CN114628038B - A SKIR information dissemination method based on online social network - Google Patents

Abstract

The invention discloses a SKIR information dissemination method based on an online social network, comprising the following steps: Step 1, divide the user state into unknown information state S, informed state K, propagation state I, and senseless state R; Step 2, obtain Information propagation probability between different processes; Step 3, combine the classical propagation model and mean field theory, use the information propagation probability determined in Step 2 to establish a SKIR information propagation model; Step 4, Analyze the SKIR information propagation model obtained in Step 3 , deduce the equilibrium point of the system; step 5, analyze the stability of the equilibrium point obtained in step 4, and obtain the stability condition of the equilibrium point of the system. By simulating the dissemination process of information on the social network in the real world, the present invention predicts its dissemination range and dissemination speed, and can obtain the factors affecting the information dissemination orientation in time, which helps to control the dissemination of bad information, thereby preventing the occurrence of social crisis events. , thereby maintaining the security and stability of social networks.

Description

A SKIR information dissemination method based on online social network

technical field

The invention belongs to the field of communication technology, and relates to communication security technology, in particular to a SKIR information dissemination method based on an online social network.

Background technique

In the early stage of research on infectious diseases, the construction of infectious disease transmission models has theoretical guidance and practical significance for understanding the transmission process and transmission mechanism of viruses, as well as for virus prevention and control. When constructing the transmission model, the population is first divided into three states: susceptible state (S), the individual is in a healthy state before being infected, but may be infected with the virus later; infection state (I), the individual has been infected Infected, and will infect other healthy individuals; immune status (R), infected individuals are cured and no longer receive such viral infections.

Similar to the spread of infectious diseases, in the process of information dissemination, the system users are divided into the following three states: (1) unknown state S: system users have the conditions to receive information but have not received information, (2) dissemination state I : The user has been exposed to the information and spread the information to other users; (3) Immune state R: Due to the timeliness of the information or the user's own factors, the user is no longer interested in the information and will not continue to spread. Due to the many similarities between information dissemination and the spread of infectious diseases, most of the current research on information dissemination models in social networks is based on infectious disease models, so information dissemination models are also based on SI, SIS and SIR infectious disease models.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies of the prior art, and to provide a method for simulating the dissemination process of information on the social network in the real world, predicting its dissemination range and dissemination speed, so as to obtain the factors affecting the information dissemination orientation in time, which is helpful for the government and the Relevant departments control the dissemination of bad information, so as to prevent the occurrence of social crisis events, and thus maintain the safety and stability of social networks. SKIR information dissemination method based on online social networks.

The object of the present invention is to be achieved through the following technical solutions: a SKIR information dissemination method based on an online social network, comprising the following steps:

Step 1. Divide the user state into unknown information state S, informed state K, propagation state I, and senseless state R, and describe the information propagation process through state transition;

Step 2. Calculate the probability of information dissemination between different processes;

Step 3. Combine the classical propagation model and the mean field theory, and use the information propagation probability determined in Step 2 to establish a SKIR information propagation model;

Step 4, analyze the SKIR information propagation model obtained in step 3, and derive the system balance point;

Step 5. Carry out stability analysis on the equilibrium point obtained in step 4, and obtain the stability condition of the equilibrium point of the system.

Further, the specific implementation method of the step S1 is as follows: the user and the attention relationship of the online social network are respectively represented by nodes and edges: the user set is represented by N={N ₁ , N ₂ ,...,N _num }, If there are edges between nodes, it means that there is a concern relationship, and there is the possibility of information exchange;

Combined with the real world situation, users are divided into the following four states: the unknown information state S means that the information has not been contacted; the informed state K means that the information is known, but it has not been spread immediately, and the ability to participate in the spread again is retained; the spread state I means Information is being propagated; the insensitive state R indicates that information is known and will not be propagated in the future.

