Information reciprocating circulation propagation analysis method based on Markov chain

Abstract

The invention provides an information reciprocating circulation propagation analysis method based on a Markov chain. The method comprises the following steps: S1, constructing an SIRI information propagation model used for online social network propagation analysis; s2, constructing a node state transition probability matrix P based on the Markov chain theory, wherein a matrix element pij represents the probability of transition of a node from a state u to a state v; and S3, analyzing an information spreading process by adopting the node state transition probability model constructed in the step S2. According to the method, the SIRI model driven by the two parameters of the user activeness and the information popularity is remarkably superior to a reference model in the aspects of predicting the information spreading range and simulating the repeated behaviors of the user, and the reasonability and the effectiveness of the SIRI model are indicated.

Description

Technical Field

[0001] The present invention relates to the field of information dissemination, and in particular to a Markov chain-based information cyclic dissemination analysis method. Background Art

[0002] In an era of digitalization and globalization, information dissemination has evolved from a linear and slow process to a dynamic, multifaceted, and near-instantaneous phenomenon. The advent of the internet, social media platforms, and advanced communications technologies have revolutionized how we perceive, consume, and disseminate information. Generally speaking, information dissemination refers to the process by which a piece of data, news, opinion, or knowledge is transmitted from one entity to another, either through direct interaction or through mediated channels. This process plays a crucial role in shaping public opinion, promoting social change, fostering economic development, and maintaining national security within online social networks.

[0003] In recent years, the amount of information in online social networks has exploded exponentially. In the internet age, the spread of information is constrained by a variety of factors, including its speed and reach, as well as the diverse channels through which it is disseminated. Within online social networks, countless pieces of information are not completely independent; rather, they are interconnected and mutually influential. In social networks, as relevant information generated by a specific subject propagates through the network, interactions, exchanges, and sharing of this information between user nodes and their neighbors can positively promote the spread of this information. On the other hand, if the subject's information is not accepted by the audience during a specific period, or if the audience expresses negative sentiment towards the information, this can stagnate or even inhibit the spread of this information.

[0004] Most research on information diffusion in online social networks focuses on the irreversible linear process of information transmission, where a user's status changes from susceptible to infected and finally recovered, as a single or multiple pieces of information spread. Few studies consider the possibility of users transitioning between two or more states during the information diffusion process. Although existing information diffusion theory has matured, the process of information diffusion is fraught with complexity and uncertainty under varying environmental conditions. Traditional single-source diffusion theories often struggle to comprehensively and accurately describe and predict the dynamic evolution of information diffusion. In online social networks, in particular, the paths and patterns of information diffusion are influenced by numerous factors, including the heterogeneity of user behavior, the timeliness of information, and changes in network topology. Therefore, while traditional linear diffusion models can describe the one-way transmission of information from susceptible to infected and finally recovered, their limitations become increasingly apparent when faced with the cyclical spread of information in complex network environments. Summary of the Invention

[0005] The present invention aims to at least solve the technical problems existing in the prior art, and in particular innovatively proposes a Markov chain-based information reciprocating cycle propagation analysis method.

[0006] In order to achieve the above-mentioned object of the present invention, the present invention provides a Markov chain-based information reciprocating cycle propagation analysis method, comprising the following steps:

[0007] S1. Construct a SIRI information propagation model for online social network propagation analysis. The states of network nodes in the SIRI information propagation model include susceptible state (S state), infected state (I state) and recovered state (R state). The susceptible state indicates that the node has not received information, the infected state indicates that the node is propagating information, and the recovered state indicates that the node has stopped propagating information. The recovered state node can be transformed back to the infected state through reinfection conditions. Reinfection is introduced to allow the recovered node to be transformed back to the infected state under certain conditions, thereby simulating the cyclic propagation phenomenon of information in social networks.

[0008] Moreover, the probability of successful information transmission from a certain node j to another node i is θ, that is, the probability that node j changes from the susceptible state (S) to the infected state (I) is θ; when node i is not interested in this type of information, the probability of the node giving up the information is δ, that is, the probability that the infected state (I) changes to the recovered state (R) is δ; the probability of changing from the recovered state (R) to the infected state (I) is γ; the larger the value of θ, δ, that is, the greater the probability of user state transformation, also means that a certain type of information has a greater propagation rate in the entire propagation process and a wider range of diffusion.

[0009] S2, construct the node state transition probability matrix P based on Markov chain theory, where the matrix element p ij represents the probability of a node transitioning from state u to state v;

[0010] S3, use the node state transition probability model constructed in step S2 to analyze the information propagation process, and iteratively calculate the state transition probability matrix:

[0011] In the initial stage of information dissemination, all nodes in the network are in a susceptible state. As information spreads, some nodes transition to an infected state, further spreading the information. Over time, infected nodes gradually lose interest and transition to a recovered state based on a dropout condition. The dropout condition is that when the information popularity exceeds a set dropout threshold, the node transitions from infected to recovered. The lower the popularity of the information, the lower the interest of infected user nodes in the information, the higher the dropout rate, and the greater the probability of node state transition. Then, some recovered nodes reactivate and transition to an infected state based on a reinfection condition. The reinfection condition is that when the user activity exceeds a set activity threshold, the node transitions from recovered to infected. More active users have higher rates of information acceptance and forwarding, thus forming a circular information propagation cycle. Using the Markov chain's transition probability matrix, the dynamic changes in node states are simulated, revealing the laws of information dissemination in the network.

[0012] Preferably, the node state transition probability matrix P is expressed as:

[0013]

[0014] Among them, StateofX(t n ) represents the node time t n The state of the moment;

[0015] StateofX(t n-1 ) represents the node time t n-1 The state of the moment;

[0016] p 11 represents the probability that the node maintains its susceptible state unchanged;

[0017] p 12 represents the probability of a node transferring from the susceptible state to the infected state;

[0018] p 22 represents the probability that a node maintains its infection state unchanged;

[0019] p 23 represents the probability of a node transferring from the infected state to the recovered state;

[0020] p 32 represents the probability of a node transferring from the recovered state to the infected state;

[0021] p 33 It represents the probability that the node maintains its own recovery state unchanged.

