This article is from WeChat public account: Jizhi Club (ID: swarma_org) , author: Guo Ruidong


Every time we see a rumor, we will sigh why the spread of rumors can be faster and wider than when we read rumors. Recently, a research team composed of Alessandro Vespignani, a complex network scholar from Northeastern University, published a paper in Nature Physics to try to answer this question. The researchers first introduce how to model the propagation of information, and then analyze the two modeling methods for different social structures, and discuss the critical phase transition point of avalanche evolution in the range and spread of information in social networks.

Three states of information dissemination

Social communication models for human interaction networks have become increasingly popular in recent years. However, these models are difficult to deal with social technologyThe complexity and practical challenges of the surgical system. In this paper, the researchers discovered the critical phase transition contained in Maki-Thompson, a classic rumor propagation model.

Similar to disease transmission models such as SIR, the Maki–Thompson model for information transmission also divides the population into three states, namely:

Unknown person , that is, did not hear the news; Propagator , who understood and actively spread the news; Silent person , who understood Information but no longer disseminate information.

For different information, if the communicator tells the information to the unknown, then there is a λ probability that the unknown will become the communicator.

If the communicator passes this information to other communicators or silencers, there is a probability that the communicator will become a silencer because the information is no longer fresh.

Assuming that the crowd is evenly distributed, that is, everyone in the network is the same, there is no higher proportion of communication between certain people, and a smaller proportion of communication between certain people, then the information can eventually be spread The proportion of people depends only on the ratio of the above two parameters, that is, the proportion of propagation and the proportion of no longer propagating.

If the probability of successful propagation is the same as the probability of silence, eventually this message will spread throughout the network.

Figure 1: Relationship between Propagation / Non-Propagation Probability Ratio and Final Network Propagation Degree

As shown in the figure, when the crowd is uniform, the result of the spread (how many people know this message and the speed of spread in the end) only by Probability α and probability λ Decide.

For the spread of rumors, as long as the number of rumors reaches as many as non-rumors, the rumors can spread throughout the network.

Urban community and virtual community

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People in reality are different, some people have more interactions, and there are small circles of all kinds, forming a so-called social structure. After the model introduces the social structure, there will be a nonlinear critical point.

Figure 2: Comparison of two ways of modeling crowd structure

The above picture shows two modeling methods: Metropolis Network (fixed community) and virtual community network.

Left picture a is the metropolitan network. It is described in detail in the book “Network Science of Barabara”, referring to the crowd divided into multiple blocks, and the average number of people in each block is N. People in the area first spread the information internally, and then propagate to people outside the area with a probability of p / k , where p is the propagation probability, k < / em> is the number of other areas connected to this area.

Compared with the regional metropolitan network, the propagation model of the virtual community represented by b on the right is suitable for modeling online forums and interest groups. The model divides the population into V communities, and the size of the communities conforms to a specific probability distribution. Each user may become active at each moment, and then use μ probability to communicate with people in this community, with a 1- μ probability to establish a cross-community connection, so that a step-by-step formation of information dissemination network.

Need enough cross-community connections for information to spread

Figure 3: Comparison of information dissemination results under metropolitan networks and virtual communities

As shown in the figure, the researcher builds a model based on the above assumptions. Through multiple Monte Carlo simulations, under the premise of only one initial communicator, compare how many people finally know the information (that is, belonging to communicators or silencers) , that is, the vertical axis in the figure. The left picture corresponds to the metropolitan model, and the right picture corresponds to the virtual community model.

The different colors in the left picture a represent the probability that the information transmitted by the communicator will make others become communicators. In the picture on the left, the probability that the communicator becomes a silencer due to propagation is λ is 0.1, even if this message is only transmitted, there is a 10% probability that others will also become communicators.

However, due to the poor mobility between different communities, the number of people who can eventually reach is still very small. This explains why the popularization of rumors cannot reach more people. No one believes after spreading the rumor post in the family and friends group, it is equivalent to not spreading between the communities.

Right picture b Consider the information that has strong persuasion and “must turn”, which means that the probability that an unknown person becomes a communicator due to the information is 1 But if the information is disseminated to an already known person, the person may no longer continue to disseminate it. This is information saturation. The different colors in the figure represent that different proportions of communicators no longer spread due to information saturation. But once the communicator spreads to a person who knows the news, it stops spreading (corresponding to the dark blue line) .

The imaginary vertical line in the figure, which is the critical phase change point of information diffusion-before reaching the phase change point, even if the propagation probability is (figure a ) The probability of interaction with the community (figure b) is increasing, but the information cannot spread to the entire community. Once the probability of propagation and the probability of interaction within the community exceed the phase transition point, the possibility of information spreading to the entire community will greatly increase.

According to the above propagation model, in an open forum, as long as people have sufficient probability to establish a connection with people outside the community during the propagation process, it is possible to spread the message throughout the entire network.

Propagation in the real network

The above studies are all based on simulated network structure, so is there a similar critical phenomenon in the real network? Beyond this point, will the news have the opportunity to spread more widely?

The paper co-author network is a data set commonly used by researchers. The following figure shows that in this network structure, the Monte Carlo method is used to simulate the propagation of information. The left and right figures still represent the metropolitan network model and virtual community model, respectively. The horizontal and vertical axes are similar to the above figure.

Figure 4: The relationship between the final effect of information dissemination in the real network and the mobility between communities

As you can see from the picture, the critical phenomenon still exists. The researchers further analyzed the final results of information dissemination in the network under different states and made a visualization.

Figure 5: Comparison of the impact of reaching the critical point on information dissemination in the paper co-authoring network

Each dot in the figure represents a community (Research Group) , the size of the dots represents the number of people in the community, and the shades of colors represent the community What percentage of people believe this information. From left to right represent different times, the upper and lower figures compare different states around the critical point.

The secret of the “10w +” article needs further study

This research has implications for how to make information spread as widely as possible on the Internet. Each message will have a different value of α or λ in the model described above due to the difference of its own content, thus making it spread in social networks The range and rate are different.

According to the research in this article, the reason why Shuangwen can obtain 10w + more easily than the popular science is because Shuangwen can easily cross the boundaries between communities and draw on people ’s empathy. Spread to different communities.

Therefore, for science writers, if they want more people to understand scientific knowledge, they must respect the laws of information dissemination on the Internet. Specifically, what you write must be simple and interesting enough to spread across the community, not just within the research circle. This is the most important thing. Secondly, it is necessary to increase the propagation probability α , so that your article is authoritative and useful (can help readers become smarter) , to achieve a higher percentage of people to spread.

For the model proposed in this article, we believe that there are two points that deserve further study.

First of all, in the original model, after spreading, the spreader will only make the spread person become a spreader by a certain percentage.Broadcasters, however, in the dissemination of information, not everyone who knows the information will be willing to forward it. Therefore, a parameter can be added to indicate that after the information is successfully transmitted, what percentage of those who receive the information will become silent and what percentage will become the communicator. This parameter represents the quality of information. The lower the value, the higher the quality of information. After adding this parameter, we can characterize the dynamic characteristics of information with different propagation capabilities in a complex network.

The second improvement is to add the status of rebutters to the classification of people in the model. Suppose that in each initial community or area, according to a certain probability distribution, a certain percentage of people are refutors. When these people receive rumors, there is a certain probability that the communicator becomes a rebuttal. The participation of the rebuttal can study the interaction between rumors and repelling rumors.

Thesis title:

Phase transitions in information spreading on structured populations

Thesis address:

This article is from WeChat public account: Jizhi Club (ID: swarma_org) , author: Guo Ruidong