CN111079024B - Public opinion propagation model construction method based on reinforced effect SCIR network - Google Patents

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

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CN111079024B
CN111079024B CN201911072179.0A CN201911072179A CN111079024B CN 111079024 B CN111079024 B CN 111079024B CN 201911072179 A CN201911072179 A CN 201911072179A CN 111079024 B CN111079024 B CN 111079024B
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王运明
郭天一
初宪武
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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 steps of firstly, based on a traditional SCIR model, formulating public opinion propagation rules according to the enhanced effect and a direct immunization strategy and combining with real network public opinion propagation conditions; secondly, analyzing the possible conditions existing in the public opinion propagation process, and providing state transition probability; finally, according to public opinion propagation rules, state transition probability is provided, differential equations of the public opinion propagation model are established, and a final propagation model is generated, so that the process of the SCIR network with the reinforced effect in public opinion propagation can be effectively and accurately reflected.

Description

Public opinion propagation model construction method based on reinforced 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 a reinforced effect SCIR network.
Background
Social networks have become an important part in people's life, and along with the application of new technologies such as 5G, various intelligent social software has been developed, so that social groups with a large number of users and great influence are formed. The social network has the characteristics of instantaneity, sociability, interactivity and the like, so that network users can express own opinion aiming at hot-spot social phenomena and problems, and are continuously reviewed and forwarded by other users, and public opinion can be rapidly propagated in the network. However, if the relevant departments do not manage and control the transmission of negative public opinion, the society is seriously affected. Therefore, researching the propagation law of the online social network has important theoretical significance and application value in controlling the propagation of the network public opinion on the social network. However, the existing models for public opinion propagation have certain limitations, and there is a problem that it is difficult to accurately simulate the propagation state of public opinion in an actual social network.
Existing studies indicate that real social networks and BA scaleless networks have similar characteristics. The following characteristics should be considered in studying real social networks:
(1) Small world characteristics
Also called six degree space theory or six degree split theory (Six degrees of separation), i.e. most networks, although of large scale, have a rather short path between any two nodes (vertices), reflecting the fact that the number of interrelations can be small but can connect to the world.
(2) No scale characteristics
Most of the real world networks are not random networks, a few nodes often have a large number of connections, while most of the nodes have few, the degree distribution of the nodes conforms to the power rate distribution, which is called Scale-free property of the network. The scaleless property reflects that complex networks have severe heterogeneity with severe non-uniform distribution of connection conditions (degrees) between nodes: a few nodes in the network, called Hub points, have extremely many connections, while most nodes have only a very small number of connections. A few Hub points dominate the operation of a scaleless network. In a broad sense, the scaleless nature of a scaleless network is an inherent property that describes the severely heterogeneous distribution of a large number of complex systems as a whole.
(3) Community structural features
Humans are grouped together and the species are grouped together. Nodes in complex networks often also exhibit clustered characteristics. For example, there is always a circle of acquaintances or friends in a social network, where each member knows the other members. The clustering degree is the degree of network clustering; this is a cohesive tendency of the network. The connected group concept reflects the distribution and interrelation of small networks aggregated in a large network. For example, it may reflect the relationship of this circle of friends with another circle of friends.
Analyzing a real social network with 1000 nodes by using Gephi, wherein the average degree is 25.004, the maximum degree is 648, and the minimum degree is 1, so that the non-scale characteristic is reflected; the average path length is 2.432, meeting the small world characteristics; the average clustering coefficient is 0.608, which shows the characteristic of the community structure.
There are a large number of influencing variables in the spreading process of public opinion, and direct immunization is an important one. The direct immunization of the social network public opinion transmission means that related departments adopt actions such as publishing real information and the like to enable users which do not transmit the public opinion to be directly converted into immune users, and the transmission of the public opinion is refused, so that the influence of the public opinion on society is reduced.
Public opinion is a social phenomenon, and is a typical psychological characteristic of social groups. The social psychology shows that the strengthening effect is that the individual is subjected to the accumulative influence of repeated prompts of peers before opinion adoption or behavior decision is made, and the social strengthening effect has a nonlinear accumulative effect and has a remarkable influence on human decision.