[0022] Preferably, after combining the state transition probabilities θ, δ, and γ, the node state transition probability matrix P is expressed as:

[0023]

[0024] Where S(t) represents the number of nodes in state S at time t;

[0025] I(t) represents the number of nodes in state I at time t;

[0026] R(t) represents the number of nodes in state R at time t;

[0027] d ij represents the network matrix element value, d ij =1 means that node i is connected to node j, d ij =0 means no connection;

[0028] represents the probability that node i is infected to state I at time t;

[0029] N is the total number of nodes;

[0030] θ represents the probability that each I-state node j successfully propagates its information to S-node i;

[0031] 1-θ represents the probability that each I-state node j fails to successfully propagate its own information to the S-state node i.

[0032] Preferably, the probability of node i belonging to any state among susceptible state, infected state and recovered state at time t is expressed by the mathematical expectation of the state, thereby obtaining the SIRI probability model:

[0033]

[0034] in, They represent the probability that node i belongs to the susceptible state, infected state, and recovered state at time t, respectively, and

[0035] E(·) means finding the mathematical expectation;

[0036] N is the total number of nodes;

[0037] Indicates that node i is in the susceptible state at time t;

[0038] Indicates that node i is in the infected state at time t;

[0039] Indicates that node i is in the recovery state at time t.

[0040] Preferably, the SIRI probability model can be obtained by mean field theory, and the probability model is expressed as follows:

[0041]

[0042] in, They represent the probability that node i belongs to the susceptible state, infected state, and recovered state at time t+1, respectively, and d ij is the value of row i and column j in the network node adjacency matrix.

[0043] Preferably, at time t, the number of nodes in the network in the S, I, and R states are S(t), I(t), and R(t), respectively. For all network nodes:

[0044]

[0045] Where S(t) represents the number of nodes in state S at time t;

[0046] I(t) represents the number of nodes in state I at time t;

[0047] R(t) represents the number of nodes in state R at time t;

[0048] N is the total number of nodes;

[0049] Indicates that node i belongs to the susceptible state at time t;

[0050] Indicates that node i is in the infected state at time t;

[0051] Indicates that node i is in the recovery state at time t;

[0052] And S(t)+I(t)+R(t)=1.

[0053] Preferably, according to the mean field theory, the evolution process of the SIRI information propagation model can be expressed as a differential equation as follows:

[0054]

[0055] Where θ represents the probability of successful information dissemination;

[0056] δ represents the probability that a node forgets and abandons information;

[0057] γ represents the probability that a node in state R receives and transmits information again.

[0058] The SIRI propagation model analyzes the process of information dissemination from the perspective of probability and mathematical statistics, and reveals and explains its inherent propagation laws and evolution mechanisms in different ways.

[0059] In summary, by adopting the above technical solution, the present invention uses mathematical methods to study the problem of information diffusion modeling in online social networks, and obtains a new information diffusion method. The effectiveness of the proposed method and model is verified through prediction and evaluation of information diffusion, as well as simulation experiments using real data sets. The beneficial effects of the present invention include:

[0060] (1) The Markov chain and complex network communication dynamics theory are introduced into information dissemination modeling, the evolution of the state of user nodes during the dissemination process is simulated, and a probabilistic model of node state transition is constructed.

[0061] (2) A "re-infection" state is proposed, combining the dual key parameters of user attributes (activity) and information attributes (popularity) to couple user behavior heterogeneity and information timeliness, and constructing the online social network information reciprocating cycle propagation model SIRI.

[0062] (3) A comparative analysis experiment was conducted on three network topologies and four real-world Weibo topic datasets to observe the impact of different user activity and different information attribute strengths on the SIRI model. The experimental results show that the proposed SIRI method can better reveal the reciprocating cyclical propagation process of information, demonstrating the rationality and effectiveness of the SIRI method.

[0063] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments with reference to the following drawings, in which:

[0065] Figure 1 It is the framework diagram of the SIRI model of the present invention.

[0066] Figure 2 It is the SIRI flow chart of the present invention.

[0067] Figure 3 This is the node conversion process of the present invention.

[0068] Figure 4 This is the network node distribution diagram of the present invention.

[0069] Figure 5 The SIRI model of the present invention and the traditional model.

[0070] Figure 6 It is the information propagation curve under different network structures of the present invention.

[0071] Figure 7It is the node density change curve of different states under different network structures of the present invention.

[0072] Figure 8 This is a comparison between the simulation experiment of the present invention and the real data.

[0073] Figure 9 It is the information propagation curve under the influence of different user activity (γ) of the present invention.

[0074] Figure 10 It is the information propagation curve under the influence of different information popularity (δ) of the present invention. DETAILED DESCRIPTION

[0075] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0076] The Markov chain-based information reciprocal propagation analysis method proposed in this paper is a new SIRI model for the reciprocal propagation of information in online social networks. First, a "reinfection" state is proposed, which more accurately describes the phenomenon of cyclic propagation of information in social networks and improves the single limitation of the traditional SIR model caused by linear processes. Secondly, based on Markov chain theory, a probability model of node state transition is constructed from the perspective of probability theory, and a network information propagation model is constructed from the perspective of statistics. This reveals the state transitions that user nodes may experience during the propagation process. Combined with the Markov chain transition probability matrix, a probability distribution model of the "reinfection" state is constructed, providing a mathematical foundation for the dynamic process of information propagation. Finally, a large number of comparative experiments and results analysis are conducted using SIR, SEIR, and SIRI on three classic network topologies: NW small-world networks, BA scale-free networks, and HP online social supernetworks, as well as four real-world datasets of Weibo topics. The SIRI model, driven by the dual parameters of user activity and information popularity, significantly outperforms the baseline model in predicting the scope of information propagation and simulating user repetitive behavior, demonstrating the rationality and effectiveness of the SIRI model.

