Emergence of Complexity in Financial Networks

  • Guido Caldarelli
  • Stefano Battiston
  • Diego Garlaschelli
  • Michele Catanzaro
Part III Information Networks & Social Networks
Part of the Lecture Notes in Physics book series (LNP, volume 650)


We present here a brief summary of the various possible applications of network theory in the field of finance. Since we want to characterize different systems by means of simple and universal features, graph theory could represent a rather powerful methodology. In the following we report our activity in three different subfields, namely the board and director networks, the networks formed by prices correlations and the stock ownership networks. In most of the cases these three kind of networks display scale-free properties making them interesting in their own. Nevertheless, we want to stress here that the main utility of this methodology is to provide new measures of the real data sets in order to validate the different models.


Degree Distribution Minimal Span Tree Director Network Preferential Attachment Random Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1. Albert, R. and Barabási, A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47-97 (2002).Google Scholar
  2. 2. D. J. Watts and Strogatz, Nature 393, 440 (1998).Google Scholar
  3. 3. P. Erdős, A. Rényi, Bull. Inst. Int. Stat. 38, 343 (1961).Google Scholar
  4. 4. B.A. Huberman and L.A. Adamic Nature 399, 130 (1999).Google Scholar
  5. 5. R. Albert, H. Jeong, and A. L. Barabási Nature 401, 130 (1999).Google Scholar
  6. 6. G. Caldarelli, R. Marchetti and L.Pietronero, Europhysics Letters 52, 386 (2000).Google Scholar
  7. 7. R. Pastor-Satorras, A. Vazquez and A. Vespignani, Phys. Rev. Lett. 87, 258701 (2001).Google Scholar
  8. 8. M. E. J. Newman, D. J. Watts, and S. H. Strogatz, Proc. Natl. Acad. Sci. USA 99, 2566 (2002).Google Scholar
  9. 9. A. L. Barabási and R. Albert, Science 286, 509 (1999)Google Scholar
  10. 10. G. Caldarelli, A. Capocci, P. De Los Rios and M.A. Muñoz, Phys. Rev. Lett. 89, 278701 (2002)Google Scholar
  11. 11. M.E.J. Newman, M. Girvan to appear in Proceedings of the XVIII Sitges Conference on Statistical Mechanic 99, 12583 (2003).Google Scholar
  12. 12. M.Boguna, R. Pastor-Satorras, A. Vespignani ArXiv:cond-mat/0301149).Google Scholar
  13. 13. M.E.J. Newman Phys. Rev. E 67, 026126 (2003).Google Scholar
  14. 14. G. Bianconi and A.-L. Barabási Europhysics Letters 54, 436 (2001).Google Scholar
  15. 15. G. Caldarelli, A. Capocci, P. De Los Rios and M.A. Muñoz, Physical Review Letters 89, 258702 (2002).Google Scholar
  16. 16. D.S. Callaway, J.E. Hopcroft, J.M. Kleinberg, M.E.J. Newman and S.H. Strogatz Phys.Rev.E 64, 041902 (2001).Google Scholar
  17. 17. Davis, G.F., Yoo, M., Baker, W.E., The small world of the American corporate elite, 1982-2001, Strategic Organization 1: 301-326 (2003).Google Scholar
  18. 18. M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Random graphs with arbitrary degree distributions and their applications, Phys. Rev. E 64, 026118 (2001).Google Scholar
  19. 19. M. E. J. Newman, Assortative mixing in networks, Phys. Rev. Lett. 89, 208701 (2002).Google Scholar
  20. 20. M. E. J. Newman and Juyong Park, Why social networks are different from other types of networks, Phys. Rev. E, in press.Google Scholar