In view of the fact that the existing public opinion propagation network does not consider the situation that the user re-propagates public opinion and the like due to direct immunity and reinforcing effect generated by related departments on public opinion supervision, the process of public opinion propagation in the real social network is difficult to accurately describe. Therefore, it is necessary to build 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 a traditional SCIR model, a public opinion propagation rule is formulated according to the enhanced effect and a direct immunization strategy and combining with the real network public opinion propagation situation; secondly, analyzing the possible conditions existing in the public opinion propagation process, and providing state transition probability; finally, according to public opinion propagation rules, state transition probability is provided, differential equations of the public opinion propagation model are established, and a final propagation model is generated, so that the process of the SCIR network with the reinforced effect in public opinion propagation can be effectively and accurately reflected.
In order to achieve the above purpose, the technical scheme of the invention is as follows: a public opinion propagation model construction method based on a reinforced effect SCIR network comprises the following specific steps:
s1: firstly, according to public opinion propagation rules in a social network, combining a reinforcing effect and direct immunity, and formulating the public opinion propagation rules;
s2: calculating state transition probability;
s3: and establishing a public opinion propagation model differential equation of the reinforced effect SCIR network.
Further, the step S1 is specifically implemented as follows:
(1) After the unknown state S contacts the propagation state I, there are 3 transition states: with probability P in part SC Transition to the hesitation state C, partly with probability P SI Transition to propagation state I, another part will be at probability P SR Transition to immune state R;
(2) Hesitation state C contacts propagation state I, a portion of which is propagated with probability P CI Transition to propagation state I, another part will be at rate P CR Transition to immune state R;
(3) Propagation state I with probability P IR Transition to immune state R;
(4) The immune state R can be represented by probability P under the action of social strengthening effect RC Transition to hesitation state C.
Further, the step S2 is specifically implemented as follows:
analyzing the transition probability of each state node, and when the node is at the time t, the transition probability of each state is as follows:
(1) Assuming that node j is in S state at time t, then
Figure BDA0002261294670000031
By n 1 =n 1 (t) represents the number of I nodes in the neighbor nodes of node j at time t, assuming node j has k edges, n 1 Is a random variable subject to binomial distribution:
Figure BDA0002261294670000032
wherein,,
Figure BDA0002261294670000033
the probability of connecting from an S node with k edges to an I node for time t:
Figure BDA0002261294670000034
p(k 1 i k) is a degree-dependent function, representing a node with a degree k and a node with a degree k 1 Conditional probability of node adjacency;
Figure BDA0002261294670000035
representing a possession k 1 The nodes of the strip edge are in the probability of being in a transmission state under the condition that the nodes are connected to an easy-to-infect node with the degree of k;
by p I (k 1 T) represents the scale k at t 1 The density of I-state nodes of (c) then approximates:
Figure BDA0002261294670000036
then the node with the degree k is at [ t, t+Δt ]]Average probability of becoming C-state in time period
Figure BDA0002261294670000037
The method comprises the following steps:
Figure BDA0002261294670000038
similarly, the node with the degree k is in [ t, t+delta t]Average probability of becoming I-state over a period of time
Figure BDA0002261294670000039
The method comprises the following steps:
Figure BDA0002261294670000041
similarly, the node with the degree k is in [ t, t+delta t]Average probability of becoming R-state in time period
Figure BDA0002261294670000042
The method comprises the following steps:
Figure BDA0002261294670000043
the node with the degree k is in [ t, t+delta t]Average probability of maintaining S-state during time period
Figure BDA0002261294670000044
The method comprises the following steps:
Figure BDA0002261294670000045
(2) Assuming that node j is in the C state at time t, there are:
Figure BDA0002261294670000046
thus there is
Figure BDA0002261294670000047
(3) Assuming that node j is in the I state at time t, there are:
Figure BDA0002261294670000048
thus there is
Figure BDA0002261294670000049
(4) Assuming that node j is in the R state at time t, there are:
Figure BDA00022612946700000410
by n 2 =n 2 (t) represents the number of I nodes in the neighbor nodes of the node j at the moment t, and obeys the random variable of binomial distribution, and the node with the degree of k is in [ t, t+delta t ] similar to the S state]Average probability of becoming C-state in time period
Figure BDA00022612946700000411
The method comprises the following steps:
Figure BDA00022612946700000412
therefore, the node with the degree k is at [ t, t+Δt ]]Average probability of maintaining R-state over a period of time
Figure BDA00022612946700000413
The method comprises the following steps:
Figure BDA00022612946700000414
further, in step S3, a public opinion propagation model differential equation of the enhanced SCIR network is established as follows:
Figure BDA0002261294670000051
finally, the public opinion propagation model based on the SCIR network with the enhanced effect is obtained.
