Thursday, July 8
10591. A Popularity Model for Information Spreading: Twitter as a Case Study
Computational Social Science Social Media Complex Systems Complex Networks Collective Action & Social Movements Dynamics Network Science Social Network Analysis Diffusion Inequalities Social Influence
Thursday, July 8
9:00 am - 10:00 am
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Authors: Lilia Perfeito; Joana Gonçalves-Sá

Extreme inequality is present in multiple human activities. This inequality gives rise to so-called heavy-tailed distributions whereby few elements are responsible for most of the observations. One such example are the sizes of Twitter cascades (Figure 1A), i.e., the number of times a tweet is retweeted, with most tweets being retweeted few times, and few tweets being retweeted many times. Several processes can lead to heavy-tailed distributions and discriminating between them has been the subject of much debate. In particular, it has been argued that such distributions emerge from the properties of the networks. Here, we fit a simple model of information spread to Twitter and analyze cascade growth as a function of tweet popularity. In our model, the size of a cascade over time is given by:

dN(t)/dt = N(t)*a*e^(-g*t), where N(t) is the number of tweets in a cascade at time t and tweet popularity is measured through the parameters a (maximum growth rate of the cascade) and g (the rate at which the growth of the cascade slows down with time). We further introduce the concept of Twitter time, a “relativistic” measure that uses as reference user activity (more in some times of day than in others) and smooths activity over daily periods.

Our simple model captures well the dynamics of over 98 % of the tweet cascades larger than 100 (see Fig. 1B for examples). This means that we do not need to invoke any property of the social network to observe a scale-free distribution of Twitter cascade sizes. Popularity varies substantially between cascades, but our results suggest the resulting distributions are better fitted by a Gamma distribution than a power law (Figure 1C). When we simulate cascade growth using these distributions of popularity, we recover a power law tail of cascade sizes.

These results have two important consequences: 1) we can interpret the distribution of cascade sizes in light of the distribution of popularity and without any knowledge on the underlying network structure; 2) more powerful statistical analyses can be performed on popularity because, unlike the power law distribution, the moments of the Gamma distribution are well defined.

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