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Related Experiment Videos

Sampling properties of random graphs: the degree distribution.

Michael P H Stumpf1, Carsten Wiuf

  • 1Centre for Bioinformatics, Division of Molecular Biosciences, Imperial College London, Wolfson Building, London SW7 2AZ, United Kingdom. m.stumpf@imperial.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
Summary

Network sampling affects node degree distributions. We identified conditions for subnets to match true network distributions, finding random sampling works for random graphs but often fails for real networks.

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Area of Science:

  • Network science
  • Graph theory
  • Statistical analysis

Background:

  • Understanding how sampling methods affect network properties is crucial for accurate analysis.
  • Degree distribution is a fundamental characteristic of network structure.

Purpose of the Study:

  • To investigate the impact of random sampling and connectivity-dependent sampling on network degree distributions.
  • To derive conditions ensuring subnet degree distributions match the original network's distribution.
  • To analyze the behavior of classical random graphs under different sampling regimes.

Main Methods:

  • Derivation of a necessary and sufficient condition for preserving degree distribution families.
  • Analysis of random graph models under two distinct sampling schemes.

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  • Comparison of theoretical findings with real-world network data (E. coli protein interaction network).

    • Main Results:

    • A condition was derived to guarantee that subnet and true network degree distributions belong to the same probability distribution family.
    • Completely random sampling preserves degree distribution for classical random graphs but often fails for other networks.
    • Degree-dependent sampling invalidates the closure property even for classical random graphs.

    Conclusions:

    • The choice of sampling scheme significantly impacts network analysis, particularly degree distribution.
    • Real-world networks often deviate from classical random graph properties, requiring careful consideration of sampling methods.
    • Findings provide insights into analyzing biological networks like protein-protein interaction networks.