Accelerating growth and size-dependent distribution of human online activities.

Research on human online activities usually assumes that total activity T increases linearly with active population P, that is, T∝P(γ) (γ=1). However, we find examples of systems where total activity grows faster than active population. Our study shows that the power law relationship T∝P(γ) (γ>1) is in fact ubiquitous in online activities such as microblogging, news voting, and photo tagging. We call the pattern "accelerating growth" and find it relates to a type of distribution that changes with system size. We show both analytically and empirically how the growth rate γ associates with a scaling parameter b in the size-dependent distribution. As most previous studies explain accelerating growth by power law distribution, the model of size-dependent distribution is worth further exploration.