Quantifying randomness in real networks

Chiara Orsini (), Marija M. Dankulov, Pol Colomer- de-Simón, Almerima Jamakovic, Priya Mahadevan, Amin Vahdat, Kevin E. Bassler, Zoltán Toroczkai, Marián Boguñá, Guido Caldarelli, Santo Fortunato and Dmitri Krioukov ()
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Chiara Orsini: CAIDA, University of California San Diego
Marija M. Dankulov: Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade
Pol Colomer- de-Simón: Departament de Física Fonamental, Universitat de Barcelona
Almerima Jamakovic: Communication and Distributed Systems group, Institute of Computer Science and Applied Mathematics, University of Bern
Priya Mahadevan: Palo Alto Research Center, Palo
Amin Vahdat: Google
Kevin E. Bassler: University of Houston
Zoltán Toroczkai: University of Notre Dame
Marián Boguñá: Departament de Física Fonamental, Universitat de Barcelona
Guido Caldarelli: IMT Alti Studi
Santo Fortunato: Aalto University School of Science
Dmitri Krioukov: CAIDA, University of California San Diego

Nature Communications, 2015, vol. 6, issue 1, 1-10

Abstract: Abstract Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks—the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain—and find that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness, and release software to generate dk-random graphs.

Date: 2015
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DOI: 10.1038/ncomms9627

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