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Networks as constrained thermodynamic systems.

Derek J Raine1, Yohann Grondin, Michel Thellier

  • 1Department of Physics and Astronomy, University of Leicester, Leicester, LE1 7RH, UK.

Comptes Rendus Biologies
|May 14, 2003
PubMed
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This study presents a method to construct networks with specific nodal degree distributions by applying thermodynamic principles. This approach may reveal macroscopic variables for characterizing complex biological systems.

Area of Science:

  • Network science
  • Statistical mechanics
  • Systems biology

Background:

  • Understanding the structure and function of complex networks is crucial in various scientific fields.
  • Existing methods for network construction often lack control over specific nodal degree distributions.

Purpose of the Study:

  • To develop a general method for constructing networks with a specified distribution of nodal degrees.
  • To explore the relationship between network constraints and macroscopic properties.

Main Methods:

  • Treating network construction as a thermodynamic system.
  • Rewiring network connections to satisfy constraints while maximizing entropy.
  • Using an analogy between network constraints and thermodynamic energy.

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Main Results:

  • A general construction method for networks with specified nodal degree distributions is provided.
  • The method is illustrated with an exponential network example.
  • A characterization of the correspondence between intensive and extensive network variables is obtained.

Conclusions:

  • The proposed thermodynamic approach offers a novel way to engineer network structures.
  • This framework may yield valuable macroscopic variables for characterizing complex systems, particularly in living organisms.