CN114218723A - Multi-dimensional information propagation network community visualization method, system, device and medium - Google Patents

Multi-dimensional information propagation network community visualization method, system, device and medium Download PDF

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CN114218723A
CN114218723A CN202111354271.3A CN202111354271A CN114218723A CN 114218723 A CN114218723 A CN 114218723A CN 202111354271 A CN202111354271 A CN 202111354271A CN 114218723 A CN114218723 A CN 114218723A
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王振宇
黄振华
吴俊贤
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South China University of Technology SCUT
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Abstract

The invention discloses a multidimensional information propagation network community visualization method, a multidimensional information propagation network community visualization system, a multidimensional information propagation network community visualization device and a multidimensional information propagation network community visualization medium, wherein the method comprises the following steps: carrying out community discovery on the information transmission network so as to increase the modularity of the transmission network structure and acquiring the community structure of the node according to the community discovery result; after the communities are divided, calculating repulsive force and attractive force between nodes in the communities and between the nodes in the communities, simulating the nodes into particles, and iteratively moving the particles according to the repulsive force and the attractive force until convergence; and acquiring the layout node coordinates of each node and acquiring the visualization result of the information propagation network. According to the invention, the community structure is fully utilized, the repulsive force and attractive force are calculated after the community structure is divided, the problems of collapse and the like in the visual layout of the existing method are effectively solved, and the information transmission process can be better shown and understood through visualization of information transmission. The invention can be widely applied to the technical field of information transmission.

Description

Multi-dimensional information propagation network community visualization method, system, device and medium
Technical Field
The invention relates to the technical field of information dissemination, in particular to a method, a system, a device and a medium for multi-dimensional information dissemination network community visualization.
Background
Layout algorithms provide an intuitive way to visualize and understand complex networks. Complex networks, such as social networks, and protein interaction networks, often show community structures in order to achieve better, more efficient visualization of complex networks, explore community structures in the visualization, and apply them to a broad exclusive and attractive layout framework.
Unlike visualization that does not use a specific community detection method (e.g., force-directed placement algorithm), which can improve the quality of graphical visualization by combining a force-directed algorithm with a community detection algorithm, existing network visualization methods mostly do not fully utilize the community structure based on a force-directed algorithm, resulting in a layout with interwoven nodes/edges or "hair balls" problems, especially as the size and complexity of the network increases.
Disclosure of Invention
In order to solve at least one of the technical problems in the prior art to a certain extent, the invention aims to provide a method, a system, a device and a medium for visualizing a multi-dimensional information dissemination network community.
The technical scheme adopted by the invention is as follows:
a multi-dimensional information propagation network community visualization method comprises the following steps:
carrying out community discovery on the information transmission network so as to increase the modularity of the transmission network structure and acquiring the community structure of the node according to the community discovery result;
after the communities are divided, calculating repulsive force and attractive force between nodes in the communities and between the nodes in the communities, simulating the nodes into particles, and iteratively moving the particles according to the repulsive force and the attractive force until convergence;
and acquiring the layout node coordinates of each node and acquiring the visualization result of the information propagation network.
Further, the multidimensional information propagation network community visualization method further comprises the following steps:
the user social relationship network is visualized, the relationship between the information dissemination network and the user social relationship network is constructed by utilizing the similarity of the networks, and the relationship between the two networks is analyzed from two dimensions of the information dissemination and the user social relationship.
Further, the community structure comprises user population, user age and male and female proportion of the users.
Further, after the community is divided, calculating repulsive force and attractive force between nodes in the community and nodes in the community interval, simulating the nodes as particles, and iteratively moving the particles according to the repulsive force and the attractive force until convergence, including:
establishing new node type particles according to all users and information of the users in the community structure, and respectively mapping personal information and activity paths of the users into n +1 particles and n +2 particles;
observing users with the information quantity not reaching a preset threshold value, classifying the users into n-type crowds, observing the n-type crowds for a first preset time, and reserving information data obtained through observation;
and (3) clicking the data of the user with the information quantity reaching a preset threshold value, training a prediction model, and acquiring a complete user behavior sequence as the input of the prediction model after the prediction model is trained.
Further, the node type particle is that each node is regarded as a particle, repulsive force exists between every two nodes, and two nodes in the same community have attractive force or two nodes with connection have attractive force.
