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Phase transitions in an aging network.

Kamalika Basu Hajra1, Parongama Sen

  • 1Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India. kamalikabasu2000@yahoo.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2004
PubMed
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This study explores growing networks where new nodes attach based on existing node degree and age. Scale-free behavior emerges only under specific conditions, while small-world properties are more widespread.

Area of Science:

  • Network science
  • Statistical physics

Background:

  • Growing networks are fundamental models in complex systems.
  • Understanding attachment mechanisms is key to network evolution.

Purpose of the Study:

  • To investigate the phase diagram of a growing network model.
  • To determine conditions for scale-free behavior and small-world properties.

Main Methods:

  • A growing network model where attachment probability depends on node degree and age.
  • Analysis of the phase diagram in the alpha-beta plane.

Main Results:

  • Scale-free behavior (Pk ~ k^-gamma, gamma=3) is observed only on a specific line in the alpha-beta phase diagram.
  • Small-world properties are present across a broader region of the phase diagram.

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Conclusions:

  • The interplay between node degree and age significantly influences network topology.
  • Specific parameter regimes are required for scale-free properties, but small-world characteristics are more robust.