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Explosive percolation transitions in growing networks.

S M Oh1, S-W Son2, B Kahng1

  • 1CCSS, CTP and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea.

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|April 15, 2016
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Summary
This summary is machine-generated.

Explosive percolation (EP) transitions in growing networks are studied. When m ≥ 3, the transition becomes second order, unlike static networks, with critical exponent β decreasing algebraically with increasing m.

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Area of Science:

  • Network science
  • Statistical physics
  • Complex systems

Background:

  • Explosive percolation (EP) models typically studied on static networks exhibit second-order transitions with a small critical exponent β.
  • Social networks, however, are dynamic and growing, necessitating investigation of EP in such evolving systems.

Purpose of the Study:

  • To investigate the nature of the explosive percolation transition in growing networks.
  • To analyze the impact of network growth dynamics on EP critical behavior and exponents.

Main Methods:

  • Extension of an existing growing network model incorporating the Achiloptas process with m node candidates.
  • Utilizing rate-equation approach and numerical simulations to analyze the transition.
  • Comparison with static random network models.

Main Results:

  • Growing networks with m ≥ 3 node candidates exhibit a second-order EP transition due to suppressed large cluster growth.
  • The critical exponent β decreases algebraically with increasing m in growing networks.
  • The exponent β decreases exponentially with increasing m in static random networks.

Conclusions:

  • The explosive percolation transition in growing networks differs significantly from static networks, showing a second-order phase transition for m ≥ 3.
  • The algebraic decay of the critical exponent β with m in growing networks provides a new understanding of network dynamics' influence on percolation phenomena.