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Minimum spanning trees on random networks.

R Dobrin1, P M Duxbury

  • 1Department of Physics/Ast. and Center for Fundamental Materials Research, Michigan State University, East Lansing, Michigan 48824, USA. dobrin@pa.msu.edu

Physical Review Letters
|June 1, 2001
PubMed
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The geometry of minimum spanning trees (MST) on random graphs exhibits universality. This allows MST energy characterization using a universal scaling distribution, simplifying analysis across various disorder types.

Area of Science:

  • Statistical physics
  • Graph theory
  • Complex systems

Background:

  • Minimum Spanning Trees (MST) are fundamental in graph theory.
  • Universality in disordered systems is a key area of research.
  • Understanding random graph properties is crucial for various applications.

Purpose of the Study:

  • To demonstrate the geometric universality of MST on random graphs.
  • To characterize MST energy using a universal scaling distribution.
  • To relate MST energy across different disorder distributions.

Main Methods:

  • Analysis of minimum spanning tree geometry on random graphs.
  • Derivation of a scaling distribution for MST energy under uniform disorder.
  • Comparison of MST energy across various disorder models.

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Main Results:

  • The geometry of MST on random graphs is shown to be universal.
  • A universal scaling distribution, P(epsilon), is found for MST energy.
  • MST energy for other disorder distributions is directly related to P(epsilon).

Conclusions:

  • Geometric universality simplifies MST energy characterization.
  • The findings provide a unified approach to studying MST energy in disordered systems.
  • Implications for universality in disordered systems and related models like invasion percolation.