By adopting the technical method, the invention can obtain the following technical effects: according to the public opinion network model construction method, the influence of direct immunity on uninfected users and the effect of reinforcing effect on immune users are considered, so that a public opinion propagation model based on a reinforcing effect SCIR network is provided, the propagation situation of public opinion in a real social network is more fitted, and further the propagation of public opinion is favorably monitored and controlled, and the influence of negative public opinion on society is reduced.
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For a clearer description of an embodiment of the invention or of the prior art, the drawings that are used in the description of the embodiment or of the prior art will be briefly described, it being obvious that the drawings in the description below are only some embodiments of the invention, and that other drawings can be obtained from them without inventive effort for a person skilled in the art.
FIG. 1 is a true social network topology with 1000 nodes;
FIG. 2 is a public opinion propagation model based on an enhanced SCIR network;
FIG. 3 is P SR An influence result graph for each state node;
FIG. 4 is P RC And (5) influencing the result graph of each state node.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more clear, the following is a clear and complete description of the technical solutions of the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention:
the continuous development and progress of network technology make various intelligent social software develop, and nowadays, social software such as microblog, weChat and the like becomes an important tool for people to acquire information and make comments, so that social groups with a large number of users and great influence are formed. Along with the continuous improvement of the informatization degree of the network, the relationship and the network structure of users in the social network are increasingly complex, the information interaction is more frequent and the mode is more various, the characteristics of socialization, link multiple interleaving and the like are shown, and the social network has the characteristics of a typical complex network. At the same time, the psychological characteristics of the user can also affect the spread of public opinion. Therefore, the related departments can have a great influence on society without supervising and controlling the transmission of public opinion. However, the existing public opinion propagation network model has a certain limitation, and it is difficult to effectively analyze the public opinion propagation problem in the actual social network.
In view of the fact that the existing public opinion propagation network does not consider the influence of direct immunity and social reinforcement on user behaviors at the same time, it is difficult to simulate the propagation situation of public opinion in a real social network. The application provides a public opinion propagation model construction method based on a reinforced effect SCIR network, which comprises the steps of firstly, formulating public opinion propagation rules based on a SCIR network frame and according to the condition of social network public opinion propagation; secondly, according to public opinion propagation rules, the state transition probability of various nodes is proposed; and finally, establishing a public opinion propagation model differential equation of the reinforced effect SCIR network according to the public opinion propagation rule and the state transition probability to generate a final public opinion propagation model, so that the specific condition of public opinion propagation in the real social network can be effectively and accurately simulated.
Examples
A public opinion propagation model construction method based on a reinforced effect SCIR network comprises the following specific steps:
s1: formulating public opinion propagation rules, and formulating possible transformation conditions of various knots in the public opinion propagation process according to the public opinion propagation rules in a social network by combining reinforcing effect and direct immunity, wherein the method specifically comprises the following steps:
(1) After the unknown state S contacts the propagation state I, there are 3 transition states: with probability P in part SC Transition to the hesitation state C, partly with probability P SI Transition to propagation state I, another part will be at probability P SR Transition to immune state R.
(2) Hesitation state C contacts propagation state I, a portion of which is propagated with probability P CI Transition to propagation state I, another part will be at rate P CR Transition to immune state R.
(3) Propagation state I with probability P IR Transition to immune state R.
(4) The immune state R can be represented by probability P under the action of social strengthening effect RC Transition to hesitation state C.
