than or equal to 0 and less than or equal to 1.
In practical applications, the first local irreplaceability value and the first intensity may also be preprocessed. Data preprocessing is usually an important preferred step in data analysis, and the preprocessed data values change, but the importance ranking of each network node is not affected, because the ranking is a relative comparison.
The first local irreplaceability value may be treated as:
Figure BDA0002634199860000131
wherein, the
Figure BDA0002634199860000132
A second local irreplaceability value representing node i, p representing the number of classification classes of the node: for example, nodes are classified two by importance, and then p is 2, which is classified as insignificant and heavyTo do this, the importance can also be quantified, such as setting the importance of the unimportant node to 0 and the importance of the important node to 1; or, if the nodes are classified into four classes, eight classes, and the like according to importance, p is 4, 8 … …; the above-mentioned
Figure BDA0002634199860000133
Is the maximum value, the minimum value of each of the first local irreplaceability values.
The first intensity may be treated as:
Figure BDA0002634199860000134
wherein, the
Figure BDA0002634199860000135
Representing a second strength of node i, said p representing the number of classification classes of the network node, said
Figure BDA0002634199860000136
The first intensity is the maximum value and the minimum value of each first intensity.
S202: according to the value of the preset index, constructing an elastic potential energy model H corresponding to the network; wherein,
Figure BDA0002634199860000137
wherein, the
Figure BDA0002634199860000138
An out-node set representing node j, said WjiThe weight value of the edge j → i connecting the node j and the node i, SiThe SjTo quantify the importance value of the importance of node i and node j, T is the rest length of the elastic potential energy between node i and node j, and T is determined according to the strength and/or the local irreplaceability.
Specifically, the preset index value may be understood as an estimated value of the importance of the evaluation node, which represents the importance information of the node in the local network and does not accurately represent the importance position of the node in the global network. In order to more accurately measure the importance ranking of the nodes in the global network, an elastic potential energy model H corresponding to the network needs to be constructed, which specifically comprises the following steps:
a: constructing a first local elastic potential energy H of the network nodes according to the weight W of the edges connected among the nodes and the static length T of the elastic potential energy among the nodesji(ii) a Wherein the first local elastic potential energy HjiThe calculation formula of (2) is as follows:
Figure BDA0002634199860000141
specifically, for the problem of network node importance evaluation, in the existing evaluation model, the static length t (rest length) of the elastic potential energy between nodes is set to 1, but the effect of the method is poor. In the present application, the rest length T may be optionally determined according to the intensity or the local irreplaceability, or may be determined by both the intensity and the local irreplaceability.
B: according to a first local elastic potential energy H of the network nodejiConstructing an elastic potential energy model H corresponding to the network; the calculation formula of the elastic potential energy model H corresponding to the network is as follows:
Figure BDA0002634199860000142
wherein, the
Figure BDA0002634199860000143
An out-node set representing node j, said WjiThe weight value of the edge j → i connecting the node j and the node i, SiThe SjTo quantify the importance value of the importance of node i, node j, the T is determined according to the strength value and/or the local irreplaceability value.
In an alternative embodiment, the resting length T is calculated by:
Figure BDA0002634199860000144
wherein λ is1Representing the influence degree of the partial irreplaceability of the connected nodes i and j on the importance of the nodes,
Figure BDA0002634199860000145
a first local irreplaceability value, λ, representing a node i, j connected to it2Indicating the influence degree of the strength of the connected nodes i and j on the importance of the nodes,
Figure BDA0002634199860000146
represents the first intensity value of the connected node i and node j, and satisfies that lambda is more than or equal to 01≤1，0≤λ2≤1，λ1+λ2＝1。
Wherein, when lambda1When the value of (a) is 0, it means that the static length T is determined by the intensity, that is:
Figure BDA0002634199860000151
wherein, when lambda2When the value of (a) is 0, it means that the static length T is determined by local irreplaceability, that is:
Figure BDA0002634199860000152
in another alternative embodiment, the static length T is calculated by:
Figure BDA0002634199860000153
wherein,
Figure BDA0002634199860000154
a second local irreplaceability value representing a node i, j connected to it,
Figure BDA0002634199860000155
and a second intensity value representing the nodes i and j connected with each other.
