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This study introduces stochasticity to (u,v)-flower nets, creating flexible network models. Despite random growth, key properties like degree exponent stabilize in large networks.

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Area of Science:

  • Network Science
  • Graph Theory
  • Statistical Physics

Background:

  • Recurrence graphs, specifically (u,v)-flower nets, exhibit power-law degree distributions and small-world properties.
  • Existing deterministic models lack flexibility in interpolating between different network structures.

Purpose of the Study:

  • To introduce stochasticity into (u,v)-flower net growth for enhanced model flexibility.
  • To analyze the statistical properties and limiting behavior of stochastic and mixed flower networks.

Main Methods:

  • Stochastic multiplicative growth process for generating ensembles of networks.
  • Analysis of degree distributions, number of links, nodes, and loops.
  • Deterministic recursive growth for mixed flower networks.

Main Results:

  • Stochastic flower nets show ensemble spreads but unique degree and loopiness exponents in the thermodynamic limit.
  • Mixed flower networks, deterministically grown, eliminate ensemble spreads and allow exact analysis.
  • The stochastic variant interpolates between deterministic flower graphs.

Conclusions:

  • Stochasticity adds flexibility to (u,v)-flower net models, with predictable exponents in large graph limits.
  • Deterministic growth in mixed flower networks simplifies analysis and removes ensemble variability.
  • Both stochastic and deterministic approaches offer valuable insights into complex network formation.