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Weight-driven growing networks.

T Antal1, P L Krapivsky

  • 1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 24, 2005
PubMed
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This study reveals a universal node weight distribution in growing networks, independent of link weights. The node weight distribution follows a power law, n(w) ~ w(-3), for large weights.

Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Growing networks are fundamental to many real-world systems.
  • Node and link weights influence network structure and dynamics.
  • Understanding emergent properties in evolving networks is crucial.

Purpose of the Study:

  • To investigate the node weight distribution in growing networks with fixed, randomly assigned link weights.
  • To determine if the node weight distribution exhibits universal behavior.
  • To analyze the impact of different link weight distributions on the node weight distribution.

Main Methods:

  • Modeling a growing network with a weight-driven attachment rule.
  • Defining node weight as the sum of incident link weights.

Related Experiment Videos

  • Deriving the analytical form of the node weight distribution for large weights.
  • Examining specific cases, such as exponential link weight distributions.

    • Main Results:

    • The node weight distribution n(w) exhibits a universal power-law tail: n(w) ~ w(-3) as w approaches infinity.
    • This universal tail is independent of the underlying link weight distribution.
    • For exponential link weight distributions, the node weight distribution is algebraic across the entire weight range.

    Conclusions:

    • Growing networks with weight-driven attachment rules develop a universal node weight distribution tail.
    • This universality simplifies the prediction of network properties.
    • The findings have implications for understanding the structure and evolution of complex systems.