A fixed degree sequence model for the one-mode projection of multiplex bipartite graphs

Abstract

A bipartite structure is a common property of many real-world network data sets such as agents which are affiliated with societies, customers who buy, rent, or rate products, and authors who write scientific papers. The one-mode projection of these networks onto either set of entities (e.g., societies, products, and articles) is a well-established approach for the analysis of such data and deduces relations between these entities. Some bipartite data sets of key importance contain several distinct types of relations between their entities. These networks require a projection method which accounts for multiple edge types. In this article, we present the multiplex extension of an existing projection algorithm for simplex bipartite networks, i.e., networks that contain a single type of relation. We use synthetic data to show the robustness of our method before applying it to a real-world network of user ratings for films, namely, the Netflix data set. Based on the assumption that co-ratings of films contain information about the films’ similarity, we analyse the multiplex projection as an approximation of the similarity landscape of the films. Besides comparing the projection to the coarse-grained classification of films into genres, we validate the resulting similarities based on ground truth data sets containing film series. Our analysis confirms the predictive power of the network of positive co-ratings. We furthermore explore the potential of additional, mixed co-rating patterns in improving the prediction of similarities and highlight necessary criteria for this approach.