Further, the specific implementation method of the step 2 is:

迁入迁出率为μ、传播无感率为η；The probability of an unknown node browsing information is α, the probability of direct transmission is β, the rate of hesitant knowledge is ε, and the probability of indirect transmission is

The immigration rate is μ, and the transmission insensitivity rate is η;

的概率变为传播状态I继续传播信息；本模型假设会有μ的人口迁入率，为了保持模型总人数保持不变，迁出率也设为μ。When the user's node state becomes the propagation state I, the neighbor node has a probability of α to browse the message. If the message is not browsed, the neighbor node keeps the unknown information state S unchanged, otherwise the neighbor node changes to the propagation state I with probability β, The probability ε becomes the informed state K, and the probability η becomes the non-sensing state R; the nodes in the informed state K and the propagating state I have the probability η to become the non-sensing state R, and the nodes in the informed state k will also have

The probability of changing to the propagation state I continues to spread information; this model assumes that there will be a population immigration rate of μ, in order to keep the total number of people in the model unchanged, the emigration rate is also set to μ.

Further, the specific implementation method of step 3 is as follows: at time t, the density of the nodes in the unknown information state S, the nodes in the informed state K, the nodes in the propagation state I and the nodes in the non-inductive state R in the network are respectively denoted by S. (t), K(t), I(t), R(t) means that it satisfies

S(t)+K(t)+I(t)+R(t)=1

Based on the basic assumptions and state transition rules, construct the state transition formula shown in the formula:

k is the average degree of the network.

Further, the specific implementation method of step 4 is: in order to solve the model equilibrium point, the value of the state transition formula is set to 0, and the state transition equation is obtained:

Solve the equation and get two equilibrium points of the system: one is the disease-free equilibrium point E ₀ =(1,0,0,0), the other is the diseased equilibrium point E ₀ ^* =(S ^* ,K ^* , I ^* ,1-S ^* -K ^* -I ^* ); where,

Further, the specific implementation method of step 5 is: the Jacobian matrix in the state transition equation is:

Bringing the equilibrium point E ₀ =(1,0,0,0) into the Jacobian matrix, we get:

Calculate its eigenvalues to get:

λ _1,2 = -μ

成立时，系统在平衡点E₀＝(1,0,0,0)处的 Jacobian矩阵的特征值均有负实部，系统的平衡点E₀渐进稳定，信息就无法在网络中进行传播。λ ₁ =λ ₂ < ₀ and λ ₃ <λ ₄ , so only the sign of λ ₄ needs to be discussed. When λ ₄ <0 holds, the Jacobian matrix has a The eigenvalues all have negative real parts, that is, when

When established, the eigenvalues of the Jacobian matrix at the equilibrium point E ₀ =(1,0,0,0) all have negative real parts, the equilibrium point E ₀ of the system is asymptotically stable, and information cannot be propagated in the network.

The beneficial effects of the present invention are: on the basis of the improved SIR model, the present invention proposes a new social network information dissemination model by defining the state transition probability function between different nodes and comprehensively considering various factors affecting the dissemination. Simulation experiments in different network environments, compared with the SIR model, the proportion of the model propagation nodes of the present invention is significantly lower than that of the SIR model, and the information propagation process is smoother. It is wider, but the information cannot cover the entire network, which conforms to the actual social network information dissemination law. By simulating the dissemination process of information on social networks in the real world, predicting its dissemination range and speed, it is possible to obtain the factors that affect the orientation of information dissemination in time, which is helpful for the government and relevant departments to control the dissemination of bad information, thereby preventing social crisis events The occurrence of social network, and then maintain the security and stability of social network, so that it can better serve users.

Detailed ways

The technical solutions of the present invention are further described below.

A kind of SKIR information dissemination method based on online social network of the present invention, comprises the following steps:

Step 1. Divide the user state into unknown information state S, informed state K, propagation state I, and senseless state R, and describe the information dissemination process through state transition; the specific implementation method is as follows: using the user and following relationship of the online social network respectively as Node and edge representation: N={N ₁ , N ₂ ,...,N _num } is used to represent the user set, and if there are edges between nodes, it means that there is a concern relationship, and there is the possibility of information exchange;

Combined with the real world situation, users are divided into the following four states: the unknown information state S means that the information has not been contacted; the informed state K means that the information is known, but it has not been spread immediately, and the ability to participate in the spread again is retained; the spread state I means Information is being propagated; the insensitive state R indicates that information is known and will not be propagated in the future.

