Information Diffusion and Opinion Leader Mathematical Modeling Based on Microblog

Public emergency occurs every day, and the information diffusion of an online social network (OSN) shows the characteristics of large capacity, a wide range of far-reaching effects. In order to analyze the role of opinion leader in OSN and the life cycle of Sina Microblog information diffusion, the public emergency information diffusion model and a new method grading opinion leader model are proposed. Firstly, the people of OSN are divided into three kinds: supporter, neutral, and objector. Information interaction formula of opinion leader is built up according to the properties of all kinds of subjects (public people, rumor maker, and opinion leader), and the statistical analysis of the microblog information data is obtained by the computer technology. Second, the communication power is constructed as a function related to the three factors (the number of forwarding, the degree of activity, and the number of fans), and then a weight calculation method based on the analytic hierarchy process is established. Communication power is combined with the new proposed model, and the information diffusion of opinion leader and microblog life cycle is researched. The simulation results show that the established public emergency information diffusion model can truly reflect the actual situation. Opinion leaders have a strong communication in microblog information diffusion. Opinion leaders can influence those who are unsteady about certain public emergency. The value of error is 13.7% and 5.1% by comparing the true data. It is proved that the new proposed models are reasonable and effective for the communication life of the analysis opinion leader in microblog information diffusion.

SECTION I. Introduction

A. Background and Research Status

Microblog can be treated as an online social platform; each user can be regarded as a node. A number of nodes are interconnected to form the entire microblog network. In order to be more scientific and reasonably to analyze the microblog network structure and study the node properties, the researchers generally put the complex network theory, multi-network theory and social network analysis method as the basic support theory. Complex network is a branch of complexity theory, with complex structure, diverse nodes, varied network structure and other forms of expression, is a framework for the representation of complex systems. Multi-network theory refers to a network structure with multi-layer network, each node in the same network nodes, however there are some differences in the link attributes between different nodes. Social network analysis method regards the entire network as a number of nodes, each node has a certain linkage, the link within the network structure determines the information transmission path and its characteristics [1]–​[3].

The scale of the network has been gradually expanded in current actual social network. As can be seen from Table 1, the number of users in several typical social networks both at home and abroad has exceeded one billion and continues to grow at a faster speed. As a result, researchers are only getting more accurate research on OSN (Online Social Network) information simulations in near real world environments. It has become one of the hot and difficult problems at home and abroad on how to build the large-scale network information diffusion simulation system [4]–​[6].

TABLE 1 Number of Online Social Network Sites Users

The term of opinion leader was first proposed by the spread scholar Lazarsfield in the 1940s.Opinion leaders are “activists” who influence others. Which plays a medium role in the mass communication process. They will spread the information to the public when they access to information, so that the formation of two-level diffusion of information diffusion. In recent years, the emergence of microblog has changed the think-way of people, while microblog developed at a very rapid pace that people cannot imagine [7]–​[9]. The information diffusion in the social network presents many new features compared with the traditional media information diffusion, such as the user has created content, “points to points” mode of transmission, real-time transmission and fastness. In the microblog, the analysis of opinion leaders has a lot of factors, such as the number of forwarded, the number of comments, the number of active days, the number of fans and so on. Using these factors, we can study the communication power of opinion leaders and propose diffusion mathematics models.

The subject of microblog information dissemination is mainly formed by the disseminators, information, and recipients. In the course of the research, communicators and receivers (i.e., users) are usually regarded as nodes, and their mutual concerns are regarded as side. It is the side which formed by the association of nodes. The whole microblog network can be abstracted into a kind of directed network diagram. On the basis of the Leaderrank algorithm, Moldovan et al. [1] put forward the improved Leader Rank algorithm based on the emotional tendency and user activity between users. The method of opinion leaders based on topic evolution is proposed [10], [11]. Nagy et al. [12] and Aghdam and Navimipour [13] presented the research method based on the user attributes and coverage. Khan et al. [14] and Karlsen [15] proposed the opinion leader recognition algorithm MFP(multi-feature PageRank). Qu et al. [16] and Liu et al. [17] explored an opinion leader ITP algorithm based on improved topological potential. Chen and Liu [18] and Varshney et al. [19] proposed a method of opinion leader detection for a specific topic. Arnaboldi et al. [20] and Kermani et al. [21] mainly use various algorithms to identify the opinion leaders. At the beginning of the study, it is very important for the opinion leaders to be recognized. After the end of the recognition, the communication needs of the opinion leaders need to be analyzed. Stai et al. [22] and Mbaru and Barnes [23] proposed the microblog opinion leader influence modeling and measurement analysis method based on message diffusion. Gentina et al. [10] set up the opinion leader identification mode by using rough set theory. Monajemi et al. [24] measured, counted and analyzed the microblogs data, and proposed a new triangle algorithm to detect the threshold number of fan users.

