Social Network Analysis and Mining

, Volume 3, Issue 4, pp 1209–1224 | Cite as

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

  • Emőke-Ágnes HorvátEmail author
  • Katharina Anna Zweig
Original Article


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.


Bipartite graphs One-mode projection Multiplex networks 



The authors would like to thank Andreas Spitz for useful discussions, ground truth data, and software. The authors are also grateful to the anonymous reviewers for their helpful comments. EÁH is supported by the Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences, University of Heidelberg, Germany, which is funded by the German Excellence Initiative (GSC 220).


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Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.Interdisciplinary Center for Scientific ComputingUniversity of HeidelbergHeidelbergGermany
  2. 2.Technical University of KaiserslauternKaiserslauternGermany
  3. 3.Technical University of KaiserslauternKaiserslauternGermany

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