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Network growth by copying.

P L Krapivsky1, S Redner

  • 1Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA. paulk@bu.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
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We present a new growing network model where nodes connect to existing nodes and their ancestors. This creates sparse, ultrasmall networks with logarithmic degree growth and a diameter of 2, matching real-world networks like the Internet.

Area of Science:

  • Network Science
  • Complex Systems
  • Graph Theory

Background:

  • Understanding the growth and structure of complex networks is crucial.
  • Existing models often fail to capture the ultrasmall-world properties observed in real-world networks.

Purpose of the Study:

  • To introduce a novel growing network model with specific attachment rules.
  • To analyze the resulting network's topological and geometrical properties.
  • To compare the model's predictions with empirical data from real-world networks.

Main Methods:

  • Development of a growing network model with preferential attachment to a node and its ancestors.
  • Analytical derivation of network properties, including degree distribution and diameter.
  • Comparison of model predictions with data from the Internet and a citation network.

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Main Results:

  • The model generates sparse, ultrasmall networks.
  • Average node degree grows logarithmically with network size.
  • Network diameter is consistently 2.
  • In- and out-degree distributions were determined and compared to real networks.

Conclusions:

  • The proposed model effectively replicates key features of real-world growing networks.
  • The attachment mechanism leads to efficient information propagation (small diameter).
  • The model provides a theoretical framework for understanding ultrasmall-world network formation.