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Put together, this study offers an empirical test for the threshold hypothesis of

interpersonal effects. The analysis confirms the threshold hypothesis of interpersonal effects. For the information of modest importance, smaller interpersonal effects are needed to trigger a larger diffusion; for the information of strong importance, larger interpersonal effects are necessary to make the diffusion spread to a wider audience. These findings render support for the classic J- curve model (Greenberg, 1964b) in the digital world. Thus, this study supplies a baseline to understand social networking services in social media.

The distribution of diffusion size, featured by a long-tail, is highly unequal. A few

fraction of information diffuses to a large proportion of people, while most information could not spread to more than 100 people. The findings of J-curve model of interpersonal effects indicate that interpersonal effects tend to intensify the inequality of information popularity in terms of retweets. E.g., the findings confirm that for the information of low audience interest, the strength of interpersonal effects is negatively related to diffusion size. For the information of high

In addition to the unequal distribution of diffusion sizes and its relationship with interpersonal effects, the depth of diffusion has positive influence on the diffusion size. Compared with diffusion sizes, the depth of diffusion is extremely small. E.g., the largest diffusion depth is 26, and the largest diffusion size is 417116. Information diffusion on microblogs is a branch process, and its width is much bigger than its depth. Although the massive online social network of social media is usually a small world, an average diffusion depth of 4 is not enough.

The limited diffusion depth implies that most information are trapped in the local community, and therefore it underscores the structural trapping which has been emphasized in prior studies. The proposition of structural trapping suggests that dense communities with few outgoing links naturally trap information flow (J-P Onnela et al., 2007; Weng, et al., 2013). In the seminal work on weak ties, Granovetter (Granovetter, 1973) proposes that weak ties pass information to a larger number of people thus information can traverse a longer social distance (path distance). In Onnela et al.’s study of mobile communication networks, they find that mobile social networks are “robust to the removal of strong ties” but fall apart if the weak ties are removed, “resulting in a dynamic trapping of information in communities” (J-P Onnela, et al., 2007). In Weng et al.’s study about the information diffusion on Twitter, they also find such structural trapping in terms of community concentration (Weng, et al., 2013). The findings of the positive relationship between diffusion depth and diffusion size suggest that the viral information tends not to be trapped by the local community, and it can relatively easily permeate through more communities.

The limited value of diffusion depth implies the potential of online information diffusion lies in the percolation power of the information. Information diffusion on microblogs decays

quickly with the depth of information diffusion, which may suggest that individuals of the same audience interest tends to cluster together, and thus the boundaries among social circles of different tastes block the information from propagating within the online social networks of microblogs.

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The pattern of short diffusion depth also illustrates the weakness of the information diffusion on microblogs. The diffusion mechanism for a specific piece of information is mainly based on interpersonal networks. Therefore, the information diffusion for concrete information is a bottom-up process. To make effective diffusion, a top-down diffusion process is necessary. As it has been mentioned in the literature section of microblogs, aggregated popularity manifests itself on microblogs in the form of information aggregators and search engineers on both Twitter and Sina Weibo 5.

To understand the limited diffusion size for information diffusion on social media, especially the temporality of information diffusion, an analysis of the temporal patterns of information diffusion is also necessary. To do so, I sample 8000 tweets from Sina Weibo, and analyze the temporal patterns of their information diffusion. First, I find the lifetime for most of the information is quite limited. I calculate the lifetime using one day as the unit of analysis, and find that the average lifetime is 8.78 days which is only a bit longer than one week, and the median lifetime is 2 days (See Figure 22).

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Further, the information of such small lifetime is usually accompanied by a drastic burst of public attention, and then dies out soon. To demonstrate the burst phenomena of public attention allocated to the information, I calculate the peak fraction which is the proportion of the daily information diffusion happens in the peak day. The results indicate that the average peak fraction is 0.827 (See Figure 23), which suggests most of the information diffusion for one specific piece of information (e.g., a tweet) happens within one day. Consistent with this finding, recent research also demonstrates a strong burst phenomenon in the diffusion of hashtags. For example, Glasgow and Fink (2013) study the Hashtag lifespan for the tweets of London riot. They find that the half-life span is less than 24 hours. Half-life is the time required for a quantity to fall to half its value as measured at the beginning of the time period. For example, the hashtag of #riotcleanup last for 52 days (lifespan), but its half-life is less than 20 hours.

Put together, this study confirms the threshold models of interpersonal effects for online information diffusion on microblogs. Further, the patterns of limited depth of diffusion networks and short lifetimes with strong and early bursts illustrate the potential importance of analyzing communication networks as well as the temporal patterns. Thus, further attention should be put to the aggregated popularity and the bursts of online information diffusion.