Wherein, when lambda1When the value of (a) is 0, it means that the static length T is determined by the intensity, that is:
Figure BDA0002634199860000156
wherein, when lambda2When the value of (a) is 0, it means that the static length T is determined by local irreplaceability, that is:
Figure BDA0002634199860000157
illustratively, as shown in fig. 4, another node network diagram has A, B, C, D, E, F, G seven nodes, edges between the nodes are connected in two directions, and all the edges have a weight of 1, for example, WABAnd WBAAll of which are 1, and node a has an edge pointing to node B, which also has an edge pointing to node a.
Specifically, when the value of p is 2, the degree of importance α of the influence of the node on the connected nodes is 0.5, and λ1＝λ2The importance value of node A, B, C, D, E, F, G obtained by the above elasticity model is 0.5: 1, 1, 2, 1, 1, 1, 1; namely, the importance of the node C is one class, and the importance of the remaining nodes is lower than that of the node C.
Specifically, when the value of p is 4, the degree of importance α of the influence of the node on the connected nodes is 0.5, and λ1＝λ2The importance value of node A, B, C, D, E, F, G obtained by the above elasticity model is 0.5: 1, 2, 4, 2, 3, 2, 2; that is, the importance of the node C is the highest, the importance of the node E is the second, the importance of the node B, D, F, G is the same under the four-classification, and the importance of the node a is the lowest.
Specifically, when the value of p is 8, the degree of importance α of the influence of the node on the connected nodes is 0.5, and λ1＝λ2The importance value of node A, B, C, D, E, F, G obtained by the above elasticity model is 0.5: 2, 4, 7, 3, 4, 3, 3; that is, node C has the highest importance, node B has the second highest importance, node E has the second highest importance, node D, F, G has the same importance under the eight classification, and node a has the lowest importance.
Specifically, when the value of p is 16, the degree of importance α of the influence of the node on the connected nodes is 0.5, and λ1＝λ2The importance value of node A, B, C, D, E, F, G obtained by the above elasticity model is 0.5: 3, 8, 15, 6, 8, 6, 5; that is, node C has the highest importance, node B has the second highest importance, node D, F has the same importance under the sixteen categories, node G has lower importance than node F, and node a has the lowest importance.
Continuing with the example of FIG. 4, when the degree of emphasis α on the influence of a node on a connected node is changed, e.g., λ1＝λ2When the value of p is 2 and α is 0.5, the importance value of the node A, B, C, D, E, F, G obtained by the above elastic model is: 1, 1, 2, 1, 1, 1, 1; namely, the importance of the node C is one class, and the importance of the remaining nodes is lower than that of the node C.
Specifically, when the value of p is 4, the degree of importance α of the influence of the node on the connected nodes is 0, and λ1＝λ2The importance ranking of node A, B, C, D, E, F, G from the above elasticity model is 0.5: 1, 2, 3, 1, 2, 1, 1; that is, the importance of the node C is the highest, the importance of the node B, E is the second highest, and the importance of the node A, D, F, G is the same under the four-classification.
Specifically, when the value of p is 8, the degree of importance α of the influence of the node on the connected nodes is 0, and λ1＝λ2The importance ranking of node A, B, C, D, E, F, G from the above elasticity model is 0.5: 2, 5, 8, 3, 4, 3, 3; that is, node C has the highest importance, node B has the second highest importance, node E has the slightly lower importance than node B, node D, F, G has the same importance under eight categories, and node C has the same importanceA is least important.
Specifically, when the value of p is 16, the degree of importance α of the influence of the node on the connected nodes is 0, and λ1＝λ2The importance ranking of node A, B, C, D, E, F, G from the above elasticity model is 0.5: 3, 10, 16, 6, 9, 6, 6; that is, the importance of node C is the highest, the importance of node B is the second, the importance of node E is slightly lower than that of node B, and the importance of node D, F, G is the same under the sixteen categories, and the importance of node a is the lowest.
It should be noted that, under different classification category numbers, the ordering conditions of the importance of the nodes are different, and when the classification category number is larger, the ordering of the importance of the nodes is more accurate under the condition that the number of the nodes is more; the ranking condition of the importance of the nodes can be influenced by different values of the importance degree alpha of the nodes to the connected nodes. Based on the importance classification of the elastic model, the result of the importance classification is reasonable and cannot be caused by the mutual influence coefficients (alpha and lambda)1、λ2Value of) is changed and is greatly affected.
