CN114628038B - SKIR information transmission method based on online social network - Google Patents
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Abstract
The invention discloses an SKIR information propagation method based on an online social network, which comprises the following steps: step 1, dividing user states into an unknown information state S, an informed state K, a propagation state I and a non-inductive state R; step 2, obtaining information transmission probability among different processes; step 3, combining a classical propagation model and an average field theory, and establishing an SKIR information propagation model by using the information propagation probability determined in the step 2; step 4, analyzing the SKIR information propagation model obtained in the step 3, and deducing a system balance point; and 5, performing stability analysis on the balance point obtained in the step 4 to obtain the stability condition of the system balance point. The invention predicts the propagation range and the propagation speed of the information on the real-world social network by simulating the propagation process of the information on the real-world social network, can timely acquire the factors influencing the information propagation guidance, and is favorable for controlling the propagation of bad information, thereby preventing the occurrence of social crisis events and further keeping the safety and the stability of the social network.
Description
Technical Field
The invention belongs to the technical field of communication, relates to a communication security technology, and particularly relates to an SKIR information propagation method based on an online social network.
Background
In the early stage, in the research process of infectious diseases, the establishment of an infectious disease transmission model has theoretical guidance and practical significance for understanding the transmission process and the transmission mechanism of viruses and preventing and controlling the viruses. When constructing the propagation model, the population is first divided into three states: a susceptible state (S) in which the individual is in a healthy state prior to being infected, but is likely to subsequently receive a viral infection; infection status (I), the individual has been infected and will infect other healthy individuals; immune status (R), infected individuals are cured and no longer receive such viral infections.
Similar to the infectious disease spreading process, during the information spreading process, the system users are divided into the following three states: (1) unknown state S: the system user has the condition of receiving the information but does not receive the information, (2) the propagation state I: the user has contacted the information and disseminates the information to other users; (3) immune status R: the information is no longer interesting and does not continue to be disseminated due to its timeliness or the user's own factors. Because the information transmission has many similarities with the infectious disease spread, the research on the information transmission model in the social network is mostly constructed on the basis of the infectious disease model, and therefore, the information transmission model is also mostly constructed on the basis of the SI, SIS and SIR infectious disease models.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide the SKIR information transmission method based on the online social network, which can predict the transmission range and the transmission speed of the information on the real-world social network by simulating the transmission process of the information, can timely acquire the factors influencing the information transmission guidance, is favorable for governments and related departments to control the transmission of the bad information, thereby preventing the occurrence of social crisis events and further keeping the safety and stability of the social network.
The purpose of the invention is realized by the following technical scheme: an SKIR information propagation method based on an online social network comprises the following steps:
step 1, dividing a user state into an unknown information state S, an informed state K, a propagation state I and a non-inductive state R, and describing an information propagation process through state transition;
step 2, calculating the information propagation probability among different processes;
step 3, combining a classical propagation model and an average field theory, and establishing an SKIR information propagation model by using the information propagation probability determined in the step 2;
step 4, analyzing the SKIR information propagation model obtained in the step 3, and deducing a system balance point;
and 5, performing stability analysis on the balance point obtained in the step 4 to obtain the stability condition of the system balance point.
Further, the specific implementation method of step S1 is as follows: representing users and concern relationships of an online social network by nodes and connecting edges respectively: with N ═ N 1 ,N 2 ,...,N num Representing a user set, and representing that attention relationship exists and information interaction is possible if connecting edges exist among nodes;
combining the real world situation, the user is divided into the following four states: unknown information state S represents that information has not been contacted; the informed state K represents known information but is not immediately transmitted, and the capability of participating in transmission again is reserved; the propagation state I represents that information is being propagated; the non-sensing state R represents known information and no further messages will be propagated later.
Further, the step 2 is specifically implemented as follows:
the probability of the information browsed by the unknown node is alpha, the direct propagation probability is beta, the hesitation rate is epsilon, and the indirect propagation probability is
The migration rate is mu, and the propagation insensitivity is eta;
when the node state of the user is changed into a propagation state I, the neighbor nodes have the probability of alpha to browse the message, if the message is not browsed, the neighbor nodes keep the unknown information state S unchanged, otherwise, the neighbor nodes are changed into the propagation state I with the probability of beta, the probability of epsilon is changed into an informed state K, and the probability of eta is changed into an insensitive state R; the probability that the nodes in the informed state K and the propagation state I have eta is changed into the non-inductive state R, and the nodes in the informed state K also have eta
The probability of (2) is changed into a propagation state I to continue to propagate information; the model assumes that there is a population migration rate of μ, and the migration rate is also set to μ in order to keep the total population of the model constant.
Further, the specific implementation method of step 3 is as follows: at time t, the densities of the node in the unknown information state S, the node in the informed state K, the node in the propagation state I and the node in the non-sensible state R in the network are respectively expressed by S (t), K (t), I (t), R (t), and satisfy
S(t)+K(t)+I(t)+R(t)＝1
And constructing a state transition formula shown as the formula according to the basic assumption and the state transition rule:
k is the average degree of the network.