[0077] By integrating Markov chains into the SIRI information propagation model framework, we analyze the polymorphic evolutionary mechanisms of user nodes in information interaction within complex network environments. We construct a SIRI cyclic propagation model based on the state transition matrix. We derive the dynamic transition probability of user nodes from the recovered state to the reinfected state, construct an epidemic dynamics equation, and simulate the evolutionary process of user state cycles and information propagation.

[0078] 1 SIRI propagation model

[0079] The so-called propagation model is to use statistical methods to construct a SIRI information propagation model from a system level. In the initial stage of propagation, all nodes in the network are in a state of not propagating any information, that is, all nodes are in the S state. At a certain moment, a certain type of information triggered by an external event is injected into the network, received by a small number of network nodes and propagated outward. At this time, these nodes are in the I state. As time goes by, more and more S-state nodes are exposed to this type of information or are shared by messages in the I-state, and gradually transition to the I state. As the activity of user nodes decreases and the popularity of this type of message decreases, most nodes will gradually lose interest over time and transition to the R state. A small number of R-state nodes, because of their own high activity and interest in information, will once again switch states and enter the propagation process. After multiple rounds of information propagation, when most nodes maintain their R state and no longer change, the entire propagation process is over. The framework diagram of the SIRI model is as follows Figure 1 As shown, the model method is shown in Algorithm 1.

[0080]

[0081]

[0082] 2 Analysis of the propagation process

[0083] During the entire dissemination process, users have three states: susceptible state (S), infected state (I), and recovered state (R). Whether in a homogeneous network or a heterogeneous network, nodes will always interact with each other to form the initial dissemination of information. The attributes of the nodes themselves will change with the interaction, and the edges between nodes will also change accordingly. In certain cases, when a node changes to a recovered state, it will exit the information dissemination. When most of the nodes are converted to a recovered state, it represents the end of the entire information dissemination process. However, in the information dissemination process of a real social network, the differences between individuals mean that the emotional changes caused by different individuals receiving the same message are unknown, and the state changes of various nodes are also unknown. In the present invention, the recovery state is defined as a non-terminal state. When a certain type of user changes from a susceptible state to an infected state and then to a recovered state, this type of user node has a certain probability of changing to an infected state again and entering the information dissemination process again. The state transition process of various nodes is as follows: Figure 2 shown.

[0084] exist Figure 2In the equation ( θ ), θ represents the probability of transitioning from a susceptible state to an infected state, and δ represents the probability of transitioning from a susceptible state to a recovered state. Larger values ​​of θ and δ indicate a greater probability of a user's state transition, which in turn means that a particular type of information will spread more rapidly and more widely throughout its dissemination process. γ represents the probability of transitioning from a recovered state to an infected state. Larger values ​​of γ increase the probability of transition, creating a state transition cycle between recovered and infected users. This means that a particular type of information being disseminated can better attract the interest of various users, encouraging them to engage in further dissemination. This information then spreads more widely and lasts longer. Typically, the value of γ is not too large.

[0085] Combined with the above conversion rules, the node state in the network can be set to C = {S, I1, R1, R t ,I t}, where I1, R1 represents the first time a user becomes infected or recovered. t Indicates that the user is converted from the recovered state to the infected state again, R t It means that after the user enters the cycle transition, the infected state is transformed into the recovered state, and t represents the time when the user is in the state cycle transition. In the process of multiple node state transitions, the transition of each node is a relatively random process. The state at the next moment has nothing to do with the historical state of the node, but is only related to the current state. The entire propagation process can be regarded as a Markov random process. Therefore, the distribution function can be used to describe the Markov property of the node state transition. X represents the random variable of the node state transition. The state space of the random process {X(t), t∈T} is C, and T is a discrete time series. In X(t i )=x i , x i ∈C, X(t n ) is exactly equal to the conditional distribution function of X(t n-1 )=x n-1 Under the condition X(t n ), that is,

[0086]

[0087] Where P{} represents the probability formula;

[0088] X(t i ) indicates that at time t i The state of the node at that moment, i = 1, 2, 3...n;

[0089] x i is X(t i ) represents the specific value of the node at time t i The specific state at the moment, i = 1, 2, 3...n;

[0090] n represents the time series;

[0091] Therefore, the information propagation process is essentially a Markov process, in which each network node continuously performs state transitions in the state space C. The transition probability of a node migrating from state u to state v (SI, IR, RI) is recorded as p ij .p ij As shown in formula (2).

[0092] p ij =P{X(t n )=v|X(t n-1 )=u} (2)

[0093] Among them, P{X(t n )=v|X(t n-1 )=u} means that in X(t n-1 )=u has occurred, X(t n ) = probability of v occurring;

[0094] Therefore, the probability matrix P can be obtained.

[0095]

[0096] Among them, StateofX(t n ) represents the node time t n The state of the moment;

[0097] StateofX(t n-1 ) represents the node time t n-1 The state of the moment;

[0098] Combine Figure 3 , the node state rule of the information propagation model is substituted into Equation (3), and the transition probability matrix P can be further simplified. The simplified transition probability matrix P is shown in Equation (4).