Compared with the prior art, the invention provides a method for constructing a network evaluation model, which comprises the steps of firstly obtaining the weight W of edges connected among network nodes, and calculating the value of a preset index for evaluating the importance of the network nodes; wherein the preset index comprises: and constructing an elastic potential energy model corresponding to the network according to the preset index value and the intensity and the local irreplaceability of the node, wherein the elastic potential energy model comprises the index value difference of the intensity and the local irreplaceability of the node and the like, so that the parameter of the static length is not fixed, thereby constructing a network evaluation model capable of reflecting the network node importance difference, solving the problem of poor sorting and classifying result of the network node importance and making up the defects in the prior art.
Referring to fig. 5, fig. 5 is a schematic structural diagram of a device for constructing a network evaluation model according to an embodiment of the present invention, and corresponding to the flow shown in fig. 2, the device may include:
the calculation module 501: acquiring the weight W of edges connected among the network nodes, and calculating the value of a preset index for evaluating the importance of the network nodes; wherein the preset index comprises: strength of nodes and local irreplaceability;
the building block 502: the elastic potential energy model H corresponding to the network is constructed according to the value of the preset index; wherein,
Figure BDA0002634199860000171
wherein, the
Figure BDA0002634199860000172
An out-node set representing node j, said WjiThe weight value of the edge j → i connecting the node j and the node i, SiThe SjTo quantify the importance value of the importance of node i and node j, T is the rest length of the elastic potential energy between node i and node j, and T is determined according to the strength and/or the local irreplaceability.
Specifically, the building module includes:
a first constructing unit, configured to construct a first local elastic potential energy H of the network node according to the weight W of the edge connected between the nodes and the static length T of the elastic potential energy between the nodesji(ii) a Wherein the first local elastic potential energy HjiThe calculation formula of (2) is as follows:
Figure BDA0002634199860000181
a second construction unit for constructing a network node from a first local elastic potential energy H of the network nodejiConstructing an elastic potential energy model H corresponding to the network; the calculation formula of the elastic potential energy model H corresponding to the network is as follows:
Figure BDA0002634199860000182
wherein, the
Figure BDA0002634199860000183
An out-node set representing node j, said WjiThe weight value of the edge j → i connecting the node j and the node i, SiThe SjTo quantify the importance value of the importance of node i, node j, the T is determined according to the strength value and/or the local irreplaceability value.
Specifically, the static length T is calculated in the following manner:
Figure BDA0002634199860000184
wherein λ is1Representing the influence degree of the partial irreplaceability of the connected nodes i and j on the importance of the nodes,
Figure BDA0002634199860000185
a first local irreplaceability value, λ, representing a node i, j connected to it2Indicating the influence degree of the strength of the connected nodes i and j on the importance of the nodes,
Figure BDA0002634199860000186
represents the first intensity value of the connected node i and node j, and satisfies that lambda is more than or equal to 01≤1，0≤λ2≤1，λ1+λ2＝1；
Or,
Figure BDA0002634199860000191
wherein,
Figure BDA0002634199860000192
a second local irreplaceability value representing a node i, j connected to it,
Figure BDA0002634199860000193
and a second intensity value representing the nodes i and j connected with each other.
Compared with the prior art, the invention provides a method for constructing a network evaluation model, which comprises the steps of firstly obtaining the weight W of edges connected among network nodes, and calculating the value of a preset index for evaluating the importance of the network nodes; wherein the preset index comprises: and constructing an elastic potential energy model corresponding to the network according to the preset index value and the intensity and the local irreplaceability of the node, wherein the elastic potential energy model comprises the index value difference of the intensity and the local irreplaceability of the node and the like, so that the parameter of the static length is not fixed, thereby constructing a network evaluation model capable of reflecting the network node importance difference, solving the problem of poor sorting and classifying result of the network node importance and making up the defects in the prior art.
An embodiment of the present invention further provides a storage medium, where a computer program is stored in the storage medium, where the computer program is configured to, when executed, perform the steps in any one of the above method embodiments.
