Random hypergraphs and their applications

Understand

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.