Detecting Motifs in Multiplex Corporate Networks

Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 689)

Abstract

The main topic of this paper is the discovery of motifs in multiplex corporate networks. Network motifs are small subgraphs occurring at significantly higher numbers than in similar random networks. They can be seen as the building blocks of a complex network. In real-world network data, multiple types of (possibly overlapping) relationships may be present among the nodes, forming so-called multiplex networks. Detecting motifs in such networks is difficult, as existing subgraph enumeration algorithms are not directly applicable to multiplex network data. In addition, the selection of a proper multiplex null model to test the significance of the enumerated subgraphs is nontrivial. This paper addresses these two problems, resulting in three contributions. First, we present a method based on layer encoding for adequately handling the multiplex aspect in subgraph enumeration. Second, a null model is proposed that is able to preserve the relationship between the different types of links, taking into account that a particular link type may be the result of a projection from a bipartite network. Finally, we perform experiments on corporate network data from Germany, in which around \(75\,000\) nodes represent corporations and roughly \(195\,000\) links represent connectedness of firms based on shared board members and ownership. We demonstrate how incorporating the multiplex aspect in motif detection is able to reveal new insights that could not be obtained by studying only one type of relationship. Furthermore, results uncover how the financial sector is over-represented in the more complex motifs, hinting at a surprisingly prominent role of the financial sector in the largely industry-oriented corporate network of Germany.

Notes

Acknowledgements

The first author is supported by funding from the European Research Council (ERC) under the EU Horizon 2020 research and innovation programme (grant agreement 638946). Thanks to the CORPNET group (http://corpnet.uva.nl) for useful suggestions.

References

  1. 1.
    Adams, M.: Cross holdings in Germany. J. Inst. Theor. Econ. 155(1), 80–109 (1999)Google Scholar
  2. 2.
    Alon, U.: Network motifs: theory and experimental approaches. Nat. Rev. Genet. 8(6), 450–461 (2007)CrossRefGoogle Scholar
  3. 3.
    Barabási, A.L.: Network Science. Cambridge University Press (2016)Google Scholar
  4. 4.
    Battiston, F., Nicosia, V., Chavez, M., Latora, V.: Multilayer motif analysis of brain networks. Chaos Interdiscip. J. Nonlinear Sci. 27(4), article 047,404 (2017)Google Scholar
  5. 5.
    Bender, E.A., Canfield, E.R.: The asymptotic number of labeled graphs with given degree sequences. J. Comb. Theory Ser. A 24(3), 296–307 (1978)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Benson, A.R., Gleich, D.F., Leskovec, J.: Higher-order organization of complex networks. Science 353(6295), 163–166 (2016)CrossRefGoogle Scholar
  7. 7.
    Boccaletti, S., Bianconi, G., Criado, R., Del Genio, M., Sendiña-Nadal, I., Wang, Z., Zanin, M.: The structure and dynamics of multilayer networks. Phys. Rep. 544(1), 1–122 (2014)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Dickison, M.E., Magnani, M., Rossi, L.: Multilayer Social Networks. Cambridge University Press (2016)Google Scholar
  9. 9.
    Fohlin, C.: The rise of interlocking directorates in imperial Germany. Econ. Hist. Rev. 52(2), 307–333 (1999)CrossRefGoogle Scholar
  10. 10.
    Garcia-Bernardo, J., Fichtner, J., Takes, F.W., Heemskerk, E.M.: Uncovering offshore financial centers: conduits and sinks in the global corporate ownership network. Sci. Rep. 7, 6246 (2017)CrossRefGoogle Scholar
  11. 11.
    Garcia-Bernardo, J., Takes, F.W.: The effects of data quality on the analysis of corporate board interlock networks (2017). arXiv: 1612.01510
  12. 12.
    Ghazizadeh, S., Chawathe, S.S.: SEuS: Structure extraction using summaries. In: Proceedings of the International Conference on Discovery Science, pp. 71–85 (2002)Google Scholar
  13. 13.
    Haiyan, H., Xifeng, Y., Jiawei, H., Jasmine, Z.X.: Mining coherent dense subgraphs across massive biological networks for functional discovery. Bioinformatics 21(1), 213–221 (2005)Google Scholar
  14. 14.
    Heemskerk, E.M., Takes, F.W.: The corporate elite community structure of global capitalism. New Polit. Econ. 21(1), 90–118 (2016)CrossRefGoogle Scholar
  15. 15.
    Kivelä, M., Arenas, A., Barthelemy, M., Gleeson, J.P., Moreno, Y., Porter, M.A.: Multilayer networks. J. Complex Netw. 2(3), 203–271 (2014)CrossRefGoogle Scholar
  16. 16.
    Märtens, M., Meier, J., Hillebrand, A., Tewarie, P., Van Mieghem, P.: Brain network clustering with information flow motifs. Appl. Netw. Sci. 2(1), 25 (2017)CrossRefGoogle Scholar
  17. 17.
    McKay, B.D., Piperno, A.: Practical graph isomorphism, II. J. Symb. Comput. 60, 94–112 (2014)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., Alon, U.: Network motifs: Simple building blocks of complex networks. Science 298(5594), 824–827 (2002)CrossRefGoogle Scholar
  19. 19.
    Mizruchi, M.S.: What do interlocks do? An analysis, critique, and assessment of research on interlocking directorates. Annu. Rev. Soc. 22(1), 271–298 (1996)CrossRefGoogle Scholar
  20. 20.
    Ohnishi, T., Takayasu, H., Takayasu, M.: Network motifs in an inter-firm network. J. Econ. Interact. Coord. 5(2), 171–180 (2010)CrossRefMATHGoogle Scholar
  21. 21.
    Ribeiro, P., Silva, F.: G-tries: An efficient data structure for discovering network motifs. In: Proceedings of the ACM Symposium on Applied Computing, pp. 1559–1566 (2010)Google Scholar
  22. 22.
    Saeed, S., Saeed, J.: Fast parallel all-subgraph enumeration using multicore machines. Sci. Program. 2015, 901,321 (2015)Google Scholar
  23. 23.
    Solé-Ribalta, A., De Domenico, M., Arenas, A.: Centrality rankings in multiplex networks. In: Proceedings of the International Conference on Web Science, pp. 149–155 (2014)Google Scholar
  24. 24.
    Takes, F.W., Heemskerk, E.M.: Centrality in the global network of corporate control. Soc. Netw. Anal. Min. 6(1), 97 (2016)CrossRefGoogle Scholar
  25. 25.
    Vitali, S., Glattfelder, J.B., Battiston, S.: The network of global corporate control. PloS one 6(10), e25,995 (2011)Google Scholar
  26. 26.
    Wernicke, S.: A faster algorithm for detecting network motifs. In: Proceedings of the Workshop on Algorithms in Bioinformatics, pp. 165–177 (2005)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Frank W. Takes
    • 1
    • 2
  • Walter A. Kosters
    • 2
  • Boyd Witte
    • 2
  1. 1.CORPNET Research Group (AISSR)University of AmsterdamAmsterdamNetherlands
  2. 2.Leiden Institute of Advanced Computer Science (LIACS)Leiden UniversityLeidenNetherlands

Personalised recommendations