Park and Kaye [25] analysis of opinion leader behavior, gathering information, according to the structural equation model (SEM), it is concluded that online seeking behavior on customer satisfaction level and the opinion and advice for transfer has an important positive influence. In the real life, the opinion leaders should also be analyzed and studied.

Martin et al. [26] proposed a new framework to select the opinion leaders of online communities. Use the trust relationship between users to evaluate the total trust value (TTV) of the main opinion leaders among other users; Dabarera et al. [27] proposed a novel weighted method for the search of opinion leaders based on the centrality measures. Mirkovski et al. [28] investigated the data on Facebook, increased the significance of social networking sites, and increased the role of opinion leaders in social and political communication. Junming et al. [29], the concept of “potential opinion leaders” is proposed, and design analysis algorithms are used to identify “potential opinion leaders”. The results show that the use of “potential opinion leaders” method of identification is rather more simple; Xie et al. [30] introduced the opinion leaders on the traditional SIR model elements, to study the views of leaders how to affect microblog information diffusion; they considered the social networks structure hole position, center position and edge position to identify the role of opinion leader. These papers mainly studied the application of opinion leaders in daily life and related extension contents.

The research on the role of opinion leaders in the field of public opinion in recent years shows that the opinion leaders in the online network are of great significance and role. In recent years, microblog and various types of social network software information diffusion is large, widely disseminated. In this kind of social software, opinion leaders play a great role in promoting communication. It can be found that the process of dissemination of information in the real network is subject to the network status of the information publisher and its own behavior, whether information can propagate from one node to another node and make the latter become a communicator, it has relationship not only the influence of the dissemination of the user, but also the latter’s ability to accept the user, otherwise the current research seldom considers the above factors.

B. Motivations

The above discussion implies that novel inequality methods allow us to obtain more public emergency information diffusion model and algorithm. Most references do not consider the different user behaviors of public emergency information diffusion by using computer virus propagation theory under online social network. Social network information modeling methods and algorithms are inequality presented in some references. Under the method efficiency, a novel public emergency information diffusion algorithm and mathematics model could be proposed.

C. Our Work and Contributiuons

In this paper, the public emergency information diffusion modeling problem based on microblog of online social network by mathematics method is investigated. By giving more precise estimation for public emergency event information diffusion, a new public emergency event information diffusion method is obtained. Under this method, some novel results are presented. Based on microblog information propagation theory, the nonlinear mathematics model of public emergency event information diffusion is derived. Simulation is employed to indicate the effectiveness of the proposed method and model. The main contributions of this paper are listed as follows. (1) The information diffusion process of public emergency event is considered as a process of computer agent transmission. Information diffusion theory is introduced to the public emergency. (2) A emergency public event information diffusion method and a new method grading opinion leader model are proposed. (3) A new information diffusion structure in online social network is built up. (4) The better performance is obtained by the theoretical simulation results. These results are practical and objective.

SECTION II. Data Collection

With the rapid development of Web2.0, the major social software has a very large flow of information. The largest microblog site of China is Sina microblog. People use Sina Microblog website to communicate with friends’ every time and everywhere.

Sina microblog is the world’s most microblog provider. Microblog is as the fastest way of information transmission method today, the amount of each day’s data is also difficult to imagine and calculate. The spread of microblog information is mainly through the views of leaders and the general public to carry out the diffusion of information. Microblog forwarding is a typical information diffusion behavior, hot search microblog of Sina is the fastest daily information diffusion, is the most widely disseminated a way, so this article will be concerned on hot search microblog of Sina microblog, which will mainly study the influence of opinion leaders and their information after the transmission of information characteristics and microblog life cycle.

Microblog is as a social software, has its privacy, so the use of web crawler method of microblog hot search for crawlers, crawling time from June 13 2018 to June 19, 2018 every day optional two times point. Each time point only takes 8 hot topics, two months to remove the duplication of topics received a total of 408 hot topics. Which each topic involves the uneven number of microblog, which also have the general public in order to rub the heat and the topic has nothing to do with the microblog, so each topic only take a higher 1~3review. Finally, a total of 850 microblog, which involved a total of 1230 opinion leaders. The collected data will be modeled and analyzed in the following.

