CN111079024A - Public opinion propagation model construction method based on enhanced effect SCIR network - Google Patents

Public opinion propagation model construction method based on enhanced effect SCIR network Download PDF

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CN111079024A
CN111079024A CN201911072179.0A CN201911072179A CN111079024A CN 111079024 A CN111079024 A CN 111079024A CN 201911072179 A CN201911072179 A CN 201911072179A CN 111079024 A CN111079024 A CN 111079024A
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王运明
郭天一
初宪武
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Beijing Wonderroad Magnesium Technology Co Ltd
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Abstract

The invention discloses a public opinion propagation model construction method based on an enhanced effect SCIR network, which comprises the following steps of firstly, based on a traditional SCIR model, according to an enhanced effect and a direct immunity strategy, combining with a real network public opinion propagation situation, and making a public opinion propagation rule; secondly, analyzing possible situations existing in the public sentiment propagation process and providing state transition probability; and finally, according to public opinion propagation rules, state transition probability is provided, a differential equation of a public opinion propagation model is established, a final propagation model is generated, and the process of the SCIR network with the enhanced effect in public opinion propagation can be effectively and accurately reflected.

Description

Public opinion propagation model construction method based on enhanced effect SCIR network
Technical Field
The invention belongs to the field of information transmission and control science, and particularly relates to a public opinion transmission model construction method based on an enhanced effect SCIR network.
Background
The social network becomes an important part in people's life, and simultaneously with the application of new technologies such as 5G and the like, various intelligent social software comes up at the same time, and a social group with a large number of users and great influence is formed. The social network has the characteristics of instantaneity, sociality, interactivity and the like, so that network users can express own opinions aiming at hot social phenomena and problems, and can be continuously commented and forwarded by other users, and public opinions can be quickly spread in the network. However, if the relevant departments do not supervise and control the propagation of negative public opinions, they have a serious impact on society. Therefore, the research on the propagation rule of the online social network has important theoretical significance and application value for controlling the network public sentiment to propagate on the social network correspondingly. However, the existing public opinion propagation model has certain limitations, and the problem that the public opinion propagation state in an actual social network is difficult to accurately simulate exists.
Existing research has shown that real social networks and BA scale-less networks have similar characteristics. Therefore, the following characteristics should be considered in the research of real social networks:
(1) characteristic of small world
Also known as Six degree space theory or Six degree segmentation theory (Six dimensions of separation), i.e. most networks, although large in scale, have a relatively short path between any two nodes (tops), reflecting the fact that the number of correlations may be small but the world can be connected.
(2) Non-scale characteristic
Most of the real-world networks are not random networks, a few nodes often have a large number of connections, most of the nodes are few, and the degree distribution of the nodes conforms to the power-law distribution, which is called the scaleless-free characteristic of the network. The scale-free characteristic reflects that the complex network has serious heterogeneity, and the connection conditions (degrees) among nodes of the complex network have serious uneven distribution: a few nodes in the network, called Hub points, have an extremely large number of connections, while most nodes have only a very small number of connections. A few Hub points play a dominant role in the operation of the scaleless network. In a broad sense, the scaleless nature of a scaleless network is an inherent property describing a severely uneven distribution of a large number of complex systems as a whole.
(3) Characteristics of community structure
Humans are classified as species and groups as groups. Nodes in complex networks often exhibit clustering characteristics as well. For example, there are always circles of acquaintances or friends in a social network, where each member knows about the other members. The meaning of the clustering degree is the degree of network clustering; this is a cohesive tendency of the network. The concept of connected group reflects the distribution and interconnection of small networks in each group in a large network. For example, it may reflect the interrelationship of this circle of friends with another circle of friends.
Gephi is utilized to analyze a real social network with 1000 nodes, and the average degree is 25.004, the maximum degree is 648 and the minimum degree is 1, so that the scale-free characteristic is embodied; the average path length is 2.432, and the small world characteristic is met; the average clustering coefficient is 0.608, and the community structure characteristic is embodied.
There are a number of influencing variables in the transmission of public sentiment, and direct immunity is an important part of the public sentiment. The direct immunity of the public opinion transmission in the social network refers to that related departments adopt the behaviors of issuing real information and the like to directly convert users who do not transmit the public opinion into immune users, and the public opinion is refused to be transmitted, so that the influence of the public opinion on the society is reduced.
