Dynamics of Users Activity on Web-Blogs

TL;DR

This paper analyzes user activity dynamics on web-blogs, showing that user rank follows a stretched-exponential distribution and that comment posting behavior can be modeled with functions similar to Fermi-Dirac distribution, revealing links to user personality.

Contribution

It introduces a novel approach to modeling blog comment activity over time using functions akin to Fermi-Dirac distribution, and compares distributions of user activity.

Findings

User rank distribution fits stretched-exponential better than Zipfs law.

Comment posting probability over time resembles Fermi-Dirac distribution.

Dynamics of individual blog entries may relate to user personality.

Abstract

Activity of users on Internet discussion forums is analyzed. The rank of users is shown to be approximated better by stretched-exponential function than by Zipfs law. Cumulative distribution function is found as an excellent tool in analysis of the dynamics of the collective social phenomena. We are able to approximate the number of blog comments with time by simple functions that resemble Fermi-Dirac distribution function: probability of posting a comment is given by $P(t)=P_0(t) / (1+P_0(t)$, where $P_0(t)=exp(a \cdot log(t/t_0))$. It is argued that dynamics of blog entries by a specific user ought to be related to personality of each user.