SECTION III. Information Diffusion and Model

Unlike the computer virus propagation model (such as SIR model) and some other information dissemination mode in a multi-relationship online social network, network users usually adopt a proactive approach to the information diffusion and choose the appropriate type of friend relationship according to the preference of the information. According to the function of user nodes in the social network information diffusion model (as can be seen from Fig. 1), the network user nodes can be divided into three types: diffusion node, interest node and no-interest node.

FIGURE 1.

Public emergency information diffusion model.

For a new information message, a diffusion node indicates that the node has received information from its neighbor node, and has the interest of spreading the information which received from the neighbor node. The interest node denotes that the node has not received the information from its neighbor node but it is interested in the information, and the interest node may become the diffusion node when received the information. If interest node is not interested in the information, the interest node will become the no-interest node after received the information. No-interest nodes express that it does not propagate information. Since public emergency information cannot be tested in real life. Therefore, the computer modeling and software simulation is the most effective way.

People of OSN in society can be treated as agents in computers. The interaction between people’s opinions is modeled as agent’s attributes and behaviors. Interactive rules are introduced in interaction process. It can determine whether the individual opinions can be changed and the extent of change by the rumor or opinion leader. Macro-public opinion phenomenon can often be observed from the group after repeated interaction of opinions. For a particular incident, the attitude of people is ambiguous at the beginning, it may be affected by the views of surrounding people, such as being influenced by rumors and being affected by opinion leaders, thus changing the original view. As shown in Fig. 2, this method can effectively answer micro-individual opinions how to emerge macro public opinion.

FIGURE 2.

Information interaction model based on computer agent.

In the dissemination of media, most people will form what kind of attitude, which is subject to the influence by others attitude. There are four features (such as attitude, conformity, credibility, authority) are related to information diffusion.

People often hold three kinds of attitudes toward public emergency information: support, neutrality and opposition. In the real society, people’s attitude is not clear at the beginning. Many people’s attitudes have gradually shifted from ambiguity and swinging to clear and firm opinions because of media or interpersonal influence. In this paper, we take the real numbers in the interval (0,1) as the individual opinions, (0,0.33) denotes the objections, (0.33,0.67) means neutral, (0.67,1) indicates support.

During the period of the spreading and the outbreak of public emergency, there are mainly three types of subjects: people, rumor makers and opinion leaders.

The properties of all kinds of subjects are shown in Table 2.

TABLE 2 Number of Online Social Network Sites Users

The interaction rules between agents can reflect the various factors that influence the change of agent’s opinion. $P_{i} (t)$ denotes the subject. $C_{i} (t)$ is the credibility of subject$i$ . $\tau$ is interaction threshold ($\tau =0.34$ ). At the time $t$ , if we have $\left |{ {P_{i} (t)-P_{j} (t)} }\right |<\tau$ ,it can be indicated that there are less difference between the subject $i$ and subject $j$ .

When $C_{j} (t)>C_{i} (t)$ , it can be denoted that subject $j$ can affect subject $i$ .The state transfer equation of subject $i$ at time $t+1$ can be expressed as follows

$$\begin{align} P_{i} (t+1)=&P_{i} (t){+\{}P_{j} (t)-P_{i} (t)\}\cdot a_{i} (t) \\ C_{i} (t+1)=&C_{i} (t){+\{}C_{j} (t)-C_{i} (t)\}\cdot a_{i} (t) \end{align}$$ Where, $a_{i} (t)$ represents the probability that the subject $i$ can be affected by subject $j$ . Such as the probability of rumor impact on the attitude of the public, and the public is proportional to conformity, and is inversely proportion to the credibility of popular information. It is directly proportional to rumors provocative. The impact probability of opinion leaders on followers is proportional to their conformity, and it is inversely proportion to the credibility of the public and directly proportional to the credibility of opinion leaders and it is proportional to the authority of opinion leaders.

