We build a model of information cascades on feed-based networks, taking into account the finite attention span of users, message generation rates and message forwarding rates. Through simulation of this model, we study the effect of the extent of user attention on the probability that the cascade becomes viral. In analogy with a branching process, we estimate the branching factor associated with the cascade process for different attention spans and different forwarding probabilities, and demonstrate that beyond a certain attention span, cascades tend to become viral. The critical forwarding probabilities have an inverse relationship with the attention span. Next, we develop an analytical and numerical approach that allows us to determine the branching factor for given values of message generation rates, message forwarding rates and attention spans. The branching factors obtained using this analytical approach show good agreement with those obtained through simulations. Finally, we analyze an event-specific dataset obtained from Twitter, and show that estimated branching factors correlate well with the cascade-size distributions associated with distinct hashtags.
A work related to biases in data collection, @cite_2 compares the full Twitter feed Firehose with the sampled Gardenhose Twitter Streaming API to which the majority of researchers have access.
@cite_2
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Twitter is a social media giant famous for the exchange of short, 140-character messages called "tweets". In the scientific community, the microblogging site is known for openness in sharing its data. It provides a glance into its millions of users and billions of tweets through a "Streaming API" which provides a sample of all tweets matching some parameters preset by the API user. The API service has been used by many researchers, companies, and governmental institutions that want to extract knowledge in accordance with a diverse array of questions pertaining to social media. The essential drawback of the Twitter API is the lack of documentation concerning what and how much data users get. This leads researchers to question whether the sampled data is a valid representation of the overall activity on Twitter. In this work we embark on answering this question by comparing data collected using Twitter's sampled API service with data collected using the full, albeit costly, Firehose stream that includes every single published tweet. We compare both datasets using common statistical metrics as well as metrics that allow us to compare topics, networks, and locations of tweets. The results of our work will help researchers and practitioners understand the implications of using the Streaming API.