Accelerating Growth and Size-dependent Distribution of Human Activities Online

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.

6 pages, 2 figures

References in corpus (4)

• Information dynamics shape the networks of Internet-mediated prostitution
• Zipf's Law Leads to Heaps' Law: Analyzing Their Relation in Finite-Size Systems
• Allometric Scaling of Countries
• Size-Dependency of Income Distributions and Its Implications

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