Further, the repulsive force is calculated by the formula:
Figure BDA0003356855190000021
where C is the relative strength of the regulation repulsive force, d (p)i,pj) Is the visual distance between node i and node j, and K is the optimal distance;
the calculation formula of the attractive force is as follows:
Figure BDA0003356855190000022
where λ is the weight of the edge between node i and node j.
Further, the repulsive force and the attractive force make the nodes move in an iteration mode and reduce the energy of the whole network to the maximum extent, and the total energy of the t iteration is expressed as follows:
Figure BDA0003356855190000023
wherein the content of the first and second substances,
Figure BDA0003356855190000024
is the weight of the attraction between node u and node v in the t-th iteration,
Figure BDA0003356855190000025
is the weight of the repulsive force between node u and node V in the t-th iteration, V- { u } is used to calculate the attractive force of the other nodes to node u.
The other technical scheme adopted by the invention is as follows:
a multidimensional information dissemination network community visualization system comprising:
the community discovery module is used for carrying out community discovery on the information transmission network so as to increase the modularity of the transmission network structure and obtain the community structure to which the node belongs according to the community discovery result;
the division calculation module is used for calculating weighted repulsion force and attraction force between nodes in the community and the community interval according to the repulsion force and attraction force functions after the community is divided, simulating the nodes as particles, and iteratively moving the particles according to the repulsion force and the attraction force until convergence;
and the visual presentation module is used for acquiring the layout node coordinates of each node and acquiring the visual result of the information propagation network.
The other technical scheme adopted by the invention is as follows:
a multidimensional information dissemination network community visualization device comprises:
at least one processor;
at least one memory for storing at least one program;
when executed by the at least one processor, cause the at least one processor to implement the method described above.
The other technical scheme adopted by the invention is as follows:
a storage medium having stored therein processor-executable instructions for performing the method as described above when executed by a processor.
The invention has the beneficial effects that: according to the invention, the community structure is fully utilized, the repulsive force and attractive force are calculated after the community structure is divided, the problems of collapse and the like in the visual layout of the existing method are effectively solved, and the information transmission process can be better shown and understood through visualization of information transmission.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following description is made on the drawings of the embodiments of the present invention or the related technical solutions in the prior art, and it should be understood that the drawings in the following description are only for convenience and clarity of describing some embodiments in the technical solutions of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without creative efforts.
Fig. 1 is a flow chart illustrating steps of a multidimensional information dissemination network community visualization method according to an embodiment of the present invention;
description figure 2 is a schematic diagram of the visualization result of a network community based on the method proposed by the embodiment of the present invention;
description figure 3 is a schematic diagram showing the visualization result of the FR Spring method in the same network community;
description figure 4 is a schematic diagram of the results of the HQFD method visualized in the same network community.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention. The step numbers in the following embodiments are provided only for convenience of illustration, the order between the steps is not limited at all, and the execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.
In the description of the present invention, it should be understood that the orientation or positional relationship referred to in the description of the orientation, such as the upper, lower, front, rear, left, right, etc., is based on the orientation or positional relationship shown in the drawings, and is only for convenience of description and simplification of description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention.
In the description of the present invention, the meaning of a plurality of means is one or more, the meaning of a plurality of means is two or more, and larger, smaller, larger, etc. are understood as excluding the number, and larger, smaller, inner, etc. are understood as including the number. If the first and second are described for the purpose of distinguishing technical features, they are not to be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated or implicitly indicating the precedence of the technical features indicated.
In the description of the present invention, unless otherwise explicitly limited, terms such as arrangement, installation, connection and the like should be understood in a broad sense, and those skilled in the art can reasonably determine the specific meanings of the above terms in the present invention in combination with the specific contents of the technical solutions.
For the problems in the prior art, the method provided by the embodiment improves a mechanism of fixing the calculated attraction and the repulsive force of the current force guiding algorithm, not only considers the community structure of the information propagation network, but also further considers the social network information of the user, and can overcome the problems of collapse and the like of the existing method on the visual layout, so that the information propagation visualization can better show and understand the information propagation process.
As shown in fig. 1 in the specification, the embodiment provides a multidimensional information dissemination network community visualization method, which includes the following steps:
s1, carrying out community discovery on the information propagation network to increase the modularity of the propagation network structure, and acquiring the community structure to which the node belongs according to the community discovery result.
Firstly, community discovery is carried out on the information transmission network, the modularity of the transmission network structure is enabled to be as large as possible, and the community structure of the node is calculated according to the community discovery result. The community structure comprises user groups, user ages and male and female proportions of the users, and records the user id, the content of received information, the time of the received information and the like.
