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

Authors

Lev Muchnik, The Hebrew University of Jerusalem
Sen Pei, CUNY City College
Lucas C. Parra, CUNY City College
Saulo D. S. Reis, CUNY City College
José S. Andrade Jr, Universidade Federal do Ceará
Shlomo Havlin, Bar-Ilan University
Hernán A. Makse, CUNY City College

Document Type

Article

Publication Date

May 2013

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.

Comments

This work was originally published in Scientific Reports, available at doi:10.1038/srep01783.