If $\left |{ {P_{i} (t)-P_{j} (t)} }\right |>\tau$ . It can be indicated that there is much difference of opinion on the subject. Subject $i$ will not change his attitude. The state transfer equation can be described as

$$\begin{align} P_{i} (t+1)=&P_{i} (t) \\ C_{i} (t+1)=&C_{i} (t) \end{align}$$

SECTION IV. Influence Factors of Opinion Leaders

Opinion leaders are in the daily transmission of the network which provides information for others, is the diffusion of the media, the equivalent of oral celebrities. Most people access to news channels have been gradually transformed into microblog, through microblog people can get the news the first time, and the way people are mostly through microblog to the public to publish relevant information, microblog has become the most important social media way for spreading.

And through the study of microblog can conduct public opinion analysis, further study of opinion leaders to effectively analyze useful information, can control the diffusion of information. As the rapid development of microblog, opinion leaders in this group of many people, and each opinion leader of the microblog interpretation has its own views, and in the microblog after the spread of the intensity is not the same, sometimes extreme. So first of all to the opinion leaders to grading, the opinion leaders will be based on hierarchical analysis of the weight of the method of calculation.

A. Data Analysis of Opinion Leader

Sina microblog which has more than 3 million fans of the users is defined as the opinion leader, ignoring the transmission of certain specific conditions, temporarily the number of fans less than 300 million users do not act as the leader of the diffusion of its efforts to ignore. First of all, take from the microblog list of fans to obtain the number of fans more than 3 million of 1870 users are analyzed. The number of fans of these opinion leaders is sorted and sorted by quantity, and how many people can see how many of these opinion leaders have released microloggings. Second, the list of opinion leaders will be concerned about the list of attention in the list of attention is extracted from the number of opinion leaders, the results can be analyzed in the opinion leader after the release of information, how many opinion leaders can see, see more people, the greater the probability of forming multi-level propagation. Two factors have important implications for the multi-level communication of opinion leaders.

As can be seen from the Fig. 3. The majority fans of the opinion leaders are between 3 million and 33 million, there are less opinion leaders which more than 33 million fans. The next step is to analyze the number of opinion leaders (10% of the total number of people is less than 1 which is set with 1) by 10% of opinion leaders from the ten classified opinion leaders according to the number of fans.

FIGURE 3.

Sina Microblog celebrity fans distribution map.

Fig. 4 shows that the number of opinion leaders concerned by these opinion leaders ranged from 45 to 1572, with the maximum and the minimum being the two extremes. The average number of opinion leaders of the 190 opinion leaders was 277. After the information is released, it is possible to be forwarded by the opinion leaders or forwarded by opinion leaders, which can then be forwarded by the opinion leaders to form a multi-stage forwarding, which maximizes the diffusion of information.

FIGURE 4.

The number of opinion leaders in the list.

B. Grading of Opinion Leader

After the release of the information, there will usually be a level of opinion leaders’ forward communication, and then there will be two, three and so on two, three transmissions. But there are no two or three opinion leaders directly forward, three or four opinion leaders two forward, or even after the transfer of no opinion leaders to carry out the situation of secondary forwarding. Indicators of influence on the transmission of opinion leaders are mainly active and influential, of which the degree of activity refers to the microblog or microblog forwarding frequency, active days, etc.; influence refers to the number of forwarded or commented and fans Quantity. In this paper, the weighting method is used to classify the opinion leaders, and the influencing factors are the average forwarding amount, the number of fans and the microblog activity.

According to the basic theory of communication, the information dissemination network is subject to the authority phenomenon, and the size of the authority is proportional to the degree of the node. Therefore, the influence of node $i$ is defined as follows:

$$\begin{equation} Power_{i} =\sqrt {\frac {d_{i}}{d_{\max }}} \end{equation}$$

Where, in equation (5), $d_{i}$ is the degree of the node, $d_{\max }$ is the maximum value of all node degrees, and the range of $Power_{i}$ is the continuous interval [0, 1].

The communication power formula of the opinion leader can be calculated as.

$$\begin{equation} F_{propagation} =k_{1} w_{1} V_{fans} +k_{2} w_{2} V_{forward} +k_{3} w_{3} V_{activity}\quad \end{equation}$$ Where, $k_{1},k_{2},k_{3}$ is the random numbers. In order to facilitate the comparison, it is necessary to normalize the influence factor data, and use the normalized formula to convert the data to interval [0, 1], because the difference between the first and fourth opinion leaders is large.

The next step will determine the weight of each factor in the transmission force, using the analytic hierarchy process to calculate. First, the influencing factors are stratified. Followed by two pairs of comparison to determine the value, then the value of the normalization of the weight. Finally, the validity is determined by the consistency test.

