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Eduardo M K Souza1, Guilherme M A Almeida2

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We introduce a new family of complex networks by diluting Apollonian networks. This method preserves key network properties while altering the clustering coefficient, demonstrating robustness against node removal.

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Area of Science:

  • Network Science
  • Complex Systems
  • Statistical Physics

Background:

  • Apollonian networks are complex networks with unique properties.
  • A binary version of Apollonian networks was recently introduced.
  • Understanding network robustness and properties under dilution is crucial.

Purpose of the Study:

  • To introduce a family of complex networks interpolating between Apollonian and its binary version.
  • To investigate how random node removal affects network properties, particularly the clustering coefficient.
  • To analyze the robustness of these networks against random deletion of nodes.

Main Methods:

  • Introducing a dilution process via random node removal.
  • Analyzing spectral quantities like ground-state localization degree and energy gap.
  • Investigating the loss of rotational symmetry using hub wavefunction amplitude.

Main Results:

  • The clustering coefficient can be tuned from 0.828 to 0.
  • Average path length and other properties are maintained similar to deterministic Apollonian networks.
  • The networks exhibit robustness in spectral quantities against random node deletion.

Conclusions:

  • The dilution process offers a method to control network properties while retaining core behaviors.
  • Apollonian networks demonstrate resilience to random attacks.
  • The study reveals the interplay between small-world properties, network structure, and robustness.