S2: and (3) providing 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, and when the node is at the time t, the transition probability of each state is as follows:
(1) Assuming that node j is in S state at time t, then
Figure BDA0002261294670000061
By n 1 =n 1 (t) represents the number of I nodes in the neighbor nodes of node j at time t, assuming node j has k edges, n 1 Is a random variable subject to binomial distribution:
Figure BDA0002261294670000062
wherein,,
Figure BDA0002261294670000063
the probability of connecting from an S node with k edges to an I node for time t:
Figure BDA0002261294670000064
p(k 1 i k) is a degree-dependent function, representing a node with a degree k and a node with a degree k 1 Conditional probability of node adjacency;
Figure BDA0002261294670000071
representing a possession k 1 The nodes of the bar are in the probability of propagating states under the condition that they are connected to an susceptible node of degree k.
By p I (k 1 T) represents the scale k at t 1 The density of I-state nodes of (c) then approximates:
Figure BDA0002261294670000072
then the node with the degree k is at [ t, t+Δt ]]Average probability of becoming C-state in time period
Figure BDA0002261294670000073
The method comprises the following steps:
Figure BDA0002261294670000074
similarly, the node with the degree k is in [ t, t+delta t]Average probability of becoming I-state over a period of time
Figure BDA0002261294670000075
The method comprises the following steps:
Figure BDA0002261294670000076
similarly, the node with the degree k is in [ t, t+delta t]Average probability of becoming R-state in time period
Figure BDA0002261294670000077
The method comprises the following steps:
Figure BDA0002261294670000078
the node with the degree k is in [ t, t+delta t]Average probability of maintaining S-state during time period
Figure BDA0002261294670000079
The method comprises the following steps:
Figure BDA00022612946700000710
(2) Assuming that node j is in the C state at time t, there are:
Figure BDA00022612946700000711
thus there is
Figure BDA00022612946700000712
(3) Assuming that node j is in the I state at time t, there are:
Figure BDA00022612946700000713
thus there is
Figure BDA00022612946700000714
(4) Assuming that node j is in the R state at time t, there are:
Figure BDA00022612946700000715
by n 2 =n 2 (t) represents the number of I nodes in the neighbor nodes of the node j at the moment t, and obeys the random variable of binomial distribution, and the node with the degree of k is in [ t, t+delta t ] similar to the S state]Average probability of becoming C-state in time period
Figure BDA0002261294670000081
The method comprises the following steps:
Figure BDA0002261294670000082
therefore, the node with the degree k is at [ t, t+Δt ]]Average probability of maintaining R-state over a period of time
Figure BDA0002261294670000083
The method 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 researches on social network public opinion propagation are based on BA scale-free network. To verify the effectiveness and feasibility of the public opinion propagation model based on the enhanced SCIR network presented herein, a BA network with 1000 nodes was established to simulate a real social network, with an average degree of 7.981, an average path length of 3.233, and an average cluster coefficient of 0.029. In order to enable the propagation evolution process of nodes in different states in the network to reach a stable state, the iteration times are set to be 100 times.
(1) Altering P SR
In order to analyze the influence of the supervision function of the authority department on the network public opinion transmission, namely the influence of the unknown state S to the immune state R on the public opinion transmission when the direct immunity exists. By changing P under the premise of unchanged basic parameters SR =0,P SR =0.1,P SR =0.2,P SR =0.3,P SR Direct immunization P was observed =0.5 SR Impact on the various state nodes. The simulation results are shown in fig. 3.
As can be seen from FIG. 3, the direct immunity P is increased SR Reducing peak value of the number of the nodes in the hesitation state C and the transmission state I and time required for reaching the stable state in the transmission process, and indicating the direct immunity P SR The method can inhibit the spreading of public opinion in the social network, thereby effectively controlling the influence of the public opinion on society.
(2) Altering P RC
To analyze the effect of socially enhanced effects on public opinion transmission, by varying P RC =0.005,P RC =0.01,P RC =0.05,P RC =0.1,P RC Direct immunization P was observed =0.3 RC Impact on the various state nodes. The simulation results are shown in fig. 4.
As can be seen from FIG. 4, the probability P is increased RC The time required for the C, I, R state node to reach the stable state can be reduced, the proportion of the R state node is reduced, and the P can be known RC The complexity of the network is changed, so that the spreading breadth of public opinion in the social network is affected.
