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Nature Research, Nature Communications, 1(6), 2015

DOI: 10.1038/ncomms9627

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Quantifying randomness in real networks

Journal article published in 2015 by Chiara Orsini, Marija M. Dankulov, Pol Colomer-De-Simón, Almerima Jamakovic, Priya Mahadevan, Amin Vahdat, Kevin E. Bassler, Zoltán Toroczkai ORCID, Marián Boguñá, Guido Caldarelli ORCID, Santo Fortunato, Dmitri Krioukov ORCID
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

AbstractRepresented 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.