And S2, after the communities are divided, calculating repulsive force and attractive force between nodes in the communities and nodes in the communities, simulating the nodes into particles, and iteratively moving the particles according to the repulsive force and the attractive force until convergence.
The step S2 specifically includes steps S21-S23:
s21, establishing new node type particles according to all users and information of the users in the community structure, and mapping the personal information and the activity path of the users into n +1 particles and n +2 particles respectively.
The node type particle is that each node is regarded as a particle, which is the same as a force guiding algorithm, a repulsive force exists between every two nodes, and an attractive force exists in two nodes which are related or in the same community.
The repulsive force is calculated as:
Figure BDA0003356855190000041
c is the relative strength of the adjusting repulsive force,d(pi,pj) Is the visualized distance between node i and node j, and K is the optimal distance. In this embodiment, C is set to 1.0 and K is set to
Figure BDA0003356855190000051
Where S is the area of the canvas and N is the number of vertices.
The calculation formula of the attractive force is as follows:
Figure BDA0003356855190000052
λ is the weight of the edge between node i and node j, and in this embodiment, λ is set to 1.0.
Under the influence of repulsive and attractive forces, these nodes will move iteratively and reduce the energy of the whole network to the maximum extent until they stabilize. Wherein the expression of the total energy of the t-th iteration is as follows:
Figure BDA0003356855190000053
wherein the content of the first and second substances,
Figure BDA0003356855190000054
is the weight of the attraction between node u and node v in the t-th iteration,
Figure BDA0003356855190000055
is the weight of the repulsive force between node u and node v in the t-th iteration. Is given a difference
Figure BDA0003356855190000056
And
Figure BDA0003356855190000057
the values require a high computational complexity and different weights are given to the inter-and intra-community forces in order to simplify the model. Thus, if two nodes are in a community, then they will be
Figure BDA0003356855190000058
Set to 1.0 and will be if there is a connection between communities
Figure BDA0003356855190000059
Set to a. To prevent nodes from moving away from the network core area, in practice
Figure BDA00033568551900000510
Is arranged as
Figure BDA00033568551900000511
In addition, there are some constraints, e.g.
Figure BDA00033568551900000512
Figure BDA00033568551900000513
Where τ is the minimum distance between node u and node v, v.x and v.y are the x-axis and y-axis positions of node v, L and W are the width and height of the canvas, and for a canvas size of 1.0 × 1.0, the optimal number of nodes is about 150.
And S22, observing users with the information quantity not reaching a preset threshold value, classifying the users into n-type crowds, observing the n-type crowds for a first preset time, and reserving information data obtained by observation.
In this embodiment, users whose information amount does not reach the preset threshold are observed, the users are classified into n-type groups, the groups are observed for 1-3 months, the information data collected recently are retained, and partial data with the time exceeding 6 months are discarded.
And S23, clicking the data of the user with the information quantity reaching the preset threshold value, training the prediction model, and acquiring a complete user behavior sequence as the input of the prediction model after training the prediction model.
For each user data click sequence within the threshold, a complete user behavior sequence is input when the trained model makes a prediction.
And S3, obtaining the layout node coordinates of each node, and obtaining the visualization result of the information dissemination network.
S4, visualizing the user social relationship network, constructing the relationship between the information dissemination network and the user social relationship network by utilizing the similarity of the networks, and analyzing the relationship between the two networks from the two dimensions of the information dissemination and the user social relationship.
The user social relationship network is visualized in the same way, namely the same way of visualizing the information transmission network is adopted, the relationship between the information transmission network and the user social relationship network is constructed by utilizing the similarity degree of the network, and the two dimensions of the information transmission and the user social relationship are analyzed.
