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Random geometric graphs.

Jesper Dall1, Michael Christensen

  • 1Fysisk Institut, SDU-Odense Universitet, Campusvej 55, DK-5230 Odense M, Denmark. j.dall@fysik.sdu.dk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
Summary

This study analyzes random geometric graphs, finding critical connectivity numerically. The derived cluster coefficient shows these graphs differ significantly from standard random graphs, even in high dimensions.

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Area of Science:

  • Complex systems
  • Network science
  • Computational geometry

Background:

  • Random geometric graphs are models for various real-world networks.
  • Understanding their connectivity properties is crucial for network analysis.
  • Standard random graph models may not capture the nuances of geometric constraints.

Purpose of the Study:

  • To investigate the critical connectivity of random geometric graphs.
  • To derive an analytical expression for the cluster coefficient.
  • To compare these graphs with standard random graph models.

Main Methods:

  • Assigning random coordinates to vertices in arbitrary dimensional spaces.
  • Defining edges based on adjacency of points.
  • Numerical examination of the largest cluster size to find critical connectivity.

Main Results:

  • Numerical determination of critical connectivity in random geometric graphs.
  • Derivation of an analytical expression for the cluster coefficient.
  • Demonstration that these graphs differ from standard random graphs, irrespective of dimensionality.

Conclusions:

  • Random geometric graphs exhibit unique connectivity properties.
  • The derived cluster coefficient provides a distinct characteristic.
  • Findings offer insights into graph bipartitioning for these specific graph types.

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