According to the simulation results, the quantity of users in the CI state and the time required for each node to reach the stable state in the public opinion propagation process can be influenced by adjusting the direct immune PSR and the social enhancement effect PRC, so that the depth and breadth of public opinion propagation are influenced, the reasons of wider popular information propagation range and longer propagation time are explained, the situation of public opinion propagation in a real social network is met, and the model has better theoretical guiding significance than the previous model.

Claims (2)

1. A public opinion propagation model construction method based on a reinforced 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 reinforcing effect and direct immunity, and formulating the public opinion propagation rules;
the specific implementation steps of the step S1 are as follows:
(1) After the unknown state S contacts the propagation state I, there are 3 transition states: with probability P in part SC Transition to the hesitation state C, partly with probability P SI Transition to propagation state I, another part will be at probability P SR Transition to immune state R;
(2) Hesitation state C contacts propagation state I, a portion of which is propagated with probability P CI Transition to propagation state I, another part will be at rate P CR Transition to immune state R;
(3) Propagation state I with probability P IR Transition to immune state R;
(4) The immune state R can be represented by probability P under the action of social strengthening effect RC Transition to hesitation state C;
s2: calculating state transition probability;
the specific implementation steps of the step S2 are as follows:
analyzing the transition probability of each state node, and when the node is at the time t, the transition probability of each state is as follows:
(1) Assuming that node j is in S state at time t, then
Figure QLYQS_1
By n 1 =n 1 (t) represents the number of I nodes in the neighbor nodes of node j at time t, assuming node j has k edges, n 1 Is a random variable subject to binomial distribution:
Figure QLYQS_2
wherein,,
Figure QLYQS_3
the probability of connecting from an S node with k edges to an I node for time t:
Figure QLYQS_4
p(k 1 i k) is a degree-dependent function, representing a node with a degree k and a node with a degree k 1 Conditional probability of node adjacency;
Figure QLYQS_5
representing a possession k 1 The nodes of the strip edge are in the probability of being in a transmission state under the condition that the nodes are connected to an easy-to-infect node with the degree of k;
by p I (k 1 T) represents the scale k at t 1 The density of I-state nodes of (c) then approximates:
Figure QLYQS_6
then the node with the degree k is at [ t, t+Δt ]]Average probability of becoming C-state in time period
Figure QLYQS_7
The method comprises the following steps:
Figure QLYQS_8
similarly, the node with the degree k is in [ t, t+delta t]Average probability of becoming I-state over a period of time
Figure QLYQS_9
The method comprises the following steps:
Figure QLYQS_10
similarly, the node with the degree k is in [ t, t+delta t]Average probability of becoming R-state in time period
Figure QLYQS_11
The method comprises the following steps:
Figure QLYQS_12
the node with the degree k is in [ t, t+delta t]Average probability of maintaining S-state during time period
Figure QLYQS_13
The method comprises the following steps:
Figure QLYQS_14
(2) Assuming that node j is in the C state at time t, there are:
Figure QLYQS_15
thus there is
Figure QLYQS_16
(3) Assuming that node j is in the I state at time t, there are:
Figure QLYQS_17
thus there is
Figure QLYQS_18
(4) Assuming that node j is in the R state at time t, there are:
Figure QLYQS_19
by n 2 =n 2 (t) represents the number of I nodes in the neighbor nodes of the node j at the moment t and obeys the random variable of the binomial distribution, the node with the degree of k is in [ t, t+delta t ]]Average probability of becoming C-state in time period
Figure QLYQS_20
The method comprises the following steps:
Figure QLYQS_21
therefore, the node with the degree k is at [ t, t+Δt ]]Average probability of maintaining R-state over a period of time
Figure QLYQS_22
The method comprises the following steps:
Figure QLYQS_23
s3: and establishing a public opinion propagation model differential equation of the reinforced effect SCIR network.
2. The public opinion propagation model construction method based on the enhanced effect SCIR network of claim 1 wherein the establishing public opinion propagation model differential equation of the enhanced effect SCIR network in step S3 is:
Figure QLYQS_24
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