Random hypergraphs and their applications

TL;DR

This paper introduces a mathematical model of tripartite social networks called random hypergraphs, enabling exact property calculations and comparison with real folksonomies like Flickr, revealing insights into tagging behaviors.

Contribution

It presents a novel hypergraph-based model for tripartite social networks and demonstrates how to analyze their properties mathematically.

Findings

Model matches some properties of Flickr folksonomy

Multiple tagging affects network structure

Exact calculations are possible for large networks

Abstract

In the last few years we have witnessed the emergence, primarily in on-line communities, of new types of social networks that require for their representation more complex graph structures than have been employed in the past. One example is the folksonomy, a tripartite structure of users, resources, and tags -- labels collaboratively applied by the users to the resources in order to impart meaningful structure on an otherwise undifferentiated database. Here we propose a mathematical model of such tripartite structures which represents them as random hypergraphs. We show that it is possible to calculate many properties of this model exactly in the limit of large network size and we compare the results against observations of a real folksonomy, that of the on-line photography web site Flickr. We show that in some cases the model matches the properties of the observed network well, while in others there are significant differences, which we find to be attributable to the practice of multiple tagging, i.e., the application by a single user of many tags to one resource, or one tag to many resources.