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Phase transitions in a network with a range-dependent connection probability.

Parongama Sen1, Kinjal Banerjee, Turbasu Biswas

  • 1Department of Physics, University of Calcutta, 92 A.P.C. Road, Calcutta 700009, India. parongama@vsnl.net

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 9, 2002
PubMed
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This study reveals two phase transitions in complex networks with long-range connections. A continuous transition to a random network occurs at delta=1, detectable via average bond length across dimensions.

Area of Science:

  • Complex networks
  • Statistical physics
  • Network science

Background:

  • One-dimensional networks with nearest neighbor and long-range connections exhibit small-world behavior for delta<2.
  • Above delta=2, the network behaves like a regular lattice.

Purpose of the Study:

  • To identify and characterize phase transitions in complex networks with varying long-range connection probabilities.
  • To investigate the nature of these transitions and their dimensionality dependence.

Main Methods:

  • Analysis of clustering coefficients.
  • Finite size scaling analysis of numerical simulations.
  • Examination of average bond length behavior across dimensions.

Main Results:

Related Experiment Videos

  • A transition to a random network occurs at delta=1.
  • This transition is continuous, as indicated by finite size scaling analysis.
  • Two distinct phase transitions in the network can be detected by monitoring the average bond length in any dimension.

Conclusions:

  • The study identifies two nontrivial phase transitions in these complex networks.
  • The average bond length serves as a universal indicator for these transitions across different dimensions.
  • The findings contribute to understanding the fundamental properties of complex network structures.