Abstract
A major problem in the study of complex socioeconomic systems is represented by privacy issues—that can put severe limitations on the amount of accessible information, forcing to build models on the basis of incomplete knowledge. In this paper we investigate a novel method to reconstruct global topological properties of a complex network starting from limited information. This method uses the knowledge of an intrinsic property of the nodes (indicated as fitness), and the number of connections of only a limited subset of nodes, in order to generate an ensemble of exponential random graphs that are representative of the real systems and that can be used to estimate its topological properties. Here we focus in particular on reconstructing the most basic properties that are commonly used to describe a network: density of links, assortativity, clustering. We test the method on both benchmark synthetic networks and real economic and financial systems, finding a remarkable robustness with respect to the number of nodes used for calibration. The method thus represents a valuable tool for gaining insights on privacy-protected systems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Clauset, A., Moore, C., Newman, M.: Hierarchical structure and the prediction of missing links in networks. Nature 453(7191), 98–101 (2008)
Mastromatteo, I., Zarinelli, E., Marsili, M.: Reconstruction of financial networks for robust estimation of systemic risk. J. Stat. Mech. Theory Exp. 2012(03), P03011 (2012)
Battiston, S., Gatti, D., Gallegati, M., Greenwald, B., Stiglitz, J.: Liaisons dangereuses: increasing connectivity, risk sharing, and systemic risk. J. Econ. Dyn. Control 36(8), 1121–1141 (2012)
Battiston, S., Puliga, M., Kaushik, R., Tasca, P., Caldarelli, G.: DebtRank: too central to fail? Financial networks, the fed and systemic risk. Sci. Rep. 2, 541 (2012)
Wells, S.: Financial interlinkages in the United Kingdom’s interbank market and the risk of contagion. Bank of England’s Working paper 230 (2004)
van Lelyveld, I., Liedorp, F.: Interbank contagion in the dutch banking sector. Int. J. Cent. Bank. 2, 99–134 (2006)
Degryse, H., Nguyen, G.: Interbank exposures: an empirical examination of contagion risk in the Belgian banking system. Int. J. Cent. Bank. 3(2), 123–171 (2007)
Mistrulli, P.: Assessing financial contagion in the interbank market: maximum entropy versus observed interbank lending patterns. J. Bank. Finance 35(5), 1114–1127 (2011)
Musmeci, N., Battiston, S., Caldarelli, G., Puliga, M., Gabrielli, A.: Bootstrapping Topological Properties and Systemic Risk of Complex Networks Using the Fitness Model. J. Stat. Phys. 151(3–4), 720–734 (2013)
Caldarelli, G., Chessa, A., Gabrielli, A., Pammolli, F., Puliga, M.: Reconstructing a credit network. Nature Physics 9, 125 (2013)
Park, J., Newman, M.: Statistical mechanics of networks. Phys. Rev. E 70(6), 066117 (2004)
Caldarelli, G., Capocci, A., De Los Rios, P., Muñoz, M.: Scale-free networks from varying vertex intrinsic fitness. Phys. Rev. Lett. 89(25), 258702 (2002)
Garlaschelli, D., Loffredo, M.: Fitness-dependent topological properties of the World Trade Web. Phys. Rev. Lett. 93(18), 188,701 (2004)
Garlaschelli, D., Loffredo, M.: Maximum likelihood: Extracting unbiased information from complex networks. Phys. Rev. E 78, 015101 (2008)
Gleditsch, K.S.: Expanded Trade and GDP Data. J. Confl. Res. 46(5), 712–724 (2002)
De Masi, G., Iori, G., Caldarelli, G.: A fitness model for the Italian Interbank Money Market. Phys. Rev. E 74(6), 066112 (2006)
Dorogovtsev, S.: Lectures on complex networks. Phys. J. 9(11), 51 (2010)
Garlaschelli, D., Loffredo, M.I.: Generalized Bose-Fermi Statistics and Structural Correlations in Weighted Networks. Phys. Rev. Lett. 102, 038701 (2009)
Squartini, T., Garlaschelli, D.: Analytical maximum-likelihood method to detect patterns in real networks. New Journ. Phys. 13, 083001 (2011)
Garlaschelli, D., Battiston, S., Castri, M., Servedio, V., Caldarelli, G.: The scale-free topology of market investments. Physica A 350(2), 491–499 (2005)
Watts, D.J., Strogatz, S.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440–442 (1998)
Colizza, V., Flammini, A., Serrano, M.A., Vespignani, A.: Detecting rich-club ordering in complex networks. Nature Physics 2, 110–115 (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Cimini, G. et al. (2015). Reconstructing Topological Properties of Complex Networks Using the Fitness Model. In: Aiello, L., McFarland, D. (eds) Social Informatics. SocInfo 2014. Lecture Notes in Computer Science(), vol 8852. Springer, Cham. https://doi.org/10.1007/978-3-319-15168-7_41
Download citation
DOI: https://doi.org/10.1007/978-3-319-15168-7_41
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15167-0
Online ISBN: 978-3-319-15168-7
eBook Packages: Computer ScienceComputer Science (R0)