The working principle of the method is summarized as follows: firstly, carrying out community discovery on an information transmission network to enable the modularity of a transmission network structure to be as large as possible, calculating a community structure to which a node belongs according to a community discovery result, wherein the community structure comprises user groups, user ages and user male-female ratios, recording the content including the user id, the received information and the time for receiving the information, calculating weighted repulsion force and attraction force between nodes in a community and between communities according to community division, repulsion force and attraction force functions, simulating the nodes into particles, moving the particles until convergence according to the repulsion force and the attraction force, establishing new node type particles for all users and information thereof appearing in the community structure, respectively mapping personal information and activity paths of the users into n +1 particles and n +2 particles, and the node type particles are the same as a force guide algorithm in that each node is regarded as one particle, and the repulsion force exists between every two nodes, the method comprises the steps of enabling attractiveness to exist in two nodes which are connected or located in the same community, observing users with information quantity not reaching a preset threshold value, classifying the users into n-type-like crowds, observing the crowds for 1-3 months, reserving recently collected information data, discarding part of data with time exceeding six months, clicking sequences of user data within the threshold value, inputting complete user behavior sequences when a trained model is used for prediction, finally obtaining layout node coordinates of each node, obtaining a better visualization result, visualizing a user social relationship network in the same mode, constructing a relationship between the two nodes by utilizing the similarity degree of the network, and analyzing two dimensions of information transmission and the user social relationship.
Fig. 2 is a visualization result of the method in the embodiment in a network community, fig. 3 is a visualization result of the FR Spring method in a network community, and fig. 4 is a visualization result of the HQFD method in a network community; through comparing the accompanying drawings 2-4 in the specification, it can be seen that the method provided by the embodiment has a more obvious network community structure, the internal and external structures between communities are more clearly separated, and a better visual layout can be provided for understanding the network structure. The problems of collapse and the like of the conventional method on the visual layout can be effectively solved, so that the information propagation visualization can better show and understand the information propagation process.
The embodiment further provides a multidimensional information dissemination network community visualization system, which includes:
the community discovery module is used for carrying out community discovery on the information transmission network so as to increase the modularity of the transmission network structure and obtain the community structure to which the node belongs according to the community discovery result;
the division calculation module is used for calculating weighted repulsion force and attraction force between nodes in the community and the community interval according to the repulsion force and attraction force functions after the community is divided, simulating the nodes as particles, and iteratively moving the particles according to the repulsion force and the attraction force until convergence;
and the visual presentation module is used for acquiring the layout node coordinates of each node and acquiring the visual result of the information propagation network.
The multidimensional information dissemination network community visualization system of the embodiment can execute the multidimensional information dissemination network community visualization method provided by the embodiment of the method of the invention, can execute any combination implementation steps of the embodiment of the method, and has corresponding functions and beneficial effects of the method.
The embodiment further provides a multidimensional information dissemination network community visualization device, which includes:
at least one processor;
at least one memory for storing at least one program;
when executed by the at least one processor, cause the at least one processor to implement the method as described in the description of figure 1.
The multidimensional information dissemination network community visualization device of the embodiment can execute the multidimensional information dissemination network community visualization method provided by the embodiment of the method of the invention, can execute any combination implementation steps of the embodiment of the method, and has corresponding functions and beneficial effects of the method.
The embodiment of the application also discloses a computer program product or a computer program, which comprises computer instructions, and the computer instructions are stored in a computer readable storage medium. The computer instructions may be read by a processor of a computer device from a computer-readable storage medium and executed by the processor to cause the computer device to perform the method described in the description of fig. 1.
The embodiment also provides a storage medium, which stores an instruction or a program capable of executing the multidimensional information dissemination network community visualization method provided by the embodiment of the method of the invention, and when the instruction or the program is run, the method can be executed by any combination of the embodiment of the method, and the method has corresponding functions and beneficial effects.
In alternative embodiments, the functions/acts noted in the block diagrams may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Furthermore, the embodiments presented and described in the flow charts of the present invention are provided by way of example in order to provide a more thorough understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed and in which sub-operations described as part of larger operations are performed independently.
Furthermore, although the present invention is described in the context of functional modules, it should be understood that, unless otherwise stated to the contrary, one or more of the described functions and/or features may be integrated in a single physical device and/or software module, or one or more functions and/or features may be implemented in a separate physical device or software module. It will also be appreciated that a detailed discussion of the actual implementation of each module is not necessary for an understanding of the present invention. Rather, the actual implementation of the various functional modules in the apparatus disclosed herein will be understood within the ordinary skill of an engineer, given the nature, function, and internal relationship of the modules. Accordingly, those skilled in the art can, using ordinary skill, practice the invention as set forth in the claims without undue experimentation. It is also to be understood that the specific concepts disclosed are merely illustrative of and not intended to limit the scope of the invention, which is defined by the appended claims and their full scope of equivalents.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
The logic and/or steps represented in the flowcharts or otherwise described herein, e.g., an ordered listing of executable instructions that can be considered to implement logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via for instance optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory.
