Origins of power-law degree distribution in the heterogeneity of human activity in social networks

TL;DR

This paper demonstrates that the power-law degree distribution in social networks arises from the skewed distribution of individual activity levels, with degree being primarily determined by activity volume rather than social interactions.

Contribution

It introduces a causal inference approach showing that human activity heterogeneity directly causes the power-law degree distribution, challenging interaction-based models.

Findings

Degree distribution is causally linked to activity distribution.

Degree follows a maximum entropy attachment model.

Interactions are not the primary cause of degree heterogeneity.

Abstract

The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in social networks. Here, we perform a causal inference analysis and find an underlying cause for this phenomenon. Our analysis indicates that heavy-tailed degree distribution is causally determined by similarly skewed distribution of human activity. Specifically, the degree of an individual is entirely random - following a "maximum entropy attachment" model - except for its mean value which depends deterministically on the volume of the users' activity. This relation cannot be explained by interactive models, like preferential attachment, since the observed actions are not likely to be caused by interactions with other people.