[0099]

[0100] Among them, p 11 represents the probability that the node maintains its susceptible state unchanged;

[0101] p 12 represents the probability of a node transferring from the susceptible state to the infected state;

[0102] p 22 Represents the probability that a node maintains its infection state unchanged;

[0103] p 23 represents the probability of a node transferring from the infected state to the recovered state;

[0104] p 32 represents the probability of a node transferring from the recovered state to the infected state;

[0105] p 33 Represents the probability that the node maintains its own recovery state unchanged;

[0106] In the process of information propagation, there are two nodes A and B, both of which are in the S state, that is, X(T S )=S starts, at T I1 At this moment, node A is converted to I 1A State, that is, X(T I1 )=I 1A ; Node B is converted to I 1B State, that is, X(T I1 )=I 1B After a certain period of time, the two nodes are in T R1 Transform to R state at the moment, X(T R1 )=R 1A ,X(T R1 )=R 1B In the subsequent propagation process, when the node changes to the R state, most of the nodes will keep their own state unchanged until the end of the entire propagation process, such as node B. A small number of nodes, such as node A, have the probability of entering the propagation process again. It At this moment, node A is converted to I tA ,X(T It )=I tA . Then, in T Rt At this moment, it switches to R state again, X(T Rt )=R tA . In the subsequent propagation process, some nodes will maintain their own states and no longer change, while a small number of nodes will enter the propagation again. As time goes by, after multiple cycles of conversion, most of the nodes will become R state and no longer change, which means the end of the entire propagation process. In the entire random process, the transition probability matrix P is only related to the node state and time T. Therefore, the information propagation process is a homogeneous Markov chain. According to the CK (Chapman-Kolmogorov) equation, the n-step transition probability matrix of the node state P(n) = P n In summary, it can be seen that in the process of information propagation, the distribution of network node states is completely determined by the initial distribution and the one-step transition probability.

[0107] 3SIRI model parameter analysis

[0108] According to the analysis of the propagation process, the essence of the information propagation process is the process of continuous conversion of various states between nodes at different times. The following are the conversion probabilities considered based on different node states.

[0109] (1) SI, in a complex social network, node i is usually adjacent to multiple nodes, and the network node distribution diagram is as follows: Figure 4 In a real network, node i is in state S at time t. At time t+1, node i will have two situations:

[0110] (a) Node i successfully interacts with node j in state I and is infected, changing from state S to state I. Assume that the probability of each node j in state I successfully spreading its information to node i in state S is θ, and the probability of successful transmission to all adjacent nodes in state I is recorded as θ SSt , then θ SSt (t) can be expressed as the probability of successful propagation at time t, the probability of successful propagation θ SSt (t) is shown in formula (5).

[0111]

[0112] Among them, d ij represents the network matrix element value, d ij =1 means that node i is connected to node j, d ij =0 means no connection;

[0113] represents the probability that node i is infected to state I at time t;

[0114] N is the total number of nodes;

[0115] θ is the probability that each I-state node successfully propagates its information to the S-node.

[0116] (b) Node i does not receive any information during the entire information transmission process, nor does it interact with any other node. Therefore, it will always maintain its own S state without any change. Combined with formula (5), we can get the probability θ that node i does not receive any information at time t SS (t), θ SS The probability representation of (t) is shown in formula (6).

[0117]

[0118] Assume that at time t, the number of S-state nodes is S(t). Indicates the expected value of the probability that the S state node cannot receive any information, The expression of is shown in formula (7).

[0119]

[0120] In summary, It also represents the probability that the S-state node remains in the S-state at time t+1, so the transition probability p in the transition probability matrix P is 11 As shown in formula (8).

[0121]

[0122] During the propagation process, the transformation of the S-state node to the I-state node indicates that the information propagation is successful. Combined with formula (5), the transition probability p 12 As shown in formula (9).

[0123]

[0124] (2) IR, the node transitions from state I to state R. When a node is in state I, it will gradually lose interest in the information and slowly forget it over time. Let the probability of node i giving up the information be δ, so the p in the transition probability matrix P is 23 It can be expressed as shown in formula (10).

[0125] p 23 =δ (10)

[0126] When node i is performing information dissemination, it is possible that the message will be disseminated to multiple user nodes. During the entire dissemination process, it will always be in state I and will not change its own state for a period of time. Combining equations (9) and (10), we can obtain equation (11).

[0127]

[0128] (3) RI: As the information spreads, nodes in the I state gradually transform to the R state and keep their state unchanged. However, due to the high popularity of information, there are still a small number of nodes in the R state that will enter the spread again in the subsequent process and start a new round of information spread in the I state until all nodes keep the R state unchanged, and the spread ends. Therefore, assuming that node i is at t n The probability of transitioning from state R to state I at a certain moment is γ, so the transition probability p 33 As shown in formula (12).

[0129]

[0130] According to formula (11) and formula (12), the transition probability p can be obtained 22 .

[0131]

[0132] In summary, by substituting each transition probability into formula (4), we can obtain the transition probability matrix P, which is expressed as formula (14):

[0133]

[0134] The state of node i can be expressed as At a specific time t, each independent node has only one state, so the state values ​​of node states S, I, and R are (1, 0, 0) respectively. T , (0, 1, 0) T , (0, 0, 1) T The state variable of a node is a discrete random variable. Therefore, the probability that a node belongs to a certain state at time t can be expressed as the mathematical expectation of that state. The mathematical expectation is shown in Equation (15).

[0135]

[0136] in, represents the probability that node i belongs to state S, I, or R at time t. Node i must belong to one of the three states at a certain time. Therefore, the normalization and additivity of probability must be satisfied, that is,

[0137] According to the transition probability matrix, combined with formula (15), the proposed SIRI probability model can be obtained through mean field theory, and the probability model is shown in formula (16).

[0138]

[0139] in d ij is the value of row i and column j in the network node adjacency matrix.

[0140] According to the probability model, the state transition of network nodes during the information propagation process is not only related to the efficiency of information transmission θ, the failure rate of information δ, and the prevalence rate of information γ, but also to the structure of the network.