It should be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
In the foregoing description of the specification, reference to the description of "one embodiment/example," "another embodiment/example," or "certain embodiments/examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (10)

1. A multi-dimensional information propagation network community visualization method is characterized by comprising the following steps:
carrying out community discovery on the information transmission network so as to increase the modularity of the transmission network structure and acquiring the community structure of the node according to the community discovery result;
after the communities are divided, calculating repulsive force and attractive force between nodes in the communities and between the nodes in the communities, simulating the nodes into particles, and iteratively moving the particles according to the repulsive force and the attractive force until convergence;
and acquiring the layout node coordinates of each node and acquiring the visualization result of the information propagation network.
2. The method as claimed in claim 1, wherein the method further comprises the following steps:
the user social relationship network is visualized, the relationship between the information dissemination network and the user social relationship network is constructed by utilizing the similarity of the networks, and the relationship between the two networks is analyzed from two dimensions of the information dissemination and the user social relationship.
3. The method as claimed in claim 1, wherein the community structure includes user population, user age and male and female proportion of users.
4. The method for visualizing the community in the multidimensional information dissemination network according to claim 1, wherein after the community is divided, the repulsive force and attractive force between nodes in the community and nodes in the community are calculated, the nodes are simulated as particles, and the particles are iteratively moved according to the repulsive force and the attractive force until convergence, and the method comprises the following steps:
establishing new node type particles according to all users and information of the users in the community structure, and respectively mapping personal information and activity paths of the users into n +1 particles and n +2 particles;
observing users with the information quantity not reaching a preset threshold value, classifying the users into n-type crowds, observing the n-type crowds for a first preset time, and reserving information data obtained through observation;
and (3) clicking the data of the user with the information quantity reaching a preset threshold value, training a prediction model, and acquiring a complete user behavior sequence as the input of the prediction model after the prediction model is trained.
5. The method as claimed in claim 4, wherein the node-type particle is a particle regarding each node as a particle, a repulsive force exists between every two nodes, two nodes in the same community have an attractive force, or two nodes with a relationship have an attractive force.
6. The method for visualizing communities in a multidimensional information dissemination network as claimed in claim 5, wherein the repulsive force is calculated by the following formula:
Figure FDA0003356855180000011
where C is the relative strength of the regulation repulsive force, d (p)i,pj) Is the visual distance between node i and node j, and K is the optimal distance;
the calculation formula of the attractive force is as follows:
Figure FDA0003356855180000021
where λ is the weight of the edge between node i and node j.
7. The method as claimed in claim 6, wherein the repulsive force and attractive force make the nodes move iteratively and reduce the energy of the whole network to the maximum extent, and the total energy of the t iteration is expressed as:
Figure FDA0003356855180000022
wherein the content of the first and second substances,
Figure FDA0003356855180000023
is the weight of the attraction between node u and node v in the t-th iteration,
Figure FDA0003356855180000024
is the weight of the repulsive force between node u and node v in the t-th iteration; v- { u } for metersCalculating the attractiveness of other nodes to node u.
8. A multidimensional information dissemination network community visualization system, comprising:
the community discovery module is used for carrying out community discovery on the information transmission network so as to increase the modularity of the transmission network structure and obtain the community structure to which the node belongs according to the community discovery result;
the division calculation module is used for calculating weighted repulsion force and attraction force between nodes in the community and the community interval according to the repulsion force and attraction force functions after the community is divided, simulating the nodes as particles, and iteratively moving the particles according to the repulsion force and the attraction force until convergence;
and the visual presentation module is used for acquiring the layout node coordinates of each node and acquiring the visual result of the information propagation network.
9. A multidimensional information propagation network community visualization device is characterized by comprising:
at least one processor;
at least one memory for storing at least one program;
when executed by the at least one processor, cause the at least one processor to implement the method of any one of claims 1-7.
10. A computer-readable storage medium, in which a program executable by a processor is stored, wherein the program executable by the processor is adapted to perform the method according to any one of claims 1 to 7 when executed by the processor.
CN202111354271.3A 2021-11-16 2021-11-16 Multi-dimensional information propagation network community visualization method, system, device and medium Pending CN114218723A (en)

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* Cited by examiner, † Cited by third party
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CN116859830A (en) * 2023-03-27 2023-10-10 福建天甫电子材料有限公司 Production management control system for electronic grade ammonium fluoride production
CN116859830B (en) * 2023-03-27 2024-01-26 福建天甫电子材料有限公司 Production management control system for electronic grade ammonium fluoride production

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