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Degree-dependent network growth: from preferential attachment to explosive percolation.

Hans Hooyberghs1, Bert Van Schaeybroeck2, Joseph O Indekeu3

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We developed a network growth model to study percolation transitions. Our findings reveal how degree-dependent linking probabilities influence network structure and explosive percolation.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Understanding network growth and transitions like percolation is crucial in complex systems.
  • Existing models often simplify the intricate mechanisms of link formation.

Purpose of the Study:

  • To introduce and analyze a simple network growth model with degree-dependent linking probabilities.
  • To investigate the impact of these probabilities on network characteristics and percolation phenomena.

Main Methods:

  • Derivation of dynamic equations for macroscopic network characteristics (degree distribution, correlations).
  • Application of generating functions theory to analyze the percolation transition.
  • Validation through Monte Carlo simulations using an exemplary linking rule (pk∝k-α).

Main Results:

  • The model successfully captures network growth dynamics and percolation transitions.
  • The parameter α in the linking rule allows interpolation between different network regimes.
  • Negative α favors high-degree node connections, while positive α leads to low-degree node connections and explosive percolation.

Conclusions:

  • The proposed model provides a flexible framework for studying network evolution.
  • Degree-dependent linking probabilities are key drivers of network structure and percolation behavior.
  • The study highlights the potential for explosive percolation in networks with specific linking rules.