Growing network model for community with group structure

TL;DR

This paper introduces a new model for growing communities with group structures, analyzing how groups and activity distributions evolve, supported by empirical data from online communities.

Contribution

It presents a novel growing network model incorporating group formation, with analytical and numerical analysis, and validates findings using real-world online community data.

Findings

Group size distribution follows a power law.

Activity distribution can be exponential or power law.

Empirical data confirms power law distribution of group sizes.

Abstract

We propose a growing network model for a community with a group structure. The community consists of individual members and groups, gatherings of members. The community grows as a new member is introduced by an existing member at each time step. The new member then creates a new group or joins one of the groups of the introducer. We investigate the emerging community structure analytically and numerically. The group size distribution shows a power law distribution for a variety of growth rules, while the activity distribution follows an exponential or a power law depending on the details of the growth rule. We also present an analysis of empirical data from on the online communities, the ``Groups'' in \url{http://www.yahoo.com} and the ``Cafe'' in \url{http://www.daum.net}, which shows a power law distribution for a wide range of group sizes.