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We investigate the impact of human dynamics on the information propagation in online social networks. First, statistical properties of the human behavior are studied using the data from “Sina Microblog,” which is one of the most popular online social networks in China. We find that human activity patterns are heterogeneous and bursty and are often described by a power-law interevent time distribution

Rapid development of information and communication technology has increased the wide adoption of online social network in our life. Indeed, online social network such as Sina Microblog, Twitter, and Facebook had become an indispensable part of our life. Every day we sign into our homepages more than once to view and share information. These online social networks have common characteristics: instantaneity, simplicity, and universality. Taking Sina Microblog, for example, unlike the traditional blog, it allows the use of mobile devices to disseminate information by a length of 140 characters text at anytime and anywhere. Investigating the online social network is crucial in a broad range of settings from information propagation and viral marketing to political purposes.

Recent years, online social network as a platform for the empirical study of information has been widespread concern [

Firstly, information propagation in online social network is determined by rhythms and activity patterns of human [

Secondly, the wide adoption of online social network has increased the competition among information for our limited attention. Every day we receive a lot of information from various online social networks. However, we do not have enough time and attention to disseminate each message which we received. It is an interesting question that whether such a competition may affect the velocity of information propagation. The issue of limited attention has been studied through messages posted and forwarded in online social networks [

In this paper, we propose an extended Susceptible-Infected (SI) propagation model, incorporating bursty human activity patterns and limited attention for the first time. Then, we obtain a large number of real data to test the model. Adopting the methods of theoretical research and empirical analysis, we study the information spreading process in social networking qualitatively and quantitatively. The key contributions of this study are summarized as follows.

From the empirical statistical results we find that at the group level, the interactive time (time interval between two consecutive login microblog homepage) follows power-law distribution with the

Through both the theoretical research and simulation, we prove that

In summary, although tremendous efforts have been made regarding the research about information propagation, further study based on human dynamics is still needed to unveil the role of human behaviors for the information propagation in online social network. In future studies, on the other hand, we can use other more mature theories to research the spreading dynamics, such as in the references [

The rest of this paper is organized as follows. Section

The dataset of this paper was collected from Sina Microblog (

The basic statistical results show that at the group level, the interactive time (time interval between two consecutive login microblog homepage) follows power-law distribution with the

Empirical data. (a) The distribution of interactive time at the group level. (b) The distribution of newly infected individuals, inset: the cumulative distribution of newly infected individuals, namely, the distribution of all infected individuals. The results are the average of all messages.

In this paper, we use the branching processes [

Initially all individuals are susceptible except for a single infected individual. Different with the traditional model, at a given time step, an infected individual can be inactive; that is to say, infected individual will not infect connected susceptible individuals at that time step. The time interval between two consequent active steps of an infected individual is defined as the interactive time, which is often characterized by a power-law distribution

On the other hand, the advent of online social network has greatly lowered the cost of information generation and propagation, boosting the potential reach of each message. However, the abundance of information to which we are exposed through online social networks is exceeding our capacity to consume it. Due to the limited time and attention, the individual cannot continuously check the update of information on his/her homepage. We assume that individuals interact on a directed online social network. Each individual is equipped with two lists. One is the screen where received messages are recorded and maintained a time-ordered list of messages. The other is memory where individual interested messages are recorded. Each individual can share some of the messages from the list with his/her friends. The friends in turn pay attention to a newly received message by placing it at the top of their lists. Because of the limited attention, we allow messages to survive in an individual’s screen for a finite amount of time

According to the previous description, the SI model incorporating bursty and limited attention is illustrated in Figure

Schematic of individual interaction.

To sum up, the extended SI model is defined as follows.

At time step

For each individual

At each active time step, individual

Update the time step

In addition, we also introduce two indicators to characterize the velocity of information propagation:

the first time step when the number of infected individuals exceeds half of the population, defined as half time

the mean infection time of an individual after the outbreak, defined as mean time

In our simulations, initially all individuals are susceptible except for a single infected individual. Each individual

(a) The average number of newly infected individuals

(a) The fraction of infected nodes

In power-law case, the average number of newly infected individuals

The smaller the exponent

In order to investigate the impact of attention on the propagation process, we fixed interactive time following power-law distribution with the exponent

(a) The fraction of infected nodes

The higher the degree of attention, the faster the velocity. The half time

In this section, the properties of propagation dynamics are analyzed. We prove that the decay exponent of propagation velocity equals that in the generation time distribution. Furthermore, we also proved that the exponent

If the distribution of generation time follows power-law

We consider a general theory of propagation process in online social networks. We assume that the propagation process outbreaks starting from a single infected individual at time

For

This preposition means that if the generation time distribution follows a power-law with the exponent

If the distribution of interactive time follows a power-law

When the distribution of interactive time follows a power-law

Since the generation time probability density function is related to the interactive time probability density function [

An extended SI model is proposed in this paper. Different from the analysis of the network topology, we study the information propagation in online social networks from the perspective of human dynamics. We found that human behavior affects the range and velocity of information propagation greatly.

In the future, with the development of online social systems, there may be other factors influencing information propagation in online social network. Therefore, we must improve the propagation model in order to better explain the propagation process.

The authors would like to thank Liang Huang and Byungjoon Min for helpful discussions. This work was supported by Program for New Century Excellent Talents in University (NCET-11-0597) and the Fundamental Research Funds for the Central Universities (2012RC1002).