Quality & Quantity

, Volume 49, Issue 4, pp 1585–1595 | Cite as

A multiple network approach to corporate governance

  • Fausto Bonacina
  • Marco D’ErricoEmail author
  • Enrico Moretto
  • Silvana Stefani
  • Anna Torriero
  • Giovanni Zambruno


In this work, we consider corporate governance (CG) ties among companies from a multiple network perspective. Such a structure naturally arises from the close interrelation between the Shareholding network and the Board of Directors network. In order to capture the simultaneous effects of both networks on CG, we propose to model the CG multiple network structure via tensor analysis. In particular, we consider the TOPHITS model, based on the PARAFAC tensor decomposition, to show that tensor techniques can be successfully applied in this context. By providing some empirical results from the Italian financial market in the univariate case, we then show that a tensor–based multiple network approach can reveal important information.


Multiple networks Tensor analysis Corporate governance 



We would like to thank the anonymous referees for their valuable comments and suggestions which helped us to improve the manuscript.


  1. Andersson, C.A., Bro, R.: The N-way toolbox for MATLAB. Chemom. Intell. Lab. Syst. 52(1), 1–4 (2000)CrossRefGoogle Scholar
  2. Bader, B.W., Kolda, T.G., et al.: MATLAB Tensor Toolbox Version 2.5. tgkolda/TensorToolbox/ (2012). Jan 2012
  3. Barrat, A., Barthélemy, M., Vespignani, A.: Dynamical Processes on Complex Networks, 4th edn. Cambridge University Press, Cambridge (2011)Google Scholar
  4. Battiston, F., Nicosia, V., Latora, V.: Structural measures for multiplex networks. Phys. Rev. E 89, 032804 (2014)CrossRefGoogle Scholar
  5. Battiston, S., Catanzaro, M.: Statistical properties of corporate board and director networks. Eur. Phys. J. B 38, 345–352 (2004)CrossRefGoogle Scholar
  6. Bertoni, F., Randone, P.A.: The small-world of Italian finance: ownership interconnections and board interlocks amongst Italian listed companies. Working paper (2006)Google Scholar
  7. Bianchi, M., Bianco, M.: Italian corporate governance in the last 15 years: from pyramids to coalitions?. Finance working paper No 144. European corporate governance institute (2006)Google Scholar
  8. Bianco, M., Casavola, P.: Italian corporate governance: effects on financial structure and firm performance. Eur. Econ. Rev. 43(4), 1057–1069 (1999)CrossRefGoogle Scholar
  9. Bianconi, G.: Statistical mechanics of multiplex networks: entropy and overlap. Phys. Rev. E 87, 062806 (2013)CrossRefGoogle Scholar
  10. Menichetti, G., Remondini, D., Panzarasa, P., Mondragón, R. J., Bianconi, G., Weighted multiplex networks arXiv:1312.6720 (2013)
  11. Bonacich, P.: Power and centrality: a family of measures. Am. J. Sociol. 92(5), 1170–1182 (1987)CrossRefGoogle Scholar
  12. Bro, R., Kiers, H.A.L.: A new efficient method for determining the number of components in PARAFAC models. J. Chemom. 17, 274–286 (2003)CrossRefGoogle Scholar
  13. Cohen, R., Havlin, S.: Complex Networks: Structure, Robustness and Function. Cambridge University Press, Cambridge (2010)CrossRefGoogle Scholar
  14. D’Errico, M., Grassi, R., Stefani, S., Torriero, A.: Shareholding networks and centrality: an application to the Italian financial market. Lect. Notes Econ. Math. Syst. 613, 215–228 (2009)Google Scholar
  15. D’Errico, M., Stefani, S., Torriero, A. Informal ties in organizations: a case study. Qual. Quant. pp. 1–15 (2013). Article in Press.
  16. Estrada, E.: The Structure of Complex Networks: Theory and Applications. Oxford University Press, Oxford (2012)Google Scholar
  17. Faccio, Mara, Larry, H.P.: The ultimate ownership of Western European corporations. J. Financ. Econ. 65.3, 365–395 (2002)CrossRefGoogle Scholar
  18. Grassi, R.: Vertex centrality as a measure of information flow in Italian Corporate Board Networks. Phys. A 389(12), 2455–2464 (2010)CrossRefGoogle Scholar
  19. Harary, F.: Graph Theory. Addison-Wesley, Reading (1969)Google Scholar
  20. Harshman, R.A.: Foundations of the PARAFAC procedure: models and conditions for an “explanatory” multimodal factor analysis. UCLA Working papers in phonetics 16, 1–84 (1970)Google Scholar
  21. Kleinberg, J.M.: Authoritative sources in a hyperlinked environment. J. ACM 46(5), 604–632 (1999)CrossRefGoogle Scholar
  22. Kolda, T.G., Bader, B.W., Kenny, J.P.: Higher-order web link analysis using multilinear algebra, SANDIA REPORT, SAND2005-4548 (2005)Google Scholar
  23. Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455–500 (2009)CrossRefGoogle Scholar
  24. Perra, N., Fortunato, S.: Spectral centrality measures in complex networks. Phys. Rev. E 78, 036107 (2008)CrossRefGoogle Scholar
  25. Piccardi, C., Calatroni, L., Bertoni, F., Communities in Italian corporate networks. Phys. A: Stat. Mech. Appl. 389(22), pp. 5247–5258 (2010). ISSN 0378–4371,
  26. Rotundo, G., D’Arcangelis, A.M.: Network of companies: an analysis of market concentration in the Italian stock market. Qual. Quant. 1–18 (in press, 2013).Google Scholar
  27. Santella, P., Drago, C., Polo, A., Gagliardi E.: A Comparison among the director networks in the main listed companies in France, Germany, Italy, and the United Kingdom. MPRA Paper No. 16397 (2009)Google Scholar
  28. Solà L., Romance M., Criado R., Flores J., Garcia Del Amo A., Boccaletti S.: Centrality of nodes in multiplex networks. arXiv:1305.7445v1 (2013).
  29. Tucker, L.R.: Implications of factor analysis of three-way matrices for measurement of change. In: Harris, C.W. (ed.) Problems in Measuring Change, pp. 122–137. University of Wisconsin Press, Madison (1963)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Fausto Bonacina
    • 1
  • Marco D’Errico
    • 1
    Email author
  • Enrico Moretto
    • 2
  • Silvana Stefani
    • 1
  • Anna Torriero
    • 3
  • Giovanni Zambruno
    • 1
  1. 1.Department of Statistics and Quantitative MethodsUniversity of Milano – BicoccaMilanItaly
  2. 2.Department of EconomicsUniversity of Insubria, Varese and CNR–IMATIMilanItaly
  3. 3.Department of Mathematics, Quantitative Finance and EconometricsCatholic UniversityMilanItaly

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