Step 2. Calculate the information propagation probability between different processes; the specific implementation method is:

迁入迁出率为μ、传播无感率为η；Obtained by manual determination or by real data fitting, the probability of browsing information from unknown nodes is α, the probability of direct transmission is β, the rate of hesitant knowledge is ε, and the probability of indirect transmission is

The immigration rate is μ, and the transmission insensitivity rate is η;

的概率变为传播状态I继续传播信息；本模型假设会有μ的人口迁入率，为了保持模型总人数保持不变，迁出率也设为μ。When the user's node state becomes the propagation state I, the neighbor node has a probability of α to browse the message. If the message is not browsed, the neighbor node keeps the unknown information state S unchanged, otherwise the neighbor node changes to the propagation state I with probability β, The probability ε becomes the informed state K, and the probability η becomes the non-sensing state R; the nodes in the informed state K and the propagating state I have the probability η to become the non-sensing state R, and the nodes in the informed state k will also have

The probability of changing to the propagation state I continues to spread information; this model assumes that there will be a population immigration rate of μ, in order to keep the total number of people in the model unchanged, the emigration rate is also set to μ.

For example, the user is node A, and the initial states of his neighbor nodes B, C, and D are all unknown information states S. When A becomes the propagation state I, B, C, and D all have a probability of α to browse the message propagated by A, and the probability of 1-α is not to browse the message. Assuming that B has not browsed, then B keeps the unknown information state S unchanged; assuming that C and D have browsed, then they will become the propagation state I with the probability of β, the probability of ε becomes the informed state K, and the probability of η becomes Insensitive state R.

Step 3. Combine the classical propagation model and the mean field theory, and use the information propagation probability determined in Step 2 to establish the SKIR information propagation model; the specific implementation method is: at time t, the node of the unknown information state S in the network, the informed state K The densities of the nodes of , the nodes of the propagation state I and the nodes of the non-inductive state R are represented by S(t), K(t), I(t), R(t) respectively, which satisfy

S(t)+K(t)+I(t)+R(t)=1

Based on the basic assumptions and state transition rules, construct the state transition formula shown in the formula:

k is the average degree of the network.

Step 4, analyze the SKIR information propagation model obtained in step 3, and derive the system equilibrium point; the specific implementation method is: in order to solve the model equilibrium point, the value of the state transition formula is set to 0, and the state transition equation is obtained:

Solve the equation and get two equilibrium points of the system: one is the disease-free equilibrium point E ₀ =(1,0,0,0), the other is the diseased equilibrium point E ₀ ^* =(S ^* ,K ^* , I ^* ,1-S ^* -K ^* -I ^* ); where,

Step 5. Perform stability analysis on the equilibrium point obtained in step 4, and obtain the stability condition of the equilibrium point of the system; the specific implementation method is: the Jacobian matrix in the state transition equation is:

Bringing the equilibrium point E ₀ =(1,0,0,0) into the Jacobian matrix, we get:

Calculate its eigenvalues to get:

λ ₁ =λ ₂ =-μ

成立时，系统在平衡点E₀＝(1,0,0,0)处的 Jacobian矩阵的特征值均有负实部，系统的平衡点E₀渐进稳定，信息就无法在网络中进行传播。因此，可以通过相应的舆论控制手段来调整未知节点浏览到信息的概率为α、直接传播概率为β、犹豫知情率为ε，间接传播概率为

迁入迁出率为μ、传播无感率为η这些参数，使得上式成立，阻止不良信息传播。λ ₁ =λ ₂ < ₀ and λ ₃ <λ ₄ , so only the sign of λ ₄ needs to be discussed. When λ ₄ <0 holds, the Jacobian matrix has a The eigenvalues all have negative real parts, that is, when

When established, the eigenvalues of the Jacobian matrix at the equilibrium point E ₀ =(1,0,0,0) all have negative real parts, the equilibrium point E ₀ of the system is asymptotically stable, and information cannot be propagated in the network. Therefore, it is possible to adjust the probability that unknown nodes browse to information as α, the probability of direct transmission as β, the hesitant to know rate as ε, and the probability of indirect transmission as ε through corresponding public opinion control methods.