Public sentiment is a social phenomenon, and is a typical psychological characteristic of social groups. Social psychology indicates that the reinforcing effect means that an individual is subjected to cumulative influence of repeated prompts of a peer before opinion acceptance or behavior decision making, and the social reinforcing effect has a nonlinear cumulative effect and has a remarkable influence on human decision making.
In view of the fact that the conventional public opinion dissemination network does not consider the situations that the user retransmits the public opinion due to the direct immunity and the enhancement effect generated by the relevant departments on the public opinion supervision, the public opinion dissemination process in the real social network is difficult to accurately describe. Therefore, there is a need to establish a new public opinion propagation model suitable for SCIR network to analyze the propagation status of public opinion in real social network.
Disclosure of Invention
Aiming at the defects of the existing public opinion propagation model, the application provides a public opinion propagation model construction method based on an enhanced effect SCIR network, firstly, based on the traditional SCIR model, according to the enhanced effect and a direct immunity strategy, and by combining with the real network public opinion propagation situation, a public opinion propagation rule is made; secondly, analyzing possible situations existing in the public sentiment propagation process and providing state transition probability; and finally, according to public opinion propagation rules, state transition probability is provided, a differential equation of a public opinion propagation model is established, a final propagation model is generated, and the process of the SCIR network with the enhanced effect in public opinion propagation can be effectively and accurately reflected.
In order to achieve the purpose, the technical scheme of the invention is as follows: a public opinion propagation model construction method based on an enhanced effect SCIR network comprises the following specific steps:
s1: firstly, according to public opinion propagation rules in a social network, combining a strengthening effect and direct immunity, making public opinion propagation rules;
s2: calculating the state transition probability;
s3: and establishing a public opinion propagation model differential equation of the SCIR network with the enhanced effect.
Further, the step S1 is specifically implemented as:
(1) after the unknown state S contacts the propagation state I, there are 3 transition states: a part with a probability PSCTransition to a hesitant state C, partly with a probability PSITo a propagation state I, another part is given a probability PSRTransition to immune state R;
(2) after the hesitation state C contacts the propagation state I, a part is in probability PCITransition to propagation state I, another part will be at rate PCRTransition to immune state R;
(3) propagation state I with probability PIRTransition to immune state R;
(4) the immune state R has a probability P under the action of social reinforcement effectRCTransition to the hesitant state C.
Further, the step S2 is specifically implemented as:
analyzing the transition probability of each state node, wherein when the node is at the time t, the transition probability of each state is as follows:
(1) assuming node j is in S state at time t, then
Figure BDA0002261294670000031
By n1＝n1(t) represents the number of I nodes in the neighbor nodes of the node j at the time t, and n is n, assuming that the node j has k edges1Are random variables that obey a binomial distribution:
Figure BDA0002261294670000032
wherein the content of the first and second substances,
Figure BDA0002261294670000033
probability of connecting to I node from S node with k edges for time t:
Figure BDA0002261294670000034
p(k1i k) is a degree correlation function, and represents a node with the degree k and the degree k1The conditional probability of the node adjacency of (a);
Figure BDA0002261294670000035
indicates that one owns k1A node of the edge is in a probability of a propagation state under the condition that the node is connected to a susceptible node with a degree of k;
by pI(k1T) denotes the scale k at t1The density of the I-state nodes of (a) is then approximated by:
Figure BDA0002261294670000036
then the node with degree k is at [ t, t + Δ t]Average probability of changing to C state in time period
Figure BDA0002261294670000037
Comprises the following steps:
Figure BDA0002261294670000038
similarly, the node with degree k is at [ t, t + Δ t [ ]]Average probability of becoming I-state over time
Figure BDA0002261294670000039
Comprises the following steps:
Figure BDA0002261294670000041
similarly, the node with degree k is at [ t, t + Δ t [ ]]Average probability of becoming R state over time
Figure BDA0002261294670000042
Comprises the following steps:
Figure BDA0002261294670000043
the node with the degree of k is at [ t, t + delta t]Average probability of remaining S-state for a period of time
Figure BDA0002261294670000044
Comprises the following steps:
Figure BDA0002261294670000045
(2) assuming that node j is in the C state at time t, then:
Figure BDA0002261294670000046
then there are
Figure BDA0002261294670000047
(3) Assuming that node j is in the I state at time t, then:
Figure BDA0002261294670000048
then there are
Figure BDA0002261294670000049
(4) Assuming that node j is in the R state at time t, then:
Figure BDA00022612946700000410
by n2＝n2(t) represents the number of I nodes in the neighbor nodes of the node j at the time t, and the random variable obeys binomial distribution, and is similar to the S state, so that the node with the degree k is in [ t, t + delta t ]]Average probability of changing to C state in time period
Figure BDA00022612946700000411
Comprises the following steps:
Figure BDA00022612946700000412
therefore, the node with degree k is at [ t, t + Δ t [ ]]Average probability of maintaining R state over time
Figure BDA00022612946700000413
Comprises the following steps:
Figure BDA00022612946700000414
further, the public opinion propagation model differential equation for the enhanced effect SCIR network established in step S3 is:
Figure BDA0002261294670000051
and finally, obtaining a public opinion propagation model based on the SCIR network with the enhanced effect.