Through the weight of the results of the evaluation of the leaders of the classification, so as to better analyze the microblog life cycle. The following table grading opinion leaders. (No special circumstances, the forwarding of more than 10 million microblog are considered to participate in the water army, ignoring these forwarding, this article to develop microblog actually forward more than 100,000, will forward the amount of 10 million).

Table 3~Table 4 to get the views of the opinion leaders after the classification, the next step will be based on the views of the leader of the microblog life cycle analysis.

TABLE 3 Opinion Leader Communication Power Impact Factor Weight

TABLE 4 Opinion Leader Rating

SECTION V. Proposed Mathematics Model

A. Microblog Life Cycle Analysis

From the data collection of 850 randomly selected 20% of microblog is 170 microblog is analyzed, it can be seen that a tweet the life cycle of basically divided into the boom period and decline period, in addition to the incubation period and secondary growth.

Fig. 5 shows that the increase in transmittance over time is slowly attenuating. The incubation period is the number of microblog in the delivery of the number of people after the transfer is very slow growth time, after a certain period of time began to surge; and secondary growth is in a microblog has begun to decline or into the surge after the incubation period and then began to grow time. Through the analysis of opinion leaders can effectively analyze a microblog life cycle.

FIGURE 5.

Diagram of microblog life cycle.

B. Model Establishment

Bessel function is the solution of the Bessel equation, is a mathematical class of special functions of the general term. The solution of such an equation cannot be systematically represented by elementary functions. It can only use the automatic control theory of phase plane method for qualitative analysis.

The general Bessel function is the standard solution of the ordinary differential equation, as shown in equation (7).

$$\begin{equation} x^{2}\frac {d^{2}y}{dx^{2}}+x\frac {dy}{dx}+(x^{2}-\alpha ^{2})y=0 \end{equation}$$ Since Eq. (7) cannot be represented by elementary functions, two independent functions are used to denote the Bessel function, using the first and second Bessel functions to represent the standard solution function. $$\begin{equation} y(x)=C_{1} J_{\alpha } (x)+C_{2} Y_{\alpha } (x) \end{equation}$$ The first class of Bessel functions is represented by $J_{\alpha } (x)$ , $J_{\alpha } (x)$ is the solution when $\alpha$ is an integer or nonnegative. The method of definition is expanded by its Taylor series at the point of $x=0$ . $$\begin{equation} J_{\alpha } (x)=\sum \limits _{m=0}^\infty {\frac {(-1)^{m}}{m!\Gamma (m+\alpha +1)}\left({\frac {x}{2}}\right)^{2m+\alpha }} \end{equation}$$ In the Bessel function, which $\alpha$ represents the order of the function. $$\begin{equation} \alpha =\frac {\sqrt {l} +t_{Forward}}{2} \end{equation}$$ The second type of Bessel function, called the Neumann function $Y_{\alpha } (x)$ , is usually used to denote that it has the following relation with $J_{\alpha } (x)$ : $$\begin{equation} Y_{\alpha } (x)=\frac {J_{\alpha } (x)\cos (\alpha \pi)-J_{-\alpha } (x)}{\sin (\alpha \pi)} \end{equation}$$ Similar to the function $J$ , the positive and negative integer order of the function $Y$ also has the following relationship: $$\begin{equation} Y_{-\alpha } (x)=(-1)^{\alpha }Y_{\alpha } (x) \end{equation}$$ The third kind of Bessel function, also known as Hankel function (Hankel function), as the Bessel equation of another pair of important linear independent solutions $H_{\alpha }^{(1)}(x)$ and $H_{\alpha } ^{(2)}(x)$ , respectively, defined as: $$\begin{align} H_{\alpha }^{(1)}(x)=&\frac {J_{-\alpha } (x)-e^{-\alpha \pi }iJ_{\alpha } (x)}{i\sin (\alpha \pi)} \\ H_{\alpha }^{(2)}(x)=&\frac {J_{-\alpha } (x)-e^{\alpha \pi }iJ_{\alpha } (x)}{-i\sin (\alpha \pi)} \end{align}$$ Where $i$ is the imaginary unit.