  21. 21. M. Catanzaro, G. Caldarelli, L. Pietronero, Assortative model for social networks, cond-mat 0308073 v1Google Scholar
  22. 22. Battiston, S., Bonabeau, E., Weisbuch G., Decision making dynamics in corporate boards, Physica A, 322, 567 (2003).Google Scholar
  23. 23. Battiston, S., Weisbuch G., Bonabeau, E., Decision spread in the corporate board network, submitted.Google Scholar
  24. 24. Y. J. Campbell, A. W. Lo, A. C. Mackinlay The Econometrics of Financial Markets, (Princeton University Press, Princeton,1997) and references therein.Google Scholar
  25. 25. N Vandewalle, F Brisbois and X Tordoir Quantitative Finance 1, 372 (2001).Google Scholar
  26. 26. K. V. Mardia, J. T. Kent and J. M. Bibby Multivariate Analisys, (CA: Academic, San Diego, 1979).Google Scholar
  27. 27. J. C. Gower, Biometrika 53, 325 (1966).Google Scholar
  28. 28. R. N. Mantegna, Eur. Phys. J. B 11, 193 (1999).Google Scholar
  29. 29. V. Batagelj, A. Mrvar: Pajek – Program for Large Network Analysis. Connections, 21(1998)2, 47-57. Home page for downloads: Scholar
  30. 30. G. Bonanno, F. Lillo and R. N. Mantegna, Quantitative Finance 1, 96 (2001).Google Scholar
  31. 31. R. N. Mantegna and H. E. Stanley An introduction to econophysics: correlations and complexity in finance (Cambridge University press, Cambridge, 2000).Google Scholar
  32. 32. The Standard Industrial Classification system can be found at Scholar
  33. 33. L. Laloux, P. Cizeau, J. P. Bouchaud and M. Potters, Phys. Rev. Letters 83, 1467 (1999).Google Scholar
  34. 34. V. Plerou, P. Gopikrishnan, B. Rosenow, L. A. Nunes Amaral and H. E. Stanley, Phys. Rev. Lett. 83, 1471 (1999).Google Scholar
  35. 35. I. Rodriguez-Iturbe and A. Rinaldo, Fractal River Basins, (Cambridge University Press, Cambridge, 1997).Google Scholar
  36. 36. J.-P. Onnela, A. Chackraborti, K. Kaski, J. Kertész ArXiv:cond-mat/0303579 and ArXiv:cond-mat/0302546Google Scholar
  37. 37. M. D. Penrose, The Annals of Probability 24, 1903 (1996).Google Scholar
  38. 38. T.E. Harris, The Theory of Branching Processes (Dover, New York, 1989).Google Scholar
  39. 39. V. Pareto Cours d’Économie Politique (Macmillan, London, 1897). Reprinted in Oeuvres Complétes (Droz, Geneva, 1965).Google Scholar
  40. 40. W.W. Badger, Mathematical models as a tool for the social science (Gordon and Breach, New York, 1980).Google Scholar
  41. 41. C. Dagum, & M. Zenga, (eds.) Income and Wealth Distribution, Inequality and Poverty (Springer-Verlag, Berlin, 1990).Google Scholar
  42. 42. J. J. Persky, Pareto’s law. Journal of Economic Perspectives 6, 181-192 (1992).Google Scholar
  43. 43. Yook, S. H., Jeong, H., Barabási, A.-L. and Tu, Y. Weighted evolving networks. Phys. Rev. Lett. 86, 5835-5838 (2001).Google Scholar
  44. 44. H. Markovitz, Portfolio Selection: Efficient Diversification of Investments (Wiley, New York, 1959).Google Scholar

Authors and Affiliations

  • Guido Caldarelli
    • 1
  • Stefano Battiston
    • 2
  • Diego Garlaschelli
    • 3
  • Michele Catanzaro
    • 1
  1. 1.INFM UdR Roma1 Dipartimento di Fisica, Università La Sapienza, P.le Moro 5, 00185 RomaItaly
  2. 2.Laboratoire de Physique, Statistique ENS, 24 rue Lhomond, 75005 ParisFrance
  3. 3.INFM UdR Siena and Dipartimento di Fisica, Università di Siena, Via Roma 56, 53100 SienaItaly

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