Empirical analysis of web-based user-object bipartite networks

Understanding the structure and evolution of web-based user-object networks is a significant task since they play a crucial role in e-commerce nowadays. This Letter reports the empirical analysis on two large-scale web sites, audioscrobbler.com and del.icio.us, where users are connected with music groups and bookmarks, respectively. The degree distributions and degreedegree correlations for both users and objects are reported. We propose a new index, named collaborative clustering coefficient, to quantify the clustering behavior based on the collaborative selection. Accordingly, the clustering properties and clustering-degree correlations are investigated. We report some novel phenomena well characterizing the selection mechanism of web users and outline the relevance of these phenomena to the information recommendation problem. Introduction. – The last decade has witnessed tremendous activities devoted to the understanding of complex networks [1–5]. A particular class of networks is the bipartite networks, whose nodes are divided into two sets X and Y , and only the connection between two nodes in different sets is allowed. Many systems are naturally modeled as bipartite networks [6]: the human sexual network [7] consists of men and women, the metabolic network [8] consists of chemical substances and chemical reactions, the collaboration network [9] consists of acts and actors, the Internet telephone network consists of personal computers and phone numbers [10], etc. In addition to the empirical analysis on the above-mentioned bipartite networks, great effort has been made in how to characterize bipartite networks [11–13], how to project bipartite networks into monopartite networks [14–16] and how to model bipartite networks [17–20]. An important class of bipartite networks is the webbased user-object networks, which play the central role in e-commerce for many online selling sites and online services sites [21]. This class of networks has two specific evolving mechanisms different from the well-understood act-actor bipartite networks and human sexual networks. Firstly, connections between existent users and objects are (a)Corresponding author: [email protected] Fig. 1: (Color online) Illustration of a small user-object bipartite network. generated moment by moment while this does not happen in act-actor networks (e.g., one can not add authors to a scientific paper after its publication). Secondly, users are active (to select) while objects are passive (to be selected). This is different from the human sexual networks where in principle both men and women are active. In