[0141] Assume that there is a closed online social network. Information is generated and disseminated only within the network. Over a certain period of time, the total number of nodes on the network remains stable. At each moment, the proportion of nodes in each state changes. (When validating the model through experiments, both simulations and real-data experiments employ quantitative analysis. The simulations maintain a fixed number of 5,000 user nodes and consider the changing proportions of nodes in different connection states. The real-data comparisons are conducted to determine whether the simulated data trends match the real-world trends.) At time t, the number of nodes in the network in states S, I, and R are S(t), I(t), and R(t), respectively. Indicates the state of a node at a certain time T. For the entire network:

[0142]

[0143] Among them, S(t)+I(t)+R(t)=1.

[0144] According to the mean field theory, the evolution process of the SIRI information propagation model in online social networks can be expressed as a differential equation as shown in Equation (19).

[0145]

[0146] Among them, θ represents the probability of successful information dissemination, γ represents the probability that the node in state R receives and disseminates the information again, and δ represents the probability that the node forgets and gives up on the information.

[0147] In summary, the SIRI propagation model analyzes the process of information dissemination from the perspective of probability and mathematical statistics, and reveals and explains its inherent propagation laws and evolution mechanisms in different ways.

[0148] 4 Key parameter analysis

[0149] like Figure 1 The model framework is shown in the diagram. First, through multi-dimensional user attribute feature extraction, the heterogeneity of node state attributes is modeled. Second, based on the dynamic feature analysis of user interaction behavior, the topological dependencies and propagation patterns of message transmission between nodes are extracted, and response rules and dynamic propagation mechanisms for information interaction are constructed to characterize the multi-path and multi-frequency characteristics of information flow in complex networks. Third, the enthusiasm of individual users and the popularity of related information within a time period are quantified, and user activity γ and information popularity δ are calculated to form a dual-parameter-driven propagation dynamics equation. Finally, combined with the constructed SIRI epidemic model, user enthusiasm and information popularity are used as key parameters for simulation experiments.

[0150] By incorporating key parameters into the model, we can predict the spread of topics, explore the dynamic reasons for information dissemination, and combine it with real data to observe the trends of information dissemination in the predictive model and real online social networks.

[0151] 1) User activity: In real social networks, some network nodes are always active, playing a connecting role in the entire information dissemination network system. When a blogger publishes a message on a certain topic, some of the blogger's highly active friends will choose whether to participate in the topic message transmission based on their own interests and preferences. γ represents the activity level of user i, with 1 indicating high activity and 0 indicating low activity. Generally, highly active network node users are more likely to participate in information dissemination. The definition of activity level is shown in Equation (19).

[0152]

[0153] Here, ω is an adjustable parameter, and in this paper, ω = 20. According to the 2 / 8 principle, when the proportion of active users is controlled at 1 / 5, the value of γ corresponds to the real network. Equation (20) defines ActiveUser(i).

[0154] ActiveUser(i)=Num[orig(i)]+σ×Num[retw(i)] (20)

[0155] Where Num[orig(i)] is the user's active participation in other topics during the period before the topic news broke, and Num[retw(i)] is the user's active participation in forwarding and spreading other topics during the period before the topic news broke. Generally, the activity of forwarding messages is much higher than the activity of participating in messages. Therefore, an activity factor σ is inserted before the activity of forwarding messages.

[0156] 2) Information popularity: In a social network, the popularity of information is δ. Assume that the information transmitted in the network has m attributes, ω m Representing the strength of the mth attribute of information, we have ω1+ω2+…+ω m = 1. Then the definition of information popularity δ is as shown in formula (21).

[0157] δ:(ω1,ω2,ω3,…,ω m )(twenty one)

[0158] In order to illustrate the technical effects of the present invention, relevant experiments were carried out.

[0159] (1) Simulation analysis

[0160] Previous research has shown that the attributes and key characteristics of existing online social networks highly overlap with those of small-world and scale-free networks. Compared to NW small-world and BA scale-free networks, hypergraph-based hyperedges in hypernetworks can contain any number of nodes, which aligns with the attributes and characteristics of online social networks in specific situations. Therefore, this study, based on the NW small-world network model, the BA scale-free network model, and the HP online social hypernetwork model, constructed a base network for information dissemination and verified the rationality and effectiveness of the SIRI model.

[0161] Since the network scale is large, the number of nodes is large, and the social group effect is obvious in online social networks, in this study, the NW small-world network is constructed, with the number of nodes N=5000 and the average node degree k= <40> In the BA scale-free network, the number of nodes N = 5000, the average node degree k = <78> During the experiment, there are many random processes. To eliminate the random influence, the simulation results of the present invention are all obtained by running 50 independent simulations under the same initial conditions, and then summing the experimental data and taking the average value.

[0162] (2) Comparative experimental analysis

[0163] In order to verify the effectiveness and rationality of the SIRI model, a comparative analysis of the SIR, SEIR, and SIRI models was conducted using the small-world network as the underlying transmission network. At the beginning of the experiment, a node was randomly selected as the initial propagation node, and the other nodes were in the S state. In the SIR model, the infection probability and the recovery probability are 0.7 and 0.3 respectively; in the SEIR model, the latent probability of transitioning from latent to exposed is 0.2, and the infection probability and the recovery probability are 0.8 and 0.2 respectively; in the SIRI model, the infection probability of transitioning from susceptible to infected is 0.7, the recovery probability is 0.3, and the second infection rate of transitioning from recovered to infected again is 0.2. Figure 5 As shown, in Figure 5 The user density curves of different states in the SIR, SEIR, and SIRI models are given in Figure 2. In the SIR and SEIR models, information will spread very quickly in the initial stage, showing explosive growth. In the SIR model, the peak of information propagation comes earlier. Although the SEIR model adds the exposed node, its impact on the entire propagation process is negligible. In the SEIR model, there is an information delay, and the entire cycle of information propagation will be longer than the traditional SIR model, which corresponds to the incubation period in the information cycle theory. The SIRI model adds a cyclic propagation mechanism to the SIR model, taking into account the possibility of a few nodes re-entering the propagation system, such as Figure 5As shown in (c), in the early stages of information dissemination, information quickly explodes across the network. Experimental data demonstrate that while the SIRI model exhibits a relatively low peak in node density in state I, it significantly prolongs the information diffusion cycle in the middle and late stages of dissemination through the sustained interaction of highly active user nodes, more closely resonating with the real dynamics of social networks, where topic popularity decays and rekindles. In real online social networks, although a small number of users experience the "silent effect," where they merely receive information but do not participate in its dissemination, the vast majority of users, upon receiving it, choose whether to disseminate it based on their individual preferences and social influence. Furthermore, with the exponential growth of network information, the probability of user nodes being exposed to the same information through multiple paths and frequencies increases significantly, leading to the complex characteristics of information dissemination characterized by multi-channel cross-diffusion and heterogeneous user behavior. This is highly consistent with the multi-source nature and dynamic evolution of information dissemination in real social networks.