Further, the specific implementation method of step 4 is as follows: to solve the model equilibrium point, let the value of the state transition formula be 0, obtain the state transition equation:
solving the equation to obtain the balance points of the system, namely two points are: one is the disease-free balance point E 0 (1,0, 0), and the other is the sick balance point E 0 * ＝(S * ,K * ,I * ,1-S * -K * -I * ) (ii) a Wherein the content of the first and second substances,
further, the step 5 is specifically implemented as follows: the Jacobian matrix in the state transition equation is:
will balance point E 0 Substituting (1,0,0,0) into the Jacobian matrix yields:
calculating the characteristic value to obtain:
λ 1,2 ＝-μ
λ 1 ＝λ 2 ＜0and lambda 3 ＜λ 4 Therefore, only λ needs to be discussed 4 When sign of (a) 4 If < 0 is true, the Jacobian matrix is at equilibrium point E 0 The eigenvalues at (1,0,0,0) all have negative real parts, i.e. when
When true, the system is at equilibrium point E 0 The eigenvalues of the Jacobian matrix at (1,0,0,0) all have negative real parts, the equilibrium point E of the system 0 And the information can not be propagated in the network because of gradual stability.
The invention has the beneficial effects that: the invention provides a new social network information transmission model by defining state transition probability functions among different nodes and comprehensively considering various factors influencing transmission on the basis of an improved SIR model. By simulating the information transmission process on the real world social network and predicting the transmission range and the transmission speed, the method can timely acquire the factors influencing the information transmission guide, is helpful for governments and related departments to control the transmission of bad information, thereby preventing the occurrence of social crisis events, further keeping the safety and stability of the social network and better serving users.
Detailed Description
The technical solution of the present invention is further explained below.
The invention discloses an SKIR information transmission method based on an online social network, which comprises the following steps:
step 1, dividing a user state into an unknown information state S, an informed state K, a propagation state I and a non-inductive state R, and describing an information propagation process through state transition; the specific implementation method comprises the following steps: representing users and concern relationships of an online social network by nodes and connecting edges respectively: with N ═ N 1 ,N 2 ,...,N num Representing a user set, and representing that attention relationship exists and information interaction is possible if connecting edges exist among nodes;
combining the real world situation, the user is divided into the following four states: unknown information state S represents that information has not been contacted; the informed state K represents known information but is not immediately transmitted, and the capability of participating in transmission again is reserved; the propagation state I represents that information is being propagated; the non-sensing state R represents known information and no further messages will be propagated later.
Step 2, calculating the information propagation probability among different processes; the specific implementation method comprises the following steps:
the probability of the information browsed by the unknown node is alpha, the direct propagation probability is beta, the hesitation rate is epsilon, and the indirect propagation probability is alpha
The migration rate is mu, and the propagation insensitivity is eta;
when the node state of the user is changed into a propagation state I, the neighbor nodes have the probability of alpha to browse the message, if the message is not browsed, the neighbor nodes keep the unknown information state S unchanged, otherwise, the neighbor nodes are changed into the propagation state I with the probability of beta, the probability of epsilon is changed into an informed state K, and the probability of eta is changed into an insensitive state R; the probability that the nodes in the informed state K and the propagation state I have eta is changed into the non-inductive state R, and the nodes in the informed state K also have eta
The probability of (2) is changed into a propagation state I to continue to propagate information; the model assumes that there is a population migration rate of μ, and the migration rate is also set to μ in order to keep the population in the model unchanged.
For example, the user is node a and the initial states of his neighbor nodes B, C, D are all unknown information states S. When a changes to the propagation state I, B, C, D all have a probability of viewing a propagated message, and 1-a probability of not viewing a message. If B is not browsed, B keeps the state S of unknown information unchanged; assuming C, D browsed, they would change to propagation state I with a probability of β, an informed state K with a probability of ε, and an imperceptible state R with a probability of η.
Step 3, combining a classical propagation model and an average field theory, and establishing an SKIR information propagation model by using the information propagation probability determined in the step 2; the specific implementation method comprises the following steps: at time t, the densities 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 expressed by S (t), K (t), I (t) and R (t), and the densities meet the requirements
S(t)+K(t)+I(t)+R(t)＝1
And constructing a state transition formula shown as the formula according to the basic assumption and the state transition rule:
k is the average degree of the network.
