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.

Detecting Communities in K-Partite K-Uniform (Hyper)Networks

“…Zlatić et al discussed hyperedge distributions, node similarity, and correlations [7] . Cattuto et al studied path length, clustering coefficient, and node connectivity [44] .…”

“…Take a (user, tag, resource) hypernetwork as an example. In Zlatić's method [7] , they reduce the hypernetwork to three unipartite networks respectively for users, tags and resources based on a node similarity measure, and then use bottom-up optimization algorithm in each of the unipartite networks; in Neubauer's method [8] , they reduce the hypernetwork to a user-tag 2, 2 -network, a user-resource 2, 2 -network and a tag-resource 2, 2 -network to formulate an extended modularity and then apply modularity optimization algorithm. In Lu's method [9] , they decompose the 3-way (user, tag, resource) hyperedge into pairwise user-tag, user-resource, and tag-resource edges to build a user-tag-resource 3,2 -network, and then employ K-means algorithm.…”

“…As for community detection in K, K -(hyper)networks, a common strategy is to reduce a K, K -(hyper)network to simpler unipartite networks [6][7] , 2, 2 -networks [8] , or K, 2 -networks [9] . One major drawback of this strategy is that some valuable information of the original (hyper)network is lost during reduction [10] , and the subsequently detected communities are less accurate.…”

Hierarchical networks of scientific journals

“…In some cases, these phenomena are referred to as collaborative tagging (Lambiotte and Ausloos, 2006;Cattuto et al, 2007;Cattuto et al, 2009;Floeck et al, 2011), and the resultant large collections of tags are referred to as folksonomies, highlighting their collaborative origin and the "flat" organization of the tags in these systems (Mika, 2005;Lambiotte and Ausloos, 2006;Spyns et al, 2006;Cattuto et al, 2007Cattuto et al, , 2009Voss, 2007;Tibély et al, 2012). The natural mathematical representation of tagging systems is given by hypergraphs Zlatić et al, 2009).…”

Self-organization in social tagging systems

“…Mathematically, tagging systems are composed of fundamental units of userresource-tag triples [5,7,8], and each tagging action con- * chbyeung@gmail.com † zhangzike@gmail.com stitutes one or several hyper-links in a tripartite graph. Such user-resource-tag relations are often referred to as folksonomy.…”