Specifically, in the present embodiment, the storage medium may be configured to store a computer program for executing the steps of:
s201: acquiring the weight W of edges connected among the network nodes, and calculating the value of a preset index for evaluating the importance of the network nodes; wherein the preset index comprises: strength of nodes and local irreplaceability;
s202: according to the value of the preset index, constructing an elastic potential energy model H corresponding to the network; wherein,
Figure BDA0002634199860000194
wherein, the
Figure BDA0002634199860000195
An out-node set representing node j, said WjiThe weight value of the edge j → i connecting the node j and the node i, SiThe SjTo quantify the importance values of the importance of nodes i and j, T is the sum of the nodes i and jA resting length of elastic potential energy between nodes j, and said T is determined according to said strength and/or said local irreplaceability.
Compared with the prior art, the invention provides a method for constructing a network evaluation model, which comprises the steps of firstly obtaining the weight W of edges connected among network nodes, and calculating the value of a preset index for evaluating the importance of the network nodes; wherein the preset index comprises: and constructing an elastic potential energy model corresponding to the network according to the preset index value and the intensity and the local irreplaceability of the node, wherein the elastic potential energy model comprises the index value difference of the intensity and the local irreplaceability of the node and the like, so that the parameter of the static length is not fixed, thereby constructing a network evaluation model capable of reflecting the network node importance difference, solving the problem of poor sorting and classifying result of the network node importance and making up the defects in the prior art.
An embodiment of the present invention further provides an electronic device, which includes a memory and a processor, where the memory stores a computer program, and the processor is configured to execute the computer program to perform the steps in any one of the method embodiments described above.
Specifically, the electronic apparatus may further include a transmission device and an input/output device, wherein the transmission device is connected to the processor, and the input/output device is connected to the processor.
Specifically, in this embodiment, the processor may be configured to execute the following steps by a computer program:
s201: acquiring the weight W of edges connected among the network nodes, and calculating the value of a preset index for evaluating the importance of the network nodes; wherein the preset index comprises: strength of nodes and local irreplaceability;
s202: according to the value of the preset index, constructing an elastic potential energy model H corresponding to the network; wherein,
Figure BDA0002634199860000201
wherein, the
Figure BDA0002634199860000202
An out-node set representing node j, said WjiThe weight value of the edge j → i connecting the node j and the node i, SiThe SjTo quantify the importance value of the importance of node i and node j, T is the rest length of the elastic potential energy between node i and node j, and T is determined according to the strength and/or the local irreplaceability.
Compared with the prior art, the invention provides a method for constructing a network evaluation model, which comprises the steps of firstly obtaining the weight W of edges connected among network nodes, and calculating the value of a preset index for evaluating the importance of the network nodes; wherein the preset index comprises: and constructing an elastic potential energy model corresponding to the network according to the preset index value and the intensity and the local irreplaceability of the node, wherein the elastic potential energy model comprises the index value difference of the intensity and the local irreplaceability of the node and the like, so that the parameter of the static length is not fixed, thereby constructing a network evaluation model capable of reflecting the network node importance difference, solving the problem of poor sorting and classifying result of the network node importance and making up the defects in the prior art.
The construction, features and functions of the present invention are described in detail in the embodiments illustrated in the drawings, which are only preferred embodiments of the present invention, but the present invention is not limited by the drawings, and all equivalent embodiments modified or changed according to the idea of the present invention should fall within the protection scope of the present invention without departing from the spirit of the present invention covered by the description and the drawings.

Claims (10)

1. A method for constructing a network evaluation model is characterized by comprising the following steps:
acquiring the weight W of edges connected among the network nodes, and calculating the value of a preset index for evaluating the importance of the network nodes; wherein the preset index comprises: strength of nodes and local irreplaceability;
according to the value of the preset index, constructing an elastic potential energy model H corresponding to the network; wherein,
Figure FDA0002634199850000011
wherein, the Vj outAn out-node set representing node j, said WjiThe weight value of the edge j → i connecting the node j and the node i, SiThe SjTo quantify the importance value of the importance of node i and node j, T is the rest length of the elastic potential energy between node i and node j, and T is determined according to the strength and/or the local irreplaceability.
