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Quantifying randomness in real networks.

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Network properties can be predicted using dk-random graphs that mimic real-world network structures. This study reveals statistical dependencies between network characteristics, aiding in understanding network randomness.

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Area of Science:

  • Network science
  • Graph theory
  • Statistical physics

Background:

  • Real-world networks exhibit complex structures balancing order and disorder.
  • Understanding network properties requires analyzing statistical dependencies and randomness.

Purpose of the Study:

  • To investigate statistical dependencies between network properties using the dk-series.
  • To evaluate the ability of dk-random graphs to reproduce real network characteristics.

Main Methods:

  • Employed the dk-series, a comprehensive set of network structure characteristics.
  • Analyzed six diverse real-world networks: Internet, airport, protein interactions, web of trust, word network, and fMRI brain map.
  • Generated dk-random graphs matching observed degree distributions, degree correlations, and clustering.

Main Results:

  • Many local and global structural properties of real networks are accurately reproduced by dk-random graphs.
  • Demonstrated that specific structural properties, when fixed, lead to predictable outcomes in random graphs.
  • Found significant statistical dependencies between different network properties.

Conclusions:

  • dk-random graphs provide a powerful tool for modeling and understanding real-world networks.
  • The study highlights the importance of degree distributions, degree correlations, and clustering in network structure.
  • Implications for network analysis, modeling, and software development are discussed.