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This study explores a modified network growth model where new nodes connect to multiple existing nodes following a power-law distribution. It analyzes degree distributions and potential conflicts between connection and redirection mechanisms in network evolution.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • The Krapivsky-Redner (KR) model describes network growth with specific connection rules.
  • Real-world networks often exhibit more complex growth patterns than traditional models allow.

Purpose of the Study:

  • To investigate a generalized network growth model incorporating a power-law distribution for the number of new connections per node.
  • To analyze the in-, out-, and total-degree distributions within this modified model.
  • To examine the interplay and potential tension between the exponent governing new connections (α) and the exponent derived from the redirection mechanism (γKR(r)).

Main Methods:

  • Modification of the Krapivsky-Redner network growth model.
  • Introduction of a power-law distribution (p(m)∼m^{-α}) for the number of new connections (m) per node.
  • Analysis of degree distributions (in-degree, out-degree, total-degree).
  • Theoretical examination of the relationship between α and γKR(r).

Main Results:

  • The study focuses on the resulting degree distributions under the generalized growth rules.
  • It identifies and analyzes the potential tension between the exponent α of the power-law distribution for new connections and the exponent γKR(r) from the redirection mechanism.

Conclusions:

  • The modified network growth model offers a more realistic representation of complex network formation.
  • Understanding the relationship between α and γKR(r) is crucial for predicting network structure and dynamics in various real-world systems like social and citation networks.