[0164] Table 2 Topic experiment data

[0165]

[0166] (3) Impact analysis of different network structures

[0167] In order to study the impact of different network structures on the dynamic process and laws of information dissemination, a simulation environment was established with NW small-world network, BA scale-free network and HP online social super network as the underlying propagation network. The total number of nodes in each network is N = 5000, and the node with the largest degree value in the network is selected as the initial propagation node (if the node degrees are the same, it is randomly selected). In the propagation process, the probability of S changing to I is set to θ = 0.7, the probability of I changing to R is set to δ = 0.3, and the probability of R changing to I again is set to γ ​​= 0.2. Figure 6 Shown are the curves of susceptible S, infected I, and recovered R changing over time in the NW small-world network, BA scale-free network, and HP online social supernetwork. Figure 6 It shows that the node density in different states under the three different network structures shows roughly the same trend over time. Figure 7The graph shows the evolution of different node states under different network structures. The curve for S nodes shows a rapid downward trend in the initial stage, reaching or approaching zero. In the initial stages of information dissemination, the vast majority of user nodes receive information through various channels. Some user nodes may not choose to disseminate the information immediately. Over time, as most users participate in the dissemination process, a small number of nodes will eventually disseminate the information. At the outset of dissemination, a node is selected as the initial I-state node. As the node with the highest degree in the network, it can effectively disseminate information. In online social networks, information changes rapidly and is time-sensitive. After the I-state node curve reaches its peak, most users gradually abandon dissemination, resulting in a gradual decrease in the I-state density curve and an increase in the R-state node density curve. In the middle and late stages of the dissemination process, most users become immune to this type of information and withdraw from dissemination. A small number of active user nodes with relatively average degrees transition between I and R states throughout the dissemination process (typically, the number of transitions is relatively small), thus extending the overall dissemination process.

[0168] (4) Empirical comparative analysis

[0169] Weibo is one of China's largest social networking platforms. As of September 2024, Weibo had 578 million registered users and 257 million daily active users. Therefore, Weibo's data is highly practical and effective for research topics. To further verify the authenticity and effectiveness of the SIRI model, the author selected four topics on Weibo: Topic 1: "COVID-19"; Topic 2: "JD Mobile Phones"; Topic 3: "Scenic Spot Reviews"; and Topic 4: "Xiaomi Cars."

[0170] In the experiment, any user who comments on a topic is considered to be in state I at that moment. When the same user comments on the same topic two or more times at different moments, it indicates that the user has undergone multiple state transitions from I to R and back to I. Table 2 lists the experimental data for specific topics. Based on the real data from the four topics described above, the information dissemination trends were compared with the model's predicted trends. This study used a time slicing method, using users who participated in the topic for 15 days as the time slice. Each user who posted a comment on the topic was considered to have participated in the dissemination of information. If a user did not participate in the topic again within 24 hours after participating in the dissemination, they were considered to have lost interest in the topic and become a recovered person. If a user commented on the topic again 24 hours after becoming a recovered person (i.e., posting a comment), it was assumed that the recovered person had once again become infected and entered the dissemination process.

[0171] exist Figure 8 In this paper, the trend of I-state nodes predicted by the SIRI model is compared with the trend of users participating in information dissemination in real topics. The number of users in topics 1 and 4 is huge. At the beginning of the information dissemination, a large number of users participated in it. As time goes by, the explosive growth in the number of people leads to a positive correlation between the popularity and timeliness of the topic. Some users will withdraw from the dissemination after participating in the topic and recover in the network; some users will maintain their own status after participating in the topic and spread to other network neighbor nodes associated with them in the network; some users in the recovered state will participate in the network again within the validity period of the message. Finally, as Figure 8 As shown in Topic 1 and Topic 4, the user's dissemination trend will not change significantly within a certain period of time, but will always maintain a fairly high dissemination rate.

[0172] As shown in the data in Table 2, although the number of users in Topics 2 and 3 is far less than that in Topics 1 and 4, information dissemination occurs within a limited network. Initially, with relatively few participants, the number of users in the I state rises slowly. As topic information spreads, once the reach reaches the threshold, the final trend of users in the infected state roughly matches the predicted model. As the topic's popularity increases, some user nodes in the recovered state within the network re-enter the dissemination process, leading to a peak in dissemination.

[0173] Combined with the data given in Table 2 and Figure 8 The changing trend of real data in the topic 1 and topic 4, whether it is the information dissemination or circular dissemination with the participation of a large number of users, or the small-area information diffusion with the participation of a small number of users in topic 2 and topic 3, the final dissemination trend formed within the time-sensitive interval of the topic is basically consistent with the result predicted by the SIRI model, verifying the correctness of the model proposed in this invention.

