Long trend dynamics in social media
© Wang and Huberman; licensee Springer. 2012
Received: 23 January 2012
Accepted: 18 May 2012
Published: 18 May 2012
A main characteristic of social media is that its diverse content, copiously generated by both standard outlets and general users, constantly competes for the scarce attention of large audiences. Out of this flood of information some topics manage to get enough attention to become the most popular ones and thus to be prominently displayed as trends. Equally important, some of these trends persist long enough so as to shape part of the social agenda. How this happens is the focus of this paper. By introducing a stochastic dynamical model that takes into account the user’s repeated involvement with given topics, we can predict the distribution of trend durations as well as the thresholds in popularity that lead to their emergence within social media. Detailed measurements of datasets from Twitter confirm the validity of the model and its predictions.
The past decade has witnessed an explosive growth of social media, creating a competitive environment where topics compete for the attention of users [1, 2]. A main characteristic of social media is that both users and standard media outlets generate content at the same time in the form of news, videos and stories, leading to a flood of information from which it is hard for users to sort out the relevant pieces to concentrate on [3, 4]. User attention is critical for the understand of how problems in culture, decision making and opinion formation evolve [5–7]. Several studies have shown that attention allocated to on-line content is distributed in a highly skewed fashion [8–11]. While most documents receive a negligible amount of attention, a few items become extremely popular and persist as public trends for long a period of time [12–14]. Recent studies have focused on the dynamical growth of attention on different kinds of social media, including Digg [15–17], Youtube , Wikipedia [19–21] and Twitter [14, 22–24]. The time-scale over which content persists as a topic in these media also varies on a scale from hours to years. In the case of news and stories, content spreads on the social network until its novelty decays . In information networks like Wikipedia, where a document remains alive for months and even years, popularity is governed by bursts of sudden events and is explained by the rank shift model .
While previous work has successfully addressed the growth and decay of news and topics in general, a remaining problem is why some of the topics stay popular for longer periods of time than others and thus contribute to the social agenda. In this paper, we focus on the dynamics of long trends and their persistence within social media. We first introduce a dynamic model of attention growth and derive the distribution of trend durations for all topics. By analyzing the resonating nature of the content within the community, we provide a threshold criterion that successfully predicts the long term persistence of social trends. The predictions of the model are then compared with measurements taken from Twitter, which as we show provides a validation of the proposed dynamics.
This paper is structured as follows. In Section 2 we describe our model for attention growth and the persistence of trends. Section 3 describes the data-set and the collection strategies used in the study, whereas Section 4 discusses the measurements made on data-sets from Twitter and compares them with the predictions of the model. Section 5 concludes with a summary of our findings and future directions.
On-line micro-blogging and social service websites enable users to read and send text-based messages to certain topics of interest. The popularity of these topics is commonly measured by the number of postings about these topics [15, 19]. For instance on Twitter, Digg and Youtube, users post their thoughts on topics of interest in the form of tweets and comments. One special characteristic of social media that has been ignored so far is that users can contribute to the popularity of a topic more than once. We take this into account by denoting first posts on a certain topic from a certain user by the variable First Time Post (FTP). If the same user posts on the topic more than once, we call it a Repeated Post (RP). In what follows, we first look at the growth dynamics of FTP.
Taking logarithms on both sides, we obtain . Applying the central limit theorem to the sum, it follows that the cumulative count of FTP should obey a log-normal distribution.
Thus far we have only considered the impact of FTP on social trends by treating all topics as identical to each other. To account for the resonance between users and specific topics we now include the RP into the dynamics. We define the instantaneous number of FTP posted in the time interval t as , and the repeated posts, RP, in the time interval t as . Similarly we denote the cumulative number of all posts-including both FTP and RP-as . The resonance level of fans with a given topic is measured by , and we define the expected value of , as the active-ratio .
Which states that the persistent duration of trends associated with given topics is expected to scale linearly with the topic users’ active-ratio. From this result it follows that one can predict the trend duration for any topic by measuring its user active-ratio after the values of and are determined from empirical observations.
To test the predictions of our dynamic model, we analyzed data from Twitter, an extremely popular social network website used by over 200 million users around the world. Its interface of allows users to post short messages, known as tweets, that can be read and retweeted by other Twitter users. Users declare the people they follow, and they get notified when there is a new post from any of these people. A user can also forward the original post of another user to his followers by the re-tweet mechanism.
In our study, the cumulative count of tweets and re-tweets that are related to a certain topic was used as a proxy for the popularity of the topic. On the front page of Twitter there is also a column named trends that presents the few keywords or sentences that are most frequently mentioned in Twitter at a given moment. The list of popular topics in the trends column is updated every few minutes as new topics become popular. We collected the topics in the trends column by performing an API query every 20 minutes. For each of the topics in the trending column, we used the Search API function to collect the full list of tweets and re-tweets related to the topic over the past 20 minutes. We also collected information about the author of the post, identified by a unique user-id, the text of the post and the time of its posting. We thus obtained a dataset of 16.32 million posts on 3361 different topics. The longest trending topic we observed had a length of 14.7 days. We found that of all the posts in our dataset, 17% belonged to the RP category.
5 Discussion and conclusion
In this paper we investigated the persistence dynamics of trends in social media. By introducing a stochastic dynamic model that takes into account the user’s repeated involvement with given topics, we are able to predict the distribution of trend durations as well as the thresholds in popularity that lead to the emergence of given topics as trends within social media. The predictions of our mode were confirmed by a careful analysis of a data from Twitter. Furthermore, a linear relationship between the resonance level of users with given topics, and the trending duration of a topic was derived. The proposed model provides a deeper understanding the popularity of on-line contents. Parameters and in our model are system specific and could be calculated from hidden algorithms when applying our model to other on-line social media websites. Possible refinements may include the effect of competition between topics, sudden burst of events, the effect of marketing campaigns and the actively censoring of specific topics . In closing, we note that although the focus in this paper has been on trend dynamics that are featured on social media websites, the framework and model may be suitable to other types of content and off-line trends. The issue raised - that is, trending phenomenon under the impact of user’s repeated involvement - is therefore a general one and should provide ample opportunities for future work.
B.H. and C.W. designed the study and performed research. C.W. and B.H. wrote the paper. All authors read and approved the final manuscript.
We acknowledge useful discussions with S. Asur and G. Szabo. C.W. would like to thank HP Labs for financial support.
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