The above derivation gives the first and second types of modified Bessel functions, expressed by $I_{\alpha } (x)$ and $K_{\alpha } (x)$ separately, and is defined as:

$$\begin{align} I_{\alpha } (x)=&i^{-\alpha }J_{\alpha } (ix) \\ K_{\alpha } (x)=&\frac {\pi }{2}\frac {I_{-\alpha } (x)-I_{\alpha } (x)}{\sin (\alpha \pi)}=\frac {\pi }{2}i^{\alpha +1}H_{\alpha }^{(1)}(ix) \end{align}$$ On the impact of opinion leaders on a microblog life cycle Modeling will be modeled using the second modified Bessel function, the second modified Bessel function consists of the first two classes of Bessel functions and the first type of correction Bessel function is represented. This model is named the opinion leader level (It can be abbreviated proposed model).The independent variable $t$ of the function expression of this model is expressed as a time moment, and the dependent variable is expressed as the number of forwarding $N_{f}$ .So the expression is described as follows: $$\begin{equation} N_{f} =-\frac {\pi }{2}i^{\alpha +1}H_{\alpha }^{(1)}(it)+10F_{propagation} \end{equation}$$ Where the $H_{\alpha }^{(1)}(it)$ can be derived from the third type Bessel function. In order to normalize the weight of the propagation force obtained when calculating the weight $F_{propagation}$ of the opinion leader, it is necessary to multiply a coefficient before the propagation force. The model function can effectively analyze the lifecycle of different levels of opinion leaders after forwarding microblog.

When a public event occurs, only the parties and eyewitness individuals can know the event information. They constitute the initial node of the dynamic diffusion network. The number of nodes is $V_{0}$ . The interaction between these individuals constitutes the initial edge of the network, and the number of edges is $E_{0}$ . Next, the event information spreads and spreads in the above individual’s respective interpersonal relationship networks. The propagation intensity is related to the event influence surface, and is represented by the influence surface coefficient $r$ . Diffusion propagation leads to constant new nodes joining the network and updating the network. As time passes, the information is fully disseminated, the network gradually converges, and the number of network nodes tends to a fixed value $K$ . $K$ is equal to the total population of the affected area. The product of $N$ and the influence surface coefficient $r$ is $K=rN$ . The number of network nodes at time $t$ satisfies the following relationship:

$$\begin{equation} V_{t} =\frac {KV_{0} e^{rt}}{K+V_{0} (e^{rt}-1)} \end{equation}$$ Where, the number of newly added network nodes at time $t$ is $N_{v}$ , which is $N_{v} =V_{t} -V_{t-1}$ . Each new node $i$ chooses an existing node $j$ to establish a connection and inherit some of its viewpoint values. The probability that node $j$ is selected is proportional to the influence of node $j$ .

SECTION VI. Simulation Analysis

A. Parameter Settings

Randomly selected from the data collection of hot search microblog which randomly selected three forwarding more topics, first of all the leaders of the number of fans and the degree of activity simulation analysis, followed by the respondents from the time to find opinion leaders, and calculate the spread of opinion leaders Force, in the calculation of the transmission power of the factors are collected nearly a year of data, and finally the real data and proposed model simulation analysis.

As for a certain public emergency, such as “a big earthquake”. When the value of rumor attitude is (0,0.33) between the random number. The interaction between the subject and the rumor is shown in Fig. 6. It can be seen from Fig. 7 that the number of people has increased over time who affected by rumors.

FIGURE 6.

Different kind people affected by rumors.

FIGURE 7.

Different kind people affected by opinion leader.

The changing process of the numbers under the influence of rumor is shown in Fig. 6. The number of neutrals and objectors are decreased gradually. The number of supporters remained basically unchanged; the number of people who are affected by rumors was constantly increasing. The number of 310 people were affected by rumored, it is indicated that online rumor mainly affects two groups of people: one is similar with attitude and the other is a neutral one with a fluctuating attitude; on the other hand, the number of attitudes and online rumors is quite different. This part of the supporters show that the attitude is very firm, not easily affected by rumors, always stick to their own views.

The number of people who affected by opinion leaders is increased rapidly. When the credibility of opinion leader takes a random number between (0,0.7), attitude value takes (0,0.33) between the random number. As can be seen from Fig. 7. Many people have been influenced by opinion leader.

As can be seen from Fig. 6 and Fig. 7, influential and authoritative opinion leaders are not just ordinary citizens, but an important participant who can guide public opinion in the dissemination of emergency information. It has a vocal effect. Opinion leaders are an invisible facilitator in the dissemination of emergency information. Their attitude and attitude are of the utmost importance. If their attitudes for emergencies are criticized or questioned. It will evolve into a huge network public opinion crisis driven by the superposition effect of emergency information dissemination.

