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Benford's Distribution in Complex Networks.

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Leading digit distribution in networks often follows Benford's law. This study rigorously tested this claim on real and artificial complex networks, finding insufficient evidence for widespread conformity, with only weak indications for specific network measures under narrow parameter ranges.

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Area of Science:

  • Network Science
  • Data Analysis
  • Statistical Physics

Background:

  • Benford's Law describes the non-uniform distribution of leading digits in many real-world datasets.
  • Previous research suggested Benford's Law might apply to online social networks.
  • The applicability of Benford's Law to complex network structures remained largely unverified.

Purpose of the Study:

  • To rigorously test the adherence of complex network structural properties to Benford's Law.
  • To investigate conformity in both real-world and artificial network models.
  • To extend the scope of Benford's Law analysis to various network types and generative models.

Main Methods:

  • Development and application of rigorous statistical tests for Benford's Law conformity.
  • Analysis of structural properties of diverse real-world complex networks.
  • Examination of artificial networks generated by popular network models.

Main Results:

  • No sufficient evidence found for widespread conformity of network structural properties with Benford's Law in real or artificial networks.
  • Weak evidence suggests potential adherence for degree centrality, betweenness centrality, and local clustering coefficient in scale-free networks.
  • Observed adherence was limited to very narrow parameter ranges for these specific network measures.

Conclusions:

  • The claim that Benford's Law commonly applies to online social networks and other complex networks is not supported by this rigorous analysis.
  • Network structural properties generally do not conform to Benford's distribution.
  • Further research may explore specific network characteristics or parameter ranges where limited adherence might occur.