Article Preview
Top1. Introduction
Thanks to the fast development of Web2.0, many online social networks have emerged, where the observation of information diffusion, or social influence, in large-scale data becomes possible. Social influence has been studied by many researchers, including the validation of influence (Anagnostopoulos et al., 2008; Crandall et al., 2008) the propagation of influence among multiple types of social (Gruhl et al., 2004; Cha et al., 2009; Hong et al., 2011) the maximization of influence spread in the whole network kempe, and the probabilistic modeling of direct influence (Tang et al., 2009; De Choudhury et al., 2007). However, most relevant studies focused on direct influence, while another relevant question regarding social influence may be raised as to whether a user can exert indirect influence on his/her friends’ friends and what affects such influence. Normally, multiple intermediate persons called spreaders are involved in the indirect communication between two persons, i.e., the sender and the receiver. Those spreaders may have a combinational effect on the indirect influence propagated from the sender to the receiver.
A concept closely related to indirect influence is complex contagion. Unlike simple contagion, which can spread in social networks after just one contact with a single infected neighbor like a disease, complex contagion is a phenomenon where multiple sources of exposure to a new idea are required before an individual adopts the idea (Centola & Macy, 2005). That is to say, repeated exposures of an individual to an idea recommended by his/her multiple neighbors positively affect the probability he/she will eventually follow that idea. Romero et al. (2011) studied the spread of hashtags in Twitter and quantified the probability of a user adopting a new hashtag as the function of the number of his/her neighbors who have already adopted it. They found that the spread of political hashtags validates the complex contagion, where the adoption probability increases monotonically as the number of neighbors who had already adopted the same hashtags increases, until a plateau is finally reached. By contrast, for idiom hashtags, complex contagion does not take effect, and the adoption probability decays rapidly when more neighbors have adopted the same hashtags.
The problem we are studying is similar to Romero et al. (2011), but we focus on message spread behavior and indirect influence on Twitter. A concrete example of this is shown in Figure 1 where Alice sends out original messages, Charlie and Carol further spread Alice’s messages (i.e., by retweeting) and Bob finally receives them. After that, Bob may choose to further spread Alice’s messages to others, just like his two neighbors Charlie and Carol have done, or not. Here, the intent of Bob to further spread Alice’s messages would reflect the intensity of the indirect influence of Alice on Bob, which can be measured as the probability that Bob will further spread Alice’s messages, given that Charlie and Carol have already spread these messages. If complex contagion takes effect, the influence intensity will be higher when both Charlie and Carol spread Alice’s messages than when either or none of the two spread them.
Figure 1. Typical information spread in a social network