Abstract
The analysis of networks characterized by links with heterogeneous intensity or weight suffers from two long-standing problems of arbitrariness. On one hand, the definitions of topological properties introduced for binary graphs can be generalized in non-unique ways to weighted networks. On the other hand, even when a definition is given, there is no natural choice of the (optimal) scale of link intensities (e.g. the money unit in economic networks). Here we show that these two seemingly independent problems can be regarded as intimately related, and propose a common solution to both. Using a formalism that we recently proposed in order to map a weighted network to an ensemble of binary graphs, we introduce an information-theoretic approach leading to the least biased generalization of binary properties to weighted networks, and at the same time fixing the optimal scale of link intensities. We illustrate our method on various social and economic networks.
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References
Caldarelli, G.: Scale-Free Networks: Complex Webs in Nature and Technology. Oxford University Press, Oxford (2007)
Barrat, A., Barthelemy, M., Pastor-Satorras, R., Vespignani, A.: The Architecture of Complex Weighted Networks. Proc. Nat. Acad. Sci. USA 101(11), 3747–3752 (2004)
Saramaki, J., Kivela, M., Onnela, J.P., Kaski, K., Kertesz, J.: Generalizations of the Clustering Coefficient to Weighted Complex Networks. Phys. Rev. E 75(2), 027105 (2007)
Newman, M.E.J.: Analysis of Weighted Networks. Phys. Rev. E 70(5), 056131 (2004)
Fagiolo, G.: Clustering in Complex Directed Networks. Phys. Rev. E 76(2), 026107 (2007)
Ahnert, S.E., Garlaschelli, D., Fink, T.M.A., Caldarelli, G.: Ensemble Approach to the Analysis of Weighted Networks. Phys. Rev. E 76(1), 016101 (2007)
Garlaschelli, D., Loffredo, M.I.: Patterns of Link Reciprocity in Directed Networks. Phys. Rev. Lett. 93(26), 268701 (2004)
Squartini, T., Picciolo, F., Ruzzenenti, F., Garlaschelli, D.: Reciprocity of Weighted Networks. Scientific Reports 3, 2729 (2013)
Garlaschelli, D., Ahnert, S.E., Fink, T.M.A., Caldarelli, G.: Low-Temperature Behaviour of Social and Economic Networks. Entropy 15(8), 3148–3169 (2003)
Ahnert, S.E., Garlaschelli, D., Fink, T.M.A., Caldarelli, G.: Applying Weighted Network Measures to Microarray Distance Matrices. Journal of Physics A 41(22), 4011 (2008)
Park, J., Newman, M.E.J.: Statistical Mechanics of Networks. Phys. Rev. E 70(6), 066117 (2004)
Garlaschelli, D., Loffredo, M.I.: Generalized Bose-Fermi Statistics and Structural Correlations in Weighted Networks. Phys. Rev. Lett. 102(3), 038701 (2009)
Bianconi, G.: Entropy of Network Ensembles. Phys. Rev. E 79(3), 036114 (2009)
Stanley, W., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, New York (1994)
Robins, G., Snijders, T., Wang, P., Handcock, M., Pattison, P.: Recent Developments in Exponential Random Graph (p *) Models for Social Networks. Social Networks 29(2), 192–215 (2007)
Jaynes, E.T.: Information Theory and Statistical Mechanics. Physical Review 106(4), 620 (1957)
Squartini, T., Fagiolo, G., Garlaschelli, D.: Randomizing World Trade. I. A Binary Network Analysis. Phys. Rev. E 84(4), 046117 (2011)
Squartini, T., Fagiolo, G., Garlaschelli, D.: Randomizing World Trade. II. A Weighted Network Analysis. Phys. Rev. E 84(4), 046118 (2011)
RyanAir website, http://www.ryanair.com
Eurostat website, http://epp.eurostat.cec.eu.int
Newman, M.E.: The Structure of Scientific Collaboration Networks. Proc. Nat. Acad. Sci. USA 98, 404–409 (2001)
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Garlaschelli, D., Ahnert, S.E., Fink, T.M.A., Caldarelli, G. (2013). Optimal Scales in Weighted Networks. In: Jatowt, A., et al. Social Informatics. SocInfo 2013. Lecture Notes in Computer Science, vol 8238. Springer, Cham. https://doi.org/10.1007/978-3-319-03260-3_30
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DOI: https://doi.org/10.1007/978-3-319-03260-3_30
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03259-7
Online ISBN: 978-3-319-03260-3
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