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Quantifying randomness in real networks

Author

Listed:
  • Chiara Orsini

    (CAIDA, University of California San Diego
    University of Pisa)

  • Marija M. Dankulov

    (Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade
    Aalto University School of Science)

  • 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
    Max Planck Institut für Physik komplexer Systeme)

  • 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
    Northeastern University)

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.

Suggested Citation

  • 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 Fortunat, 2015. "Quantifying randomness in real networks," Nature Communications, Nature, vol. 6(1), pages 1-10, December.
    • Handle: RePEc:nat:natcom:v:6:y:2015:i:1:d:10.1038_ncomms9627
    DOI: 10.1038/ncomms9627
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    Cited by:

    1. Arcagni, Alberto & Grassi, Rosanna & Stefani, Silvana & Torriero, Anna, 2017. "Higher order assortativity in complex networks," European Journal of Operational Research, Elsevier, vol. 262(2), pages 708-719.
    2. Etienne Lord & Margaux Le Cam & Éric Bapteste & Raphaël Méheust & Vladimir Makarenkov & François-Joseph Lapointe, 2016. "BRIDES: A New Fast Algorithm and Software for Characterizing Evolving Similarity Networks Using Breakthroughs, Roadblocks, Impasses, Detours, Equals and Shortcuts," PLOS ONE, Public Library of Science, vol. 11(8), pages 1-13, August.
    3. Zhou, Bin & He, Zhe & Wang, Nianxin & Wang, Bing-Hong, 2016. "A method of characterizing network topology based on the breadth-first search tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 682-686.
    4. Attar, Niousha & Aliakbary, Sadegh & Nezhad, Zahra Hosseini, 2020. "Automatic generation of adaptive network models based on similarity to the desired complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

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