title: Hypergraph topological quantities for tagged social networks.
abstract: Recent years have witnessed the emergence of a new class of social networks, which require us to move beyond previously employed representations of complex graph structures. A notable example is that of the folksonomy, an online process where users collaboratively employ tags to resources to impart structure to an otherwise undifferentiated database. In a recent paper, we proposed a mathematical model that represents these structures as tripartite hypergraphs and defined basic topological quantities of interest. In this paper, we extend our model by defining additional quantities such as edge distributions, vertex similarity and correlations as well as clustering. We then empirically measure these quantities on two real life folksonomies, the popular online photo sharing site Flickr and the bookmarking site CiteULike. We find that these systems share similar qualitative features with the majority of complex networks that have been previously studied. We propose that the quantities and methodology described here can be used as a standard tool in measuring the structure of tagged networks.
authors.affiliation: CNR-INFM Centro SMC Dipartimento di Fisica, Università di Roma Sapienza, Piazzale A Moro 5, 00185 Roma, Italy.
authors.forename: Vinko
authors.initials: V
authors.lastname: Zlatić
authors.forename: Gourab
authors.initials: G
authors.lastname: Ghoshal
authors.forename: Guido
authors.initials: G
authors.lastname: Caldarelli
mesh_terms: D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D011157:Population Dynamics; D012944:Social Support