Latent Space Generative Model for Bipartite Networks

  • Demival Vasques FilhoEmail author
  • Dion R. J. O’Neale
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)


Generative network models are useful for understanding the mechanisms that operate in network formation and are used across several areas of knowledge. However, when it comes to bipartite networks—a class of network frequently encountered in social systems, among others—generative models are practically non-existent. Here, we propose a latent space generative model for bipartite networks growing in a hyperbolic plane. It is an extension of a model previously proposed for one-mode networks, based on a maximum entropy approach. We show that, by reproducing bipartite structural properties, such as degree distributions and small cycles, bipartite networks can be better modelled and properties of one-mode projected network can be naturally assessed.


Bipartite networks Generative models Hyperbolic geometry Maximum entropy 


  1. 1.
    Orsini, C., Dankulov, M.M., Colomer-de Simón, P., Jamakovic, A., Mahadevan, P., Vahdat, A., Bassler, K.E., Toroczkai, Z., Boguñá, M., Caldarelli, G. et al.: Quantifying randomness in real networks. Nat. Commun. 6, 8627 (2015)ADSCrossRefGoogle Scholar
  2. 2.
    Denny, M.J.: The importance of generative models for assessing network structure. Soc. Sci. Res. Net. SSRN 2798493 (2016)Google Scholar
  3. 3.
    Goldenberg, A., Zheng, A.X., Fienberg, S.E., Airoldi, E.M.: A survey of statistical network models. Found. Trends Mach. Learn. 2(2), 129–233 (2010)CrossRefGoogle Scholar
  4. 4.
    Jacobs, A.Z., Clauset, A.: A unified view of generative models for networks: models, methods, opportunities, and challenges (2014). arXiv:1411.4070Google Scholar
  5. 5.
    Vasques Filho, D. Structure and dynamics of social bipartite and projected networks. Ph.D. thesis. The University of Auckland, 2018Google Scholar
  6. 6.
    Krioukov, D., Papadopoulos, F., Vahdat, A., Boguñá, M.: Curvature and temperature of complex networks. Phys. Rev. E 80(3), 035101 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    Krioukov, D., Papadopoulos, F., Kitsak, M., Vahdat, A., Boguná, M.: Hyperbolic geometry of complex networks. Phys. Rev. E 82(3), 036106 (2010)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Papadopoulos, F., Kitsak, M., Serrano, M.A., Boguñá, M., Krioukov, D.: Popularity versus similarity in growing networks. Nature 489(7417), 537–540 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    Vasques Filho, D., O’Neale, D.R.: Bipartite networks describe R&D collaboration between institutions (2019). arXiv:1909.10977Google Scholar
  10. 10.
    Opsahl, T.: Triadic closure in two-mode networks: Redefining the global and local clustering coefficients. Soc. Netw. 35(2), 159–167 (2013)CrossRefGoogle Scholar
  11. 11.
    Erdős, P., Rényi, A.: On random graphs I. Publ. Math. Deb. 6, 290–297 (1959)Google Scholar
  12. 12.
    Erdős, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci 5(1), 17–60 (1960)Google Scholar
  13. 13.
    Vasques Filho, D., O’Neale, D. R.: Degree distributions of bipartite networks and their projections. Phys. Rev. E 98(2), 022307 (2018)ADSCrossRefGoogle Scholar
  14. 14.
    Dorogovtsev, S.N., Mendes, J.F.F., Samukhin, A.N.: Structure of growing networks with preferential linking. Phys. Rev. Lett. 85(21), 4633 (2000)ADSCrossRefGoogle Scholar
  15. 15.
    Newman, M.E.J.: Clustering and preferential attachment in growing networks. Phys. Rev. E 64(2), 025102 (2001)ADSCrossRefGoogle Scholar
  16. 16.
    Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Peruani, F., Choudhury, M., Mukherjee, A., Ganguly, N.: Emergence of a non-scaling degree distribution in bipartite networks: a numerical and analytical study. Europhys. Lett. 79(2), 28001 (2007)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Dahui, W., Li, Z., Zengru, D.: Bipartite producer–consumer networks and the size distribution of firms. Phys. A 363(2), 359–366 (2006)CrossRefGoogle Scholar
  19. 19.
    Batagelj, V., Brandes, U.: Efficient generation of large random networks. Phys. Rev. E 71(3), 036113 (2005)ADSCrossRefGoogle Scholar
  20. 20.
    Guillaume, J., Latapy, M.: Bipartite graphs as models of complex networks. Phys. A 371(2), 795–813 (2006)CrossRefGoogle Scholar
  21. 21.
    Chojnacki, S., Kłopotek, M.A.: Scale invariant bipartite graph generative model. In: nternational Joint Conferences on Security and Intelligent Information Systems. Lecture Notes in Computer Science, pp. 240–250 Springer, Berlin (2012)CrossRefGoogle Scholar
  22. 22.
    Binder, J., Koller, D., Russell, S., Kanazawa, K.: Adaptive probabilistic networks with hidden variables. Mach. Learn. 29(2–3), 213–244 (1997)CrossRefGoogle Scholar
  23. 23.
    Boguná, M., Pastor-Satorras, R.: Class of correlated random networks with hidden variables. Phys. Rev. E 68(3), 036112 (2003)ADSCrossRefGoogle Scholar
  24. 24.
    Serrano, M.A., Krioukov, D., Boguná, M.: Self-similarity of complex networks and hidden metric spaces. Phys. Rev. Lett. 100(7), 078701 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    Wu, X., Wang, W., Zheng, W.X.: Inferring topologies of complex networks with hidden variables. Phys. Rev. E 86(4), 046106 (2012)ADSCrossRefGoogle Scholar
  26. 26.
    Park, J., Newman, M.E.J.: Statistical mechanics of networks. Phys. Rev. E 70(6), 066117 (2004)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Garlaschelli, D., Di Matteo, T., Aste, T., Caldarelli, G., Loffredo, M.I.: Interplay between topology and dynamics in the world trade web. Eur. Phys. J. B 57(2), 159–164 (2007)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Safar, M., Mahdi, K., Farahat, H., Albehairy, S., Kassem, A., Alenzi, K.: Approximate cycles count in undirected graphs. Int. J. Comput. Int. Sys. 7(2), 305–311 (2014)CrossRefGoogle Scholar
  29. 29.
    Newman, M.E., Park, J.: Why social networks are different from other types of networks. Phys. Rev. E 68(3), 036122 (2003)ADSCrossRefGoogle Scholar
  30. 30.
    Larremore, D.B., Clauset, A., Jacobs, A.Z.: Efficiently inferring community structure in bipartite networks. Phys. Rev. E 90(1), 012805 (2014)ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Leibniz-Institut für Europäische GeschichteMainzGermany
  2. 2.Te Pūnaha Matatini, Department of PhysicsUniversity of AucklandAucklandNew Zealand
  3. 3.Physics DepartmentUniversity of AucklandAucklandNew Zealand
  4. 4.Te Pūnaha Matatini, Centre of Research ExcellenceAucklandNew Zealand

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