# The scale-free topology of market investments

## Author Info

• Diego Garlaschelli
• Stefano Battiston
• Maurizio Castri
• Vito D. P. Servedio
• Guido Caldarelli

## Abstract

We propose a network description of large market investments, where both stocks and shareholders are represented as vertices connected by weighted links corresponding to shareholdings. In this framework, the in-degree ($k_{in}$) and the sum of incoming link weights ($v$) of an investor correspond to the number of assets held (\emph{portfolio diversification}) and to the invested wealth (\emph{portfolio volume}) respectively. An empirical analysis of three different real markets reveals that the distributions of both $k_{in}$ and $v$ display power-law tails with exponents $\gamma$ and $\alpha$. Moreover, we find that $k_{in}$ scales as a power-law function of $v$ with an exponent $\beta$. Remarkably, despite the values of $\alpha$, $\beta$ and $\gamma$ differ across the three markets, they are always governed by the scaling relation $\beta=(1-\alpha)/(1-\gamma)$. We show that these empirical findings can be reproduced by a recent model relating the emergence of scale-free networks to an underlying Paretian distribution of `hidden' vertex properties.

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File URL: http://arxiv.org/pdf/cond-mat/0310503

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number cond-mat/0310503.

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Date of revision: Dec 2004
Publication status: Published in Physica A 350 (2-4), 491-499 (2005)
Handle: RePEc:arx:papers:cond-mat/0310503

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Web page: http://arxiv.org/

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## Citations

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Cited by:
1. Yang, Chunxia & Chen, Yanhua & Niu, Lei & Li, Qian, 2014. "Cointegration analysis and influence rank—A network approach to global stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 400(C), pages 168-185.
2. Iori, Giulia & De Masi, Giulia & Precup, Ovidiu Vasile & Gabbi, Giampaolo & Caldarelli, Guido, 2008. "A network analysis of the Italian overnight money market," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 259-278, January.
3. Nicol\'o Musmeci & Stefano Battiston & Guido Caldarelli & Michelangelo Puliga & Andrea Gabrielli, 2012. "Bootstrapping topology and systemic risk of complex network using the fitness model," Papers 1209.6459, arXiv.org.
4. Stefania Vitali & Stefano Battiston, 2013. "The Community Structure of the Global Corporate Network," Papers 1301.2363, arXiv.org.
5. Ilaria Bordino & Stefano Battiston & Guido Caldarelli & Matthieu Cristelli & Antti Ukkonen & Ingmar Weber, 2011. "Web search queries can predict stock market volumes," Papers 1110.4784, arXiv.org, revised Jun 2012.
6. De Masi, G. & Giovannetti, G. & Ricchiuti, G., 2013. "Network analysis to detect common strategies in Italian foreign direct investment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1202-1214.
7. Giulia Rotundo & Anna D’Arcangelis, 2014. "Network of companies: an analysis of market concentration in the Italian stock market," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(4), pages 1893-1910, July.
8. Gao, Bo & Ren, Ruo-en, 2013. "The topology of a causal network for the Chinese financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2965-2976.
9. Wang, Junjie & Zhou, Shuigeng & Guan, Jihong, 2011. "Characteristics of real futures trading networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 398-409.
10. Massimo Riccaboni & Stefano Schiavo, 2009. "The Structure and Growth of Weighted Networks," Papers 0908.0348, arXiv.org, revised Dec 2009.
11. Giulia Rotundo & Anna D’Arcangelis, 2010. "Ownership and control in shareholding networks," Journal of Economic Interaction and Coordination, Springer, vol. 5(2), pages 191-219, December.
12. Konno, Tomohiko, 2009. "Network structure of Japanese firms. Scale-free, hierarchy, and degree correlation: analysis from 800,000 firms," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 3(31), pages 1-13.
13. Takayuki Mizuno & Wataru Souma & Tsutomu Watanabe, 2014. "The Structure and Evolution of Buyer-Supplier Networks," UTokyo Price Project Working Paper Series 019, University of Tokyo, Graduate School of Economics.
14. Stefano Battiston & Jo\~ao F. Rodrigues & Hamza Zeytinoglu, 2005. "The Network of Inter-Regional Direct Investment Stocks across Europe," Papers physics/0508206, arXiv.org.
15. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2010. "Complex stock trading network among investors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4929-4941.
16. Marco Fattore & Rosanna Grassi, 2014. "Measuring dynamics and structural change of time-dependent socio-economic networks," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(4), pages 1821-1834, July.
17. Piccardi, Carlo & Calatroni, Lisa & Bertoni, Fabio, 2010. "Communities in Italian corporate networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5247-5258.
18. Ma, Yuan-yuan & Zhuang, Xin-tian & Li, Ling-xuan, 2011. "Research on the relationships of the domestic mutual investment of China based on the cross-shareholding networks of the listed companies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 749-759.

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