Due to the adoption of the technical method, the invention can obtain the following technical effects: the public opinion network model construction method provides a public opinion propagation model based on an enhanced effect SCIR network by considering the influence of direct immunity on uninfected users and the effect of the enhanced effect on immune users, and is more suitable for the propagation condition of public opinions in a real social network, thereby being beneficial to supervision and control on the propagation of public opinions and reducing the influence of negative public opinions on the society.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a real social network topology diagram with 1000 nodes;
FIG. 2 is a public opinion propagation model based on an enhanced effect SCIR network;
FIG. 3 is PSRAn influence result graph for each state node;
FIG. 4 is PRCAnd (4) an influence result graph of each state node.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the following describes the technical solutions of the embodiments of the present invention clearly and completely with reference to the accompanying drawings in the embodiments of the present invention:
various intelligent social software is brought to the end due to continuous development and progress of network technology, and nowadays, social software such as microblogs, WeChat and the like becomes an important tool for people to acquire information and make opinions, and accordingly, social groups with a large number of users and great influence are formed. With the continuous improvement of the network informatization degree, the relationship and the network structure of users in the social network are increasingly complex, the information interaction is more frequent, the modes are more diverse, the characteristics of socialization, multiple interleaving of links and the like are shown, and the social network information system has the characteristics of a typical complex network. Meanwhile, the psychological characteristics of the user can also influence the spreading of public sentiment. Therefore, the relevant departments will have a significant impact on the society unless they supervise and control the propagation of public sentiment. However, the existing public opinion propagation network model has certain limitations, and the problem of public opinion propagation in an actual social network is difficult to analyze effectively.
In view of the fact that the influence of direct immunity and social strengthening on user behaviors is not considered in the existing public opinion propagation network, the public opinion propagation situation in a real social network is difficult to simulate. The application provides a public opinion propagation model construction method based on an enhanced effect SCIR network, which comprises the steps of firstly, making a public opinion propagation rule based on a network framework of the SCIR according to the public opinion propagation situation of a social network; secondly, according to public opinion transmission rules, state transition probabilities of various nodes are provided; and finally, establishing a public opinion propagation model differential equation of the SCIR network according to the public opinion propagation rule and the state transition probability to generate a final public opinion propagation model, thereby more effectively and accurately simulating the specific situation of public opinion propagation in a real social network.
Examples
A public opinion propagation model construction method based on an enhanced effect SCIR network comprises the following specific steps:
s1: the public opinion transmission rule is formulated, and according to the public opinion transmission rule in the social network, the possible conversion conditions of various sections in the public opinion transmission process are formulated by combining the enhancement effect and the direct immunity, specifically:
(1) after the unknown state S contacts the propagation state I, there are 3 transition states: a part with a probability PSCTransition to a hesitant state C, partly with a probability PSITo a propagation state I, another part is given a probability PSRTransition to the immune state R.
(2) After the hesitation state C contacts the propagation state I, a part is in probability PCITransition to propagation state I, another part will be at rate PCRTransition to the immune state R.
(3) Propagation state I with probability PIRTransition to the immune state R.
(4) The immune state R has a probability P under the action of social reinforcement effectRCTransition to the hesitant state C.
S2: and proposing state transition probabilities, wherein when the node is at the time t, the transition probabilities of the states are as follows:
analyzing the transition probability of each state node, wherein when the node is at the time t, the transition probability of each state is as follows:
(1) assuming node j is in S state at time t, then
Figure BDA0002261294670000061
By n1＝n1(t) represents the number of I nodes in the neighbor nodes of the node j at the time t, and n is n, assuming that the node j has k edges1Are random variables that obey a binomial distribution:
Figure BDA0002261294670000062
wherein the content of the first and second substances,
Figure BDA0002261294670000063
probability of connecting to I node from S node with k edges for time t:
Figure BDA0002261294670000064
p(k1i k) is a degree correlation function, and represents a node with the degree k and the degree k1The conditional probability of the node adjacency of (a);
Figure BDA0002261294670000071
indicates that one owns k1The node of the edge is in the probability of a propagating state if it is connected to a vulnerable node of degree k.
