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Growth dominates choice in network percolation.

Vikram S Vijayaraghavan1, Pierre-André Noël, Alex Waagen

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Network growth, combining node arrival and edge competition, can significantly delay percolation transitions. This process results in a smoother, infinite-order transition, mitigating abruptness seen in explosive percolation.

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Area of Science:

  • Network Science
  • Statistical Physics

Background:

  • Percolation theory traditionally studies edge addition to static node sets.
  • Node and edge addition can create smoother, infinite-order transitions.
  • Edge competition can cause abrupt, delayed percolation transitions.

Purpose of the Study:

  • To analyze a network process combining node arrival and edge competition.
  • To investigate the impact of node arrival on percolation transition characteristics.

Main Methods:

  • Simulating a network model incorporating both node addition and edge competition.
  • Analyzing the order of the percolation transition under combined processes.

Main Results:

  • Node arrival dominates when starting with seed nodes.
  • The combined process leads to an infinite-order percolation transition.
  • Node arrival can significantly delay percolation while maintaining a smooth transition.

Conclusions:

  • Node arrival can mitigate the delay-abruptness trade-off in explosive percolation.
  • Network growth dynamics offer new strategies for network intervention and control.