2. The method of claim 1, wherein the constructing of the elastic potential energy model H corresponding to the network comprises:
constructing a first local elastic potential energy H of the network nodes according to the weight W of the edges connected among the nodes and the static length T of the elastic potential energy among the nodesji(ii) a Wherein the first local elastic potential energy HjiThe calculation formula of (2) is as follows:
Figure FDA0002634199850000012
according to a first local elastic potential energy H of the network nodejiConstructing an elastic potential energy model H corresponding to the network; the calculation formula of the elastic potential energy model H corresponding to the network is as follows:
Figure FDA0002634199850000013
wherein, the Vj outAn out-node set representing node j, said WjiThe weight value of the edge j → i connecting the node j and the node i, SiThe SjTo quantize the node i,An importance value of importance of node j, said T being determined from said strength value and/or said local irreplaceability value.
3. The method of claim 2, wherein the resting length T is calculated by:
Figure FDA0002634199850000021
wherein λ is1Representing the influence degree of the partial irreplaceability of the connected nodes i and j on the importance of the nodes,
Figure FDA0002634199850000022
a first local irreplaceability value, λ, representing a node i, j connected to it2Indicating the influence degree of the strength of the connected nodes i and j on the importance of the nodes,
Figure FDA0002634199850000023
represents the first intensity value of the connected node i and node j, and satisfies that lambda is more than or equal to 01≤1，0≤λ2≤1，λ1+λ2＝1；
Or,
Figure FDA0002634199850000024
wherein,
Figure FDA0002634199850000025
a second local irreplaceability value representing a node i, j connected to it,
Figure FDA0002634199850000026
and a second intensity value representing the nodes i and j connected with each other.
4. The method of claim 3, wherein the first intensity is calculated by: determining a second strength of the network node, specifically:
Figure FDA0002634199850000027
wherein, the
Figure FDA0002634199850000028
Is a first strength of node i after being affected by connected node j, said
Figure FDA0002634199850000029
Is the in-degree and out-degree of the node i, DiD the abovejIs the third intensity of node i, node j, said
Figure FDA00026341998500000210
The above-mentioned
Figure FDA00026341998500000211
Is a set of ingress nodes of node i, said Vi outAnd the alpha represents the importance degree of the node on the connected nodes, and the alpha is more than or equal to 0 and less than or equal to 1.
5. The method of claim 4, wherein the second intensity is calculated by:
Figure FDA00026341998500000212
wherein, the
Figure FDA00026341998500000213
Representing a second strength of node i, said p representing the number of classification classes of the network node, said
Figure FDA0002634199850000031
The first intensity is the maximum value and the minimum value of each first intensity.
6. A method according to claim 3, wherein said first local irreplaceability value is calculated by:
Figure FDA0002634199850000032
wherein, the Wij、WjiThe weight of the side i → j, the side j → i, the Dj、DiIs the third intensity of node j, node i, the Uj、UiIs a third local irreplaceability value of the node j and the node i, the alpha represents the degree of importance of the node on the connected nodes, and alpha is more than or equal to 0 and less than or equal to 1, the
Figure FDA0002634199850000033
The above-mentioned
Figure FDA0002634199850000034
Is a set of ingress nodes of node i, said Vi outIs an outbound node set of node i, said
Figure FDA0002634199850000035
Is the first locally non-substitutable value after node i is affected by the connected nodes.
7. The method according to claim 6, characterized in that said second local irreplaceability value is calculated in such a way that:
Figure FDA0002634199850000036
wherein, the
Figure FDA0002634199850000037
A second local irreplaceability value representing a node i, said
Figure FDA0002634199850000038
Is the maximum value and the minimum value in the first local irreplaceability.
8. An apparatus for constructing a network evaluation model, the apparatus comprising:
the calculation module is used for obtaining the weight W of edges connected among the network nodes and calculating the value of a preset index for evaluating the importance of the network nodes; wherein the preset index comprises: strength of nodes and local irreplaceability;
the building module is used for building an elastic potential energy model H corresponding to the network according to the value of the preset index; wherein,
Figure FDA0002634199850000039
wherein, the Vj outAn out-node set representing node j, said WjiThe weight value of the edge j → i connecting the node j and the node i, SiThe SjTo quantify the importance value of the importance of node i and node j, T is the rest length of the elastic potential energy between node i and node j, and T is determined according to the strength and/or the local irreplaceability.
9. A storage medium, in which a computer program is stored, wherein the computer program is arranged to perform the method of any of claims 1 to 7 when executed.
10. An electronic device comprising a memory and a processor, wherein the memory has stored therein a computer program, and wherein the processor is arranged to execute the computer program to perform the method of any of claims 1 to 7.
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