Accelerating Growth and Size-dependent Distribution of Human Activities Online

TL;DR

This paper reveals that many online activity systems exhibit accelerating growth where total activity increases faster than active users, linked to size-dependent distributions that change with system size.

Contribution

It introduces a novel model of size-dependent distributions explaining accelerating growth, supported by analytical and empirical evidence.

Findings

Accelerating growth ($b3>1$) is common in online activities.

Growth rate b3 is linked to a size-dependent distribution parameter.

The size-dependent distribution model differs from traditional power law explanations.

Abstract

Research on human online activities usually assumes that total activity $T$ increases linearly with active population $P$, that is, $T\propto P^{\gamma}(\gamma=1)$. However, we find examples of systems where total activity grows faster than active population. Our study shows that the power law relationship $T\propto P^{\gamma}(\gamma>1)$ is in fact ubiquitous in online activities such as micro-blogging, 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 $\gamma$ 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 novel and worth further exploration.