[0174] (5) Influence of user activity and information attributes

[0175] In online social networks, information can spread on a large scale, and user and information attributes play a crucial role. User activity reflects the different roles they play within the network, affecting the rate and scope of information diffusion. Different users have different dissemination behaviors for the same type of information. Information popularity reflects the rate at which information decays during dissemination, as well as its timeliness. Excessively high information popularity can spread rapidly across different network layers, acting as a catalyst. However, while information with low popularity may create an effective dissemination trend within a small network, it will struggle to achieve scalable dissemination across a large social network.

[0176] In real social networks, such as Weibo, there are numerous users, but only a few possess significant followers and attention, such as well-known bloggers, celebrities, and opinion leaders. These users can be considered hubs within the Weibo network, and their connections exhibit significant heterogeneity. Most users are connected to only a few, while a few are connected to a large number of users. In simulation experiments, NW and BA scale-free networks were selected as the underlying propagation networks, and the network node with the highest degree was chosen as the initial infection node. By adjusting the user activity γ and information popularity δ, the effects of different network environments on the information propagation process and patterns were compared.

[0177] (5.1) User activity

[0178] In this study, user activity γ is analogous to communication efficiency. Highly active users, due to their frequent information exchange behavior, are equivalent to having higher communication capabilities and can transmit information to their neighboring nodes more quickly. In the process of model establishment, the user activity parameter is introduced to quantify the user's information dissemination ability and the possibility of user status transition. Figure 9 In

[15] , by changing different activity levels γ, i.e., γ = 0.2, γ = 0.5, and γ = 0.8, we observe the influence of different parameters on information dissemination. The higher the γ value, the easier it is for users to re-enter the dissemination and the easier it is for them to switch from the R state to the I state. Other simulation parameter settings are shown in Equation (22).

[0179] N=5000, k NW =40,k BA =78, θ=0.7, δ=0.3 (22)

[0180] like Figure 9 As shown, Figure 9 (a)~ Figure 9 (c) shows the change curves of various user nodes under the influence of different user activities in the NW small-world network. The results show that the degrees of users in the small-world network are mostly similar, and it is difficult to cause huge differences in the actions of acquiring or spreading information. Figure 9 (a) Figure 9 As shown in (b), when user activity levels haven't reached the threshold, one or more users won't switch back and forth between infected and recovered states. When one or more pieces of information propagate in a small-world network, the impact of user activity levels won't cause a magnitude change. Figure 9 (c) It proves that when the user's activity is high enough, the user can easily

[0181] When changing between the two states, the peak number of infected people has been slightly increased, and the changes in the number of infected and recovered people do not reach the normal numerical range. As time goes by, after most user nodes are converted to the recovered state, the process of information dissemination is declared over. Excessive user activity has indirectly extended the time period of information dissemination. Limited to the characteristics of the small-world network, if the dissemination time is long enough, this type of information will eventually be propagated to all user nodes in the entire network.

[0182] exist Figure 9 (d)~ Figure 9 (f) shows the user node change curve in the BA scale-free network. Due to the distribution of degree values ​​in the scale-free network, if a node with a very large degree value also has a high activity, then this type of node will play a vital role in the entire network. The high or low activity of a key node will affect the trend of the entire information dissemination process. When γ = 0.2, as Figure 9 As shown in (d), all nodes have the same activity, the number of infected nodes I rises and falls rapidly until it approaches 0, and the time it takes to complete the entire propagation process is significantly different from other cases, which is consistent with the law of information propagation in real networks. Figure 9 (e) and Figure 9 In (f), when γ = 0.5 or γ = 0.8, to avoid the aforementioned critical node problem, in this experiment, when user activity γ changes dramatically, a subset of nodes with maximum degrees, a subset of nodes with degrees within the average range, and a subset of nodes with slightly smaller degrees are selected for parameter changes. The total number of nodes with changed degrees is n = 4000, with n / N = 0.8. The remaining nodes remain unchanged with a uniform activity of γ = 0.2. With the above settings, the figure shows that when γ is sufficiently large, the curves of nodes in each category of the network change significantly, with the peak value of infected nodes increasing significantly. After the infected and recovered nodes reach their peak values, the two categories of nodes fluctuate back and forth for a period of time, and the curves of infected and recovered nodes exhibit significant oscillation. The amplitude change is more pronounced for γ = 0.8 than for γ = 0.5. This also indicates that, for a considerable period of time, information propagation will be difficult to calm down. The entire information propagation process will be significantly longer than in a small-world network, and the diffusion range will also be wider. Experiments in BA scale-free networks have confirmed that user activity plays a decisive role in information diffusion in complex networks. In real online social networks, such as Weibo, when user activity is high and sufficient, the speed and reach of various types of information dissemination are positively correlated with time.

[0183] (5.2) Information popularity

[0184] In online social networks, information popularity is an important indicator to measure the effect of information dissemination in the network. In this study, information popularity δ plays a catalytic role. Information with high popularity is more likely to be received by users and spread easily. The HP online social super network is selected as the underlying network to study the impact of information popularity on the law of information dissemination. Figure 10 The influence mechanism of different information popularity δ on the infected node I is described. Assume that in the entire underlying network, the total number of network nodes is constant N = 5000, and the probability of S changing to I θ = 0.7, and the user activity γ = 0.2 from R to I. When the information popularity δ is 0.3, 0.5, and 0.7 respectively, Figure 10 The I-state curve reaches different peaks at different times: 0.24 at δ = 0.3 and t = 4; 0.46 at δ = 0.5 and t = 3; and 0.66 at t = 0.7. This means that as information popularity increases, the time it takes for the I-state curve to reach its peak shortens and the peak value reaches a higher level. Over time, despite changes in δ, the I-state curve maintains a roughly similar trend, eventually slowly declining until it approaches zero, marking the end of the information diffusion process.

