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.
Using attributes of the underlying graph as explanatory variables is a common approach to studying information cascades on networks. Typically, these networks have either directional links, through follower and followee relationships or bi-directional links, through friendship statuses. @cite_0 consider a model to predict spikes of activity while considering various graph-theoretic characteristics of these networks. In contrast, our analysis is based on abstracting the cascade as a branching process, and we apply this approach to data generated from simulations on scale-free networks, and to data collected from Twitter.
@cite_0
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We propose a novel mathematical model for the activity of microbloggers during an external, event-driven spike. The model leads to a testable prediction of who would become most active if a spike were to take place. This type of insight into human behaviour has many applications, as it identifies key players who can be targeted with information in real time when the network is most receptive. The model takes account of the fact that dynamic interactions evolve over an underlying, static network that records "who listens to whom". Our fundamental assumption is that, in the case where the entire community has become aware of an external news event, a key driver of activity is the motivation to participate by responding to incoming messages. We validate the resulting algorithm on a large scale Twitter conversation concerning the appointment of a UK Premier League football club manager. We also find that the half-life of a spike in activity can be quantified in terms of the network size and the typical response rate.