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Growing optimal scale-free networks via likelihood.

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The standard model for scale-free networks is ad hoc. This study reveals that optimally building scale-free networks involves attaching new nodes to low-degree nodes, creating a "superstar network" with a central hub.

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Area of Science:

  • Network science
  • Statistical physics

Background:

  • Preferential attachment is the standard model for scale-free network growth.
  • The motivation for preferential attachment is considered ad hoc.
  • Scale-free networks exhibit a power-law degree distribution (k^{-γ}).

Purpose of the Study:

  • To investigate the optimal strategy for building scale-free networks.
  • To challenge the conventional preferential attachment model.
  • To analyze the resulting network structures and their properties.

Main Methods:

  • Utilizing exact likelihood arguments to determine optimal network growth.
  • Developing an algorithm to generate scale-free networks based on optimal strategies.
  • Analyzing network structures, including degree distribution and hub formation.

Main Results:

  • Optimal network construction involves attaching new nodes to low-degree nodes, forming a "superstar network" with a dominant hub.
  • The optimal attachment strategy asymptotically favors high-degree nodes more than standard preferential attachment.
  • The study generates viable scale-free networks for various degree exponents (γ) and observes a transition around γ≈2.

Conclusions:

  • The ad hoc preferential attachment model is suboptimal for scale-free network construction.
  • Optimal network growth leads to distinct structures like superstar networks.
  • The findings provide a new perspective on network formation and offer tools to analyze network entropy and degree exponents.