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Area of Science:

  • Complex networks
  • Network evolution
  • Statistical physics

Background:

  • Preferential attachment is a key driver of complex network evolution.
  • Existing analytical models often assume uniform network growth, which doesn't reflect real-world accelerating growth.
  • Empirical data shows time-invariant average node degree growth, motivating new models.

Purpose of the Study:

  • To develop an analytical framework for network degree dynamics incorporating heterogeneous node fitness and aging.
  • To investigate the impact of different network growth forms (uniform, exponential) on network evolution.
  • To understand the mechanisms behind the 'winner-takes-all' effect and its relation to Bose-Einstein condensation and gelation.

Main Methods:

  • Proposed an analytical framework based on the time invariance of average node degree growth.
  • Analyzed network models combining preferential attachment, heterogeneous node fitness, and aging.
  • Verified theoretical results through extensive numerical simulations.

Main Results:

  • The analytical framework is self-consistent for uniform and exponential network growth.
  • Breaking time invariance explains the 'winner-takes-all' effect, linking Bianconi-Barabási model condensation to superlinear preferential attachment gelation.
  • Aging is crucial for realistic node degree growth curves and can mitigate the 'winner-takes-all' effect.

Conclusions:

  • The study provides a unified framework for understanding complex network evolution under various growth conditions.
  • Heterogeneous fitness, aging, and specific growth forms are critical factors in network dynamics.
  • The findings offer insights into phenomena like Bose-Einstein condensation and gelation in network models.