One-mode projections of multiplex bipartite graphs

Several important social network data sets have an inherent bipartite structure: for example, agents are affiliated with societies, authors write articles, customers buy, rent, or rate products. One commonly used network analytic approach to their analysis involves projecting them, i.e., deducing relations between actors of the same type (e.g. societies, articles, or products). Some of the available large scale data sets not only represent one, but several distinct relations between the same actors thereby calling for a projection method that accounts for the multiple nature of the relations. In this article we present a statistical method that properly extends a projection algorithm developed for bipartite networks containing one single type of relation. We show the stability of the proposed method on synthetic data. Then, we apply it to a real-world network of users rating films, namely a subset of the Netflix prize data set. We show that there is a gain from differentiating between the relation types. Based on the assumption that co-ratings of films contain information about the films' similarity, we analyze the co-liking and co-disliking structures obtained by the new one-mode projection. We find that the projections of concordant ratings show a high clustering coefficient while discordant co-ratings have a very small one. This result indicates that the assumption is valid and that thus the new one-mode projection can be used as basis for recommendations.