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Filtering Statistics on Networks.

G J Baxter1, R A da Costa1, S N Dorogovtsev1

  • 1Department of Physics, University of Aveiro de & I3N, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

This study analyzes information filtering in complex systems, revealing that random graphs exhibit richer filtering statistics than deterministic ones. Graph structure and vertex degree are key factors influencing statistical richness.

Keywords:
complex networkscomplexitydegeneracyentropyfilteringinformationrelevanceresolution

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Area of Science:

  • Complex Systems Science
  • Information Theory
  • Network Science

Background:

  • Information processing in complex systems involves mapping large input spaces to smaller output states.
  • Filtering is a key aspect of information processing, characterized by multiple inputs mapping to the same output (degeneracy).

Purpose of the Study:

  • To explore the statistics of filtering simple patterns on deterministic and random graphs.
  • To identify key factors determining filtering statistics in diverse network architectures.

Main Methods:

  • Exact analytical solutions for simple filter patterns on ring graphs.
  • Numerical analysis for more complex filter patterns and network setups.
  • Comparison of filtering statistics across networks with varying architectures (deterministic vs. random) and vertex degrees.

Main Results:

  • Identified three key numbers describing filtering statistics for different patterns and networks.
  • Found that graph structure (deterministic vs. random) and vertex degree are primary determinants of filtering statistics.
  • Demonstrated that random graphs yield richer filtering statistics than deterministic graphs.

Conclusions:

  • Filtering statistics are significantly influenced by graph architecture and vertex degree.
  • Statistical richness of filtering is maximized at the smallest vertex degree greater than two.
  • Filter patterns sensitive to node neighborhoods are more affected by network properties.