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Scale-free networks from a Hamiltonian dynamics.

M Baiesi1, S S Manna

  • 1INFM, Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
PubMed
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This study introduces a network model with a fixed number of nodes and links, favoring diverse connectivity. The model generates broad degree distributions and hierarchical clustering, contrasting with growing network models.

Area of Science:

  • Network Science
  • Statistical Physics

Background:

  • Recent network models often focus on growth dynamics.
  • Understanding equilibrium states in complex networks is crucial.

Purpose of the Study:

  • To present a novel network model with a fixed size.
  • To investigate network dynamics favoring diverse connectivity.
  • To analyze emergent properties like degree distributions and clustering.

Main Methods:

  • A model with a fixed number of nodes and links was developed.
  • A dynamics favoring maximal differences in node connectivity was introduced.
  • Local rewiring moves were applied to reach equilibrium states.

Main Results:

  • The network model achieves equilibrium states with broad degree distributions.

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  • Degree distributions exhibit a power-law form over an intermediate parameter range.
  • Nontrivial hierarchical clustering emerges within the same parameter range.

    • Conclusions:

    • The proposed model offers an alternative to growing network paradigms.
    • Fixed-size networks can exhibit complex structures like power-law distributions and hierarchical clustering.
    • The dynamics favoring diverse connectivity drive these emergent properties.