By pI(k1T) denotes the scale k at t1The density of the I-state nodes of (a) is then approximated by:
Figure BDA0002261294670000072
then the node with degree k is at [ t, t + Δ t]Average probability of changing to C state in time period
Figure BDA0002261294670000073
Comprises the following steps:
Figure BDA0002261294670000074
similarly, the node with degree k is at [ t, t + Δ t [ ]]Average probability of becoming I-state over time
Figure BDA0002261294670000075
Comprises the following steps:
Figure BDA0002261294670000076
similarly, the node with degree k is at [ t, t + Δ t [ ]]Average probability of becoming R state over time
Figure BDA0002261294670000077
Comprises the following steps:
Figure BDA0002261294670000078
the node with the degree of k is at [ t, t + delta t]Average probability of remaining S-state for a period of time
Figure BDA0002261294670000079
Comprises the following steps:
Figure BDA00022612946700000710
(2) assuming that node j is in the C state at time t, then:
Figure BDA00022612946700000711
then there are
Figure BDA00022612946700000712
(3) Assuming that node j is in the I state at time t, then:
Figure BDA00022612946700000713
then there are
Figure BDA00022612946700000714
(4) Assuming that node j is in the R state at time t, then:
Figure BDA00022612946700000715
by n2＝n2(t) represents the number of I nodes in the neighbor nodes of the node j at the time t, and the random variable obeys binomial distribution, and is similar to the S state, so that the node with the degree k is in [ t, t + delta t ]]Average probability of changing to C state in time period
Figure BDA0002261294670000081
Comprises the following steps:
Figure BDA0002261294670000082
therefore, the node with degree k is at [ t, t + Δ t [ ]]Average probability of maintaining R state over time
Figure BDA0002261294670000083
Comprises the following steps:
Figure BDA0002261294670000084
further, establishing a public opinion propagation model differential equation of the enhanced effect SCIR network:
Figure BDA0002261294670000085
considering the generality and universality of the model, most of research on social network public opinion dissemination is based on a BA scale-free network. To verify the effectiveness and feasibility of the enhanced effect SCIR network-based public opinion propagation model proposed herein, a BA network with 1000 nodes was established to simulate a real social network, with an average of 7.981, an average path length of 3.233, and an average clustering coefficient of 0.029. In order to make the propagation evolution process of nodes in different states in the network reach a stable state, the iteration number is set to be 100.
(1) Changing PSR
The method is used for analyzing the influence of the supervision action of an authoritative department on network public opinion transmission, namely the influence of the public opinion transmission caused by the conversion of an unknown state S into an immune state R in the presence of direct immunity. On the premise of keeping the basic parameters unchanged, P is changedSR＝0，PSR＝0.1，PSR＝0.2，PSR＝0.3，PSR0.5, direct immunization P was observedSRImpact on individual state nodes. The simulation results are shown in fig. 3.
As can be seen from FIG. 3, the direct immunity P is increasedSRThe peak value of the numbers of nodes in the hesitation state C and the propagation state I in the propagation process and the time required for reaching the stable state are reduced, which indicates that the direct immunity PSRThe method can inhibit the propagation of public sentiment in the social network, thereby effectively controlling the influence of the public sentiment on the society.
(2) Changing PRC
To analyze the influence of social reinforcing effect on public sentiment propagation, P is changedRC＝0.005，PRC＝0.01，PRC＝0.05，PRC＝0.1，PRC0.3, direct immunization P was observedRCImpact on individual state nodes. The simulation results are shown in fig. 4.
As can be seen from FIG. 4, the probability P is increasedRCThe time required for C, I, R state nodes to reach the steady state can be reduced, the proportion of R state nodes is reduced, and P is knownRCThe complexity of the network is changed, so that the spreading degree of public sentiment in the social network is influenced.