Step 4, analyzing the SKIR information propagation model obtained in the step 3, and deducing a system balance point; the specific implementation method comprises the following steps: to solve the model equilibrium point, let the value of the state transition equation be 0, get the state transition equation:
solving the equation, two balance points of the system are obtained: one is the disease-free balance point E 0 (1,0, 0), and the other is the sick balance point E 0 * ＝(S * ,K * ,I * ,1-S * -K * -I * ) (ii) a Wherein the content of the first and second substances,
step 5, performing stability analysis on the balance point obtained in the step 4 to obtain a stability condition of the system balance point; the specific implementation method comprises the following steps: the Jacobian matrix in the state transition equation is:
will balance point E 0 Substituting (1,0,0,0) into the Jacobian matrix yields:
calculating the characteristic value to obtain:
λ 1 ＝λ 2 ＝-μ
λ 1 ＝λ 2 < 0 and λ 3 ＜λ 4 Therefore, only λ needs to be discussed 4 When a sign of (b) is 4 If < 0 is true, the Jacobian matrix is at equilibrium point E 0 The eigenvalues at (1,0,0,0) all have negative real parts, i.e. when
When established, the system is at equilibrium point E 0 The characteristic values of Jacobian matrix at (1,0,0,0) are allNegative real part, equilibrium point E of the system 0 And the information can not be propagated in the network because of gradual stability. Therefore, the probability of the information browsed by the unknown node is adjusted to be alpha, the direct propagation probability is beta, the hesitation rate is epsilon, and the indirect propagation probability is
The immigration migration rate is mu, and the propagation insensitive rate is eta, so that the above formula is established to prevent propagation of bad information.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (1)
1. An SKIR information transmission method based on an online social network is characterized by comprising the following steps:
step 1, dividing user states into an unknown information state S, an informed state K, a propagation state I and a non-inductive state R; the specific implementation method comprises the following steps: representing users and concern relationships of an online social network by nodes and connecting edges respectively: with N ═ N 1 ,N 2 ,...,N num Representing a user set, and representing that an attention relationship exists if connecting edges exist among nodes, so that information interaction can be carried out;
combining the real world situation, the user is divided into the following four states: unknown information state S represents that information has not been touched; the informed state K represents known information, but is not immediately transmitted, and the capability of participating in transmission again is reserved; the propagation state I represents that information is being propagated; the non-sensing state R represents known information and no further messages will be propagated later;
step 2, obtaining information transmission probability among different processes; the specific implementation method comprises the following steps:
the probability of the information browsed by the unknown node is alpha, the direct propagation probability is beta, the hesitation rate is epsilon, and the indirect propagation probability is
The migration rate is mu, and the propagation insensitivity is eta;
when the node state of the user is changed into a propagation state I, the neighbor nodes have the probability of alpha to browse the message, if the message is not browsed, the neighbor nodes keep the unknown information state S unchanged, otherwise, the neighbor nodes are changed into the propagation state I with the probability of beta, the probability of epsilon is changed into an informed state K, and the probability of eta is changed into an insensitive state R; the probability that the nodes in the informed state K and the propagation state I have eta is changed into the non-inductive state R, and the nodes in the informed state K also have eta
The probability of (2) is changed into a propagation state I to continue to propagate information; the model assumes that the population migration rate of mu exists, and the migration rate is also set as mu in order to keep the total population of the model unchanged;
step 3, combining a classical propagation model and an average field theory, and establishing an SKIR information propagation model by using the information propagation probability determined in the step 2; the specific implementation method comprises the following steps: at time t, the densities 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 expressed by S (t), K (t), I (t) and R (t), and the densities meet the requirements
S(t)+K(t)+I(t)+R(t)＝1
And constructing a state transition formula shown as the formula according to the basic assumption and the state transition rule:
k is the average of the network;
step 4, analyzing the SKIR information propagation model obtained in the step 3, and deducing a system balance point; the specific implementation method comprises the following steps: to solve the model equilibrium point, let the value of the state transition formula be 0, obtain the state transition equation:
solving the equation to obtain the balance points of the system, namely two points are: one is the disease-free balance point E 0 (1,0, 0), and the other is the sick balance point E 0 * ＝(S * ,K * ,I * ,1-S * -K * -I * ) (ii) a Wherein the content of the first and second substances,
step 5, performing stability analysis on the balance point obtained in the step 4 to obtain a stability condition of the system balance point; the specific implementation method comprises the following steps: the Jacobian matrix in the state transition equation is:
will balance point E 0 Substituting (1,0,0,0) into the Jacobian matrix yields:
calculating the characteristic value to obtain:
λ 1,2 ＝-μ
λ 1 ＝λ 2 < 0 and λ 3 ＜λ 4 Therefore, only λ needs to be discussed 4 When a sign of (b) is 4 If < 0 is true, the Jacobian matrix is at equilibrium point E 0 The eigenvalues at (1,0,0,0) all have negative real parts, i.e. when
When true, the system is at equilibrium point E 0 The eigenvalues of the Jacobian matrix at (1,0,0,0) all have negative real parts, the equilibrium point E of the system 0 And the information cannot be spread in the network because of gradual stability.
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| CN114628038A (en) | 2022-06-14 |
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