[0185] In summary, the present invention first analyzes the state change process of different types of nodes in online social networks, introduces the "re-infection" state, breaks through the assumption of a single propagation path, and more realistically reflects the cyclic propagation characteristics of information in social networks. Secondly, based on the Markov chain theory, it proves that the state of its network nodes has Markov properties, and derives the node state transition probability matrix and its calculation formula. Then, according to the law of information interaction between nodes, the SIRI probability model of node state transformation is proposed using the probabilistic method, and the SIRI propagation model is proposed using the mathematical statistics method. Finally, by comparing with the traditional information propagation model, simulation experiments are conducted under different network structures to prove the effectiveness of the model. By comparing the simulation experiments with real data, the development trend of real events is analyzed. The experimental results show that the proposed SIRI information reciprocating cyclic propagation model is reasonable and effective, and provides new research ideas and methods for the transformation of different node state types and network evolution in online social networks. This study not only provides new tools for information propagation prediction and public opinion control on social platforms, but its modeling framework can also be extended to complex scenarios such as multi-stage virus propagation and cross-platform information diffusion.

[0186] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to the embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the claims and their equivalents.

Claims

1. A Markov chain-based information cyclic propagation analysis method, characterized in that: The following steps are involved: S1, constructing a SIRI information propagation model for online social network propagation analysis. The states of network nodes in the SIRI information propagation model include susceptible state, infected state, and recovered state. The susceptible state indicates that the node has not received any information, the infected state indicates that the node is propagating information, and the recovered state indicates that the node has stopped propagating information. Among them, the recovered state node can be transformed into the infected state again through the reinfection condition; Moreover, the probability of successful information transmission from a node j to another node i is θ, that is, the probability that node j changes from a susceptible state to an infected state is θ; when node i is not interested in this type of information, the probability of the node giving up the information is δ, that is, the probability that the infected state changes to a recovered state is δ; the probability of changing from a recovered state to an infected state is γ; S2, construct the node state transition probability matrix P based on Markov chain theory, where the matrix element p ij represents the probability of a node transitioning from state u to state v; S3, using the node state transition probability model constructed in step S2 to analyze the information propagation process: In the initial stage of information dissemination, all nodes in the network are in a susceptible state; as information spreads, some nodes transform into an infected state and further spread the information; over time, infected nodes gradually lose interest and transform into a recovered state based on the abandonment condition. The abandonment condition for the node is that when the popularity of the information is higher than the set abandonment threshold, the node state will transform from the infected state to the recovered state; then, some recovered nodes are reactivated and transformed into the infected state based on the reinfection condition. The reinfection condition is that when the user's activity is higher than the set activity threshold, the node state will transform from the recovered state to the infected state.

2. The Markov chain-based information cyclic propagation analysis method according to claim 1, characterized in that: The node state transition probability matrix P is expressed as: Among them, StateofX(t n ) represents the node time t n The state of the moment; StateofX(t n-1 ) represents the node time t n-1 The state of the moment; p 11 represents the probability that the node maintains its susceptible state unchanged; p 12 represents the probability of a node transferring from the susceptible state to the infected state; p 22 Represents the probability that a node maintains its infection state unchanged; p 23 represents the probability of a node transferring from the infected state to the recovered state; p 32 represents the probability of a node transferring from the recovered state to the infected state; p 33 It represents the probability that the node maintains its own recovery state unchanged.

3. The Markov chain-based information cyclic propagation analysis method according to claim 1, characterized in that: After combining the state transition probabilities θ, δ, and γ, the node state transition probability matrix P is expressed as: Where S(t) represents the number of nodes in state S at time t; I(t) represents the number of nodes in state I at time t; R(t) represents the number of nodes in state R at time t; d ij represents the network matrix element value, d ij =1 means that node i is connected to node j, d ij =0 means no connection; represents the probability that node i is infected to state I at time t; N is the total number of nodes; θ represents the probability that each I-state node j successfully propagates its information to S-node i; 1-θ represents the probability that each I-state node j fails to successfully propagate its own information to the S-state node i.

4. The Markov chain-based information cyclic propagation analysis method according to claim 1, characterized in that: The probability of node i being in any of the susceptible, infected, and recovered states at time t is expressed by the mathematical expectation of the state, thus obtaining the SIRI probability model: in, They represent the probability that node i belongs to the susceptible state, infected state, and recovered state at time t, respectively, and E(·) means finding the mathematical expectation; N is the total number of nodes; Indicates that node i is in the susceptible state at time t; Indicates that node i is in the infected state at time t; Indicates that node i is in the recovery state at time t.

5. The Markov chain-based information cyclic propagation analysis method according to claim 4, characterized in that: The SIRI probability model can be obtained through mean field theory, and the probability model is expressed as follows: in, They represent the probability that node i belongs to the susceptible state, infected state, and recovered state at time t+1, respectively, and d ij is the value of row i and column j in the network node adjacency matrix.

6. The Markov chain-based information cyclic propagation analysis method according to claim 1, characterized in that: At time t, the number of nodes in the network in state S, I, and R are S(t), I(t), and R(t), respectively. For all network nodes: Where S(t) represents the number of nodes in state S at time t; I(t) represents the number of nodes in state I at time t; R(t) represents the number of nodes in state R at time t, and S(t)+I(t)+R(t)=1; N is the total number of nodes; Indicates that node i belongs to the susceptible state at time t; Indicates that node i is in the infected state at time t; Indicates that at time t, node i is in the recovery state.

7. The Markov chain-based information cyclic propagation analysis method according to claim 6, characterized in that: According to the mean field theory, the evolution process of the SIRI information propagation model can be expressed as a differential equation as follows: Where θ represents the probability of successful information dissemination; δ represents the probability that a node forgets and abandons information; γ represents the probability that a node in state R receives and transmits information again.

Images