From Table 5 to Table 6 in the forwarders are opinion leaders, but Table 6 is not the top four opinion leaders, is a low-level opinion leader, analysis of the topic three because of the June 14,2018 outbreak of “FIFA world cup” events, due to the sudden outbreak of the incident, so most of the popular microblog are issued by the computer class microblog, such opinion leaders usually lower transmission power, but in the relevant explosive news on the spread of large.

TABLE 5 “North Korea Nuclear Issue” Event Microblog Parameters

TABLE 6 “FIFA World Cup” Solution Microblog Parameters

B. Compare of Real Data and Proposed Method

For the three groups of parameters, the number of fans and the number of factors to analyze the number of fans directly affect the information can see the flow of information, and the higher the degree of activity will lead to more people continue to pay attention to this opinion leader. Rank of opinion leader communication power is shown in Table 7.

TABLE 7 Rank of Opinion Leader Communication Power

The microblog process is not the higher the spread of the higher the fan, nor is the higher the degree of activity, the higher the transmission $F_{propagation}$ . But the higher the transmission power, the number of fans and the degree of activity will not be too low, compared to the number of fans and the degree of activity, the greatest impact on the transmission is the number of forwarding. So the three topics from the extraction of the relevant microblog, will be real data and proposed model simulation, the simulation of the map analysis, the views of leaders in the diffusion of information in the role of the size and size of the transmission, and calculate its error value.

The media viewpoint values were set to three evolution experiments with no influence, 0.7 (objector), and 1.0 (supporter).

When there are 20 evolutions, the number of participants in the communication reached 300, and the network gradually became stable. The experimental results are shown in Table 8 and Fig. 8 shows.

TABLE 8 Viewpoint Comparison Table

FIGURE 8.

Expedited period media influence diagram.

For the topic of microblog, its release form is not forward, but the way to the original microblog direct reference to others microblog, release the form is equivalent to forwarding (as shown in Fig. 9). In this did not find the relevant level of opinion leaders, so in the twenty-three four in the extraction of opinion leaders to analyze, and finally calculate the error in the micro-data and the actual simulation of the error of the average value of 13.7%. The error is also due to microblog randomness. It can be found in the neglect of randomness, the views of the leaders caused by the more extreme, the relative error will be higher. Found that the original microblog was cited a total of 30,000 of the total amount of forwarding, from the extraction of the three opinion leaders which have 27,300 of the forwarding, more than half of the total forwarding volume.

FIGURE 9.

The lifecycle of microblog.

In Fig. 10. Lu Han is forwarded by their own original microblog and caused the spread for the extraction of microblog data. The error is calculated to have an average error of 5.1%. This microblog forwarding mainly from the general public, there are few opinion leaders. The original microblog forwarding volume of about 23,000, while the extraction of three people caused by the forwarding of 2.18 million. The same opinion leader in this caused a great amount of transmission.

FIGURE 10.

The second lifecycle of microblog.

For the above topics extracted from the microblog simulation analysis can be obtained, when the topic in the microblog generated when it was accepted by the people mainly through the opinion leaders to spread. Play “a mass of ten pass hundred” around. The model has a high similarity with the actual data analysis microblog life cycle process, and the model error is also low, which shows that the model is effective.

SECTION VII. Conclusion

After the weight of the opinion leaders is calculated, the communication leaders are classified according to the numerical value of the transmission power, and the propaganda effect of the opinion leaders at all levels in the microblog social network communication is analyzed. And carries on the mathematical modeling using the Bessel function for the hierarchical opinion leader communication process, carries on the contrast simulation analysis according to the model and the real data, and analyzes the error existing in the model, and the role of the opinion leader in the communication process. The simulation results show that the proposed model is effective and accurate to analyze the microblog life cycle, and the error is low. The next step we will focus on the proposed model in-depth study to reduce the error value, and reduce the microblog randomness, and microblog before the analysis, the first microblog content of the incident, the daily microblog classification and then analysis.

The limitations of the proposed model are listed as: (1) The preferences of different opinion leaders and each opinion leader’s personalized information dissemination rules law are not considered. (2) The preferences of different users and each user’s personalized information dissemination rules law are not considered. The credibility of information dissemination between opinion leaders and regular people are not researched.