Heterogeneity and Allometric Growth of Human Collaborative Tagging Behavior

TL;DR

This study investigates the relationship between heterogeneity and allometric growth in online tagging systems, showing that both power-law and log-normal distributions can produce allometric growth and confirming heterogeneity's positive role.

Contribution

It systematically compares different distributions and introduces Shannon entropy as a heterogeneity measure, expanding understanding beyond power-law models.

Findings

Power-law and log-normal distributions lead to allometric growth.

Shannon entropy effectively measures heterogeneity in tagging behavior.

Positive correlation between heterogeneity and allometric growth is confirmed.

Abstract

Allometric growth is found in many tagging systems online. That is, the number of new tags (T) is a power law function of the active population (P), or T P^gamma (gamma!=1). According to previous studies, it is the heterogeneity in individual tagging behavior that gives rise to allometric growth. These studies consider the power-law distribution model with an exponent beta, regarding 1/beta as an index for heterogeneity. However, they did not discuss whether power-law is the only distribution that leads to allometric growth, or equivalently, whether the positive correlation between heterogeneity and allometric growth holds in systems of distributions other than power-law. In this paper, the authors systematically examine the growth pattern of systems of six different distributions, and find that both power-law distribution and log-normal distribution lead to allometric growth. Furthermore, by introducing Shannon entropy as an indicator for heterogeneity instead of 1/beta, the authors confirm that the positive relationship between heterogeneity and allometric growth exists in both cases of power-law and log-normal distributions.