  Cumulative effect in social contagions underlies many studies on the spread
of innovation, behaviors, and influence. However, few large-scale empirical
studies are conducted to validate the existence of cumulative effect in the
information diffusion on social networks. In this paper, using the
population-scale dataset from the largest Chinese microblogging website, we
conduct a comprehensive study on the cumulative effect in information
diffusion. We base our study on the diffusion network of each message, where
nodes are the involved users and links are the following relationships among
them. We find that multiple exposures to the same message indeed increase the
possibility of forwarding it. However, additional exposures cannot further
improve the chance of forwarding when the number of exposures crosses its peak
at two. This finding questions the cumulative effect hypothesis in information
diffusion. Furthermore, to clarify the forwarding preference among users, we
investigate both the structural motif of the diffusion network and the temporal
pattern of information diffusion process among users. The patterns provide
vital insight for understanding the variation of message popularity and explain
the characteristics of diffusion networks.