According to the simulation results, the number of users in a CI state and the time required for each node to reach a stable state in the public opinion transmission process can be influenced by adjusting the direct immunity PSR and the social reinforcement effect PRC, so that the depth and the breadth of the public opinion transmission are influenced, the reasons that the popular information transmission range is wider and the transmission time is longer are explained, the public opinion transmission condition in a real social network is met, and the model has better theoretical guiding significance compared with the previous model.

Claims (4)

1. A public opinion propagation model construction method based on an enhanced effect SCIR network is characterized by comprising the following specific steps:
s1: firstly, according to public opinion propagation rules in a social network, combining a strengthening effect and direct immunity, making public opinion propagation rules;
s2: calculating the state transition probability;
s3: and establishing a public opinion propagation model differential equation of the SCIR network with the enhanced effect.
2. The method as claimed in claim 1, wherein the step S1 is implemented by steps of:
(1) after the unknown state S contacts the propagation state I, there are 3 transition states: a part with a probability PSCTransition to a hesitant state C, partly with a probability PSITo a propagation state I, another part is given a probability PSRTransition to immune state R;
(2) after the hesitation state C contacts the propagation state I, a part is in probability PCITransition to propagation state I, another part will be at rate PCRTransition to immune state R;
(3) propagation state I with probability PIRTransition to immune state R;
(4) the immune state R has a probability P under the action of social reinforcement effectRCTransition to the hesitant state C.
3. The method as claimed in claim 2, wherein the step S2 is implemented by steps of:
analyzing the transition probability of each state node, wherein when the node is at the time t, the transition probability of each state is as follows:
(1) assuming node j is in S state at time t, then
Figure FDA0002261294660000011
By n1＝n1(t) represents the number of I nodes in the neighbor nodes of the node j at the time t, and n is n, assuming that the node j has k edges1Are random variables that obey a binomial distribution:
Figure FDA0002261294660000012
wherein the content of the first and second substances,
Figure FDA0002261294660000013
probability of connecting to I node from S node with k edges for time t:
Figure FDA0002261294660000014
p(k1i k) is a degree correlation function, and represents a node with the degree k and the degree k1The conditional probability of the node adjacency of (a);
Figure FDA0002261294660000021
indicates that one owns k1A node of the edge is in a probability of a propagation state under the condition that the node is connected to a susceptible node with a degree of k;
by pI(k1T) denotes the scale k at t1The density of the I-state nodes of (a) is then approximated by:
Figure FDA0002261294660000022
then the node with degree k is at [ t, t + Δ t]Average probability of changing to C state in time period
Figure FDA0002261294660000023
Comprises the following steps:
Figure FDA0002261294660000024
similarly, the node with degree k is at [ t, t + Δ t [ ]]Average probability of becoming I-state over time
Figure FDA0002261294660000025
Comprises the following steps:
Figure FDA0002261294660000026
similarly, the node with degree k is at [ t, t + Δ t [ ]]Average probability of becoming R state over time
Figure FDA0002261294660000027
Comprises the following steps:
Figure FDA0002261294660000028
the node with the degree of k is at [ t, t + delta t]Average probability of remaining S-state for a period of time
Figure FDA0002261294660000029
Comprises the following steps:
Figure FDA00022612946600000214
(2) assuming that node j is in the C state at time t, then:
Figure FDA00022612946600000210
then there are
Figure FDA00022612946600000211
(3) Assuming that node j is in the I state at time t, then:
Figure FDA00022612946600000212
then there are
Figure FDA00022612946600000213
(4) Assuming that node j is in the R state at time t, then:
Figure FDA0002261294660000031
by n2＝n2(t) represents the number of nodes I in the neighbor nodes of the node j at the moment t, and obeys the random variable of binomial distribution, so that the node with the degree k is in [ t, t + delta t ]]Average probability of changing to C state in time period
Figure FDA0002261294660000032
Comprises the following steps:
Figure FDA0002261294660000033
therefore, the node with degree k is at [ t, t + Δ t [ ]]Average probability of maintaining R state over time
Figure FDA0002261294660000034
Comprises the following steps:
Figure FDA0002261294660000035
4. the method as claimed in claim 3, wherein the differential equation of the public opinion propagation model based on the enhanced effect SCIR network established in step S3 is as follows:
Figure FDA0002261294660000036
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CN113569188A (en) * 2021-06-03 2021-10-29 大连交通大学 DI-SCIR-based double-layer coupling social network public opinion propagation model construction method
CN114628038A (en) * 2022-03-11 2022-06-14 电子科技大学 SKIR information transmission method based on online social network

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