Abstract
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.
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References
1. Albert, R. and Barabási, A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47-97 (2002).
2. D. J. Watts and Strogatz, Nature 393, 440 (1998).
3. P. Erdős, A. Rényi, Bull. Inst. Int. Stat. 38, 343 (1961).
4. B.A. Huberman and L.A. Adamic Nature 399, 130 (1999).
5. R. Albert, H. Jeong, and A. L. Barabási Nature 401, 130 (1999).
6. G. Caldarelli, R. Marchetti and L.Pietronero, Europhysics Letters 52, 386 (2000).
7. R. Pastor-Satorras, A. Vazquez and A. Vespignani, Phys. Rev. Lett. 87, 258701 (2001).
8. M. E. J. Newman, D. J. Watts, and S. H. Strogatz, Proc. Natl. Acad. Sci. USA 99, 2566 (2002).
9. A. L. Barabási and R. Albert, Science 286, 509 (1999)
10. G. Caldarelli, A. Capocci, P. De Los Rios and M.A. Muñoz, Phys. Rev. Lett. 89, 278701 (2002)
11. M.E.J. Newman, M. Girvan to appear in Proceedings of the XVIII Sitges Conference on Statistical Mechanic 99, 12583 (2003).
12. M.Boguna, R. Pastor-Satorras, A. Vespignani ArXiv:cond-mat/0301149).
13. M.E.J. Newman Phys. Rev. E 67, 026126 (2003).
14. G. Bianconi and A.-L. Barabási Europhysics Letters 54, 436 (2001).
15. G. Caldarelli, A. Capocci, P. De Los Rios and M.A. Muñoz, Physical Review Letters 89, 258702 (2002).
16. D.S. Callaway, J.E. Hopcroft, J.M. Kleinberg, M.E.J. Newman and S.H. Strogatz Phys.Rev.E 64, 041902 (2001).
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).
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).
19. M. E. J. Newman, Assortative mixing in networks, Phys. Rev. Lett. 89, 208701 (2002).
20. M. E. J. Newman and Juyong Park, Why social networks are different from other types of networks, Phys. Rev. E, in press.
21. M. Catanzaro, G. Caldarelli, L. Pietronero, Assortative model for social networks, cond-mat 0308073 v1
22. Battiston, S., Bonabeau, E., Weisbuch G., Decision making dynamics in corporate boards, Physica A, 322, 567 (2003).
23. Battiston, S., Weisbuch G., Bonabeau, E., Decision spread in the corporate board network, submitted.
24. Y. J. Campbell, A. W. Lo, A. C. Mackinlay The Econometrics of Financial Markets, (Princeton University Press, Princeton,1997) and references therein.
25. N Vandewalle, F Brisbois and X Tordoir Quantitative Finance 1, 372 (2001).
26. K. V. Mardia, J. T. Kent and J. M. Bibby Multivariate Analisys, (CA: Academic, San Diego, 1979).
27. J. C. Gower, Biometrika 53, 325 (1966).
28. R. N. Mantegna, Eur. Phys. J. B 11, 193 (1999).
29. V. Batagelj, A. Mrvar: Pajek – Program for Large Network Analysis. Connections, 21(1998)2, 47-57. Home page for downloads: http://vlado.fmf.uni-lj.si/pub/networks/pajek/
30. G. Bonanno, F. Lillo and R. N. Mantegna, Quantitative Finance 1, 96 (2001).
31. R. N. Mantegna and H. E. Stanley An introduction to econophysics: correlations and complexity in finance (Cambridge University press, Cambridge, 2000).
32. The Standard Industrial Classification system can be found at http://www.osha.gov/oshstats/naics-manual.html
33. L. Laloux, P. Cizeau, J. P. Bouchaud and M. Potters, Phys. Rev. Letters 83, 1467 (1999).
34. V. Plerou, P. Gopikrishnan, B. Rosenow, L. A. Nunes Amaral and H. E. Stanley, Phys. Rev. Lett. 83, 1471 (1999).
35. I. Rodriguez-Iturbe and A. Rinaldo, Fractal River Basins, (Cambridge University Press, Cambridge, 1997).
36. J.-P. Onnela, A. Chackraborti, K. Kaski, J. Kertész ArXiv:cond-mat/0303579 and ArXiv:cond-mat/0302546
37. M. D. Penrose, The Annals of Probability 24, 1903 (1996).
38. T.E. Harris, The Theory of Branching Processes (Dover, New York, 1989).
39. V. Pareto Cours d’Économie Politique (Macmillan, London, 1897). Reprinted in Oeuvres Complétes (Droz, Geneva, 1965).
40. W.W. Badger, Mathematical models as a tool for the social science (Gordon and Breach, New York, 1980).
41. C. Dagum, & M. Zenga, (eds.) Income and Wealth Distribution, Inequality and Poverty (Springer-Verlag, Berlin, 1990).
42. J. J. Persky, Pareto’s law. Journal of Economic Perspectives 6, 181-192 (1992).
43. Yook, S. H., Jeong, H., Barabási, A.-L. and Tu, Y. Weighted evolving networks. Phys. Rev. Lett. 86, 5835-5838 (2001).
44. H. Markovitz, Portfolio Selection: Efficient Diversification of Investments (Wiley, New York, 1959).
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Caldarelli, G., Battiston, S., Garlaschelli, D., Catanzaro, M. Emergence of Complexity in Financial Networks. In: Ben-Naim, E., Frauenfelder, H., Toroczkai, Z. (eds) Complex Networks. Lecture Notes in Physics, vol 650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44485-5_18
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