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Bootstrapping topology and systemic risk of complex network using the fitness model

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  • Nicol\'o Musmeci
  • Stefano Battiston
  • Guido Caldarelli
  • Michelangelo Puliga
  • Andrea Gabrielli

Abstract

We present a novel method to reconstruct complex network from partial information. We assume to know the links only for a subset of the nodes and to know some non-topological quantity (fitness) characterising every node. The missing links are generated on the basis of the latter quan- tity according to a fitness model calibrated on the subset of nodes for which links are known. We measure the quality of the reconstruction of several topological properties, such as the network density and the degree distri- bution as a function of the size of the initial subset of nodes. Moreover, we also study the resilience of the network to distress propagation. We first test the method on ensembles of synthetic networks generated with the Exponential Random Graph model which allows to apply common tools from statistical mechanics. We then test it on the empirical case of the World Trade Web. In both cases, we find that a subset of 10 % of nodes is enough to reconstruct the main features of the network along with its resilience with an error of 5%.

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Paper provided by arXiv.org in its series Papers with number 1209.6459.

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Date of creation: Sep 2012
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Handle: RePEc:arx:papers:1209.6459

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  1. Hans Degryse & Grégory Nguyen, 2007. "Interbank Exposures: An Empirical Examination of Contagion Risk in the Belgian Banking System," International Journal of Central Banking, International Journal of Central Banking, International Journal of Central Banking, vol. 3(2), pages 123-171, June.
  2. Battiston, Stefano & Delli Gatti, Domenico & Gallegati, Mauro & Greenwald, Bruce & Stiglitz, Joseph E., 2012. "Liaisons dangereuses: Increasing connectivity, risk sharing, and systemic risk," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1121-1141.
  3. Lelyveld, Iman van & Liedorp, Franka, 2006. "Interbank Contagion in the Dutch Banking Sector: A Sensitivity Analysis," MPRA Paper 806, University Library of Munich, Germany.
  4. Giorgio Fagiolo, 2009. "The International-Trade Network: Gravity Equations and Topological Properties," Papers 0908.2086, arXiv.org.
  5. Diego Garlaschelli & Stefano Battiston & Maurizio Castri & Vito D. P. Servedio & Guido Caldarelli, 2003. "The scale-free topology of market investments," Papers cond-mat/0310503, arXiv.org, revised Dec 2004.
  6. G. De Masi & G. Iori & G. Caldarelli, 2006. "A fitness model for the Italian Interbank Money Market," Papers physics/0610108, arXiv.org.
  7. Galluccio, S. & Caldarelli, G. & Marsili, M. & Zhang, Y.-C., 1997. "Scaling in currency exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 423-436.
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