Bi-Polarization in Cascade Size Distributions

Predicting the final sizes of information cascades on online social networks (OSNs) has been a difficult problem. This is because OSNs may have complex topological structures and because user decisions may be influenced by several factors such as social reinforcement. Therefore, a considerable amount of research is being conducted with the objective of investigating in detail the effects of topology and user behavior on information diffusion. This study presents the cases where the final cascade size can be approximated without using further detailed information. Many cascade-size distributions obtained from Twitter-type information diffusion simulations reveal a new finding that as the retweet rates increase, cascades split more clearly into two groups: tiny and large cascades. This bi-polarization phenomenon is universal in that it always appears under various topological and user behavioral conditions. Moreover, the coefficient of variation of cascade sizes of the large cascade group decreases as the retweet rates increase. These findings suggest that the probability of the emergence of a large-scale cascade and its approximate final size are predictable if the global properties of topology and user behavior are time-invariant and given. A simple recurrence relation that generates bi-polarization is derived to verify the correctness of the simulation results.