The immigration rate μ and the transmission insensitivity rate η make the above formula valid and prevent the spread of bad information.

Those of ordinary skill in the art will appreciate that the embodiments described herein are intended to assist readers in understanding the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations without departing from the essence of the present invention according to the technical teaching disclosed in the present invention, and these modifications and combinations still fall within the protection scope of the present invention.

Claims (1)

1. a SKIR information dissemination method based on an online social network, is characterized in that, comprises the following steps: Step 1. Divide the user state into unknown information state S, informed state K, propagation state I, and senseless state R; the specific implementation method is as follows: the users and attention relationships of the online social network are represented by nodes and edges respectively: use N ={N ₁ ,N ₂ ,...,N _num } represents a set of users, and if there is an edge between nodes, it means that there is a concern relationship, and information interaction can be performed; Combined with the real world situation, users are divided into the following four states: the unknown information state S means that the information has not been contacted; the informed state K means that the information is known, but it has not been spread immediately, and the ability to participate in the spread again is retained; the spread state I means Information is being disseminated; the non-sensing state R indicates that information is known and will not be disseminated in the future; Step 2. Obtain the information dissemination probability between different processes; the specific implementation method is: The probability of an unknown node browsing information is α, the probability of direct transmission is β, the rate of hesitant knowledge is ε, and the probability of indirect transmission is

The immigration rate is μ, and the transmission insensitivity rate is η; When the user's node state becomes the propagation state I, the neighbor node has a probability of α to browse the message. If the message is not browsed, the neighbor node keeps the unknown information state S unchanged, otherwise the neighbor node changes to the propagation state I with probability β, The probability ε becomes the informed state K, and the probability η becomes the non-sensing state R; the nodes in the informed state K and the propagating state I have the probability η to become the non-sensing state R, and the nodes in the informed state k will also have

The probability of changing to the propagation state I continues to spread information; this model assumes that there will be a population immigration rate of μ, in order to keep the total number of people in the model unchanged, the emigration rate is also set to μ; Step 3. Combine the classical propagation model and the mean field theory, and use the information propagation probability determined in Step 2 to establish the SKIR information propagation model; the specific implementation method is: at time t, the node of the unknown information state S in the network, the informed state K The densities of the nodes of , the nodes of the propagation state I and the nodes of the non-inductive state R are represented by S(t), K(t), I(t), R(t) respectively, which satisfy S(t)+K(t)+I(t)+R(t)=1 Based on the basic assumptions and state transition rules, construct the state transition formula shown in the formula:

k is the average degree of the network; Step 4, analyze the SKIR information propagation model obtained in step 3, and derive the system equilibrium point; the specific implementation method is: in order to solve the model equilibrium point, the value of the state transition formula is set to 0, and the state transition equation is obtained:

Solve the equation and get two equilibrium points of the system: one is the disease-free equilibrium point E ₀ =(1,0,0,0), the other is the diseased equilibrium point E ₀ ^* =(S ^* ,K ^* , I ^* ,1-S ^* -K ^* -I ^* ); where,

Step 5. Perform stability analysis on the equilibrium point obtained in step 4, and obtain the stability condition of the equilibrium point of the system; the specific implementation method is: the Jacobian matrix in the state transition equation is:

Bringing the equilibrium point E ₀ =(1,0,0,0) into the Jacobian matrix, we get:

Calculate its eigenvalues to get: λ _1,2 = -μ

λ ₁ =λ ₂ < ₀ and λ ₃ <λ ₄ , so only the sign of λ ₄ needs to be discussed. When λ ₄ <0 holds, the Jacobian matrix has a The eigenvalues all have negative real parts, that is, when

When established, the eigenvalues of the Jacobian matrix at the equilibrium point E ₀ =(1,0,0,0) all have negative real parts, the equilibrium point E ₀ of